id	sid	tid	token	lemma	pos
fuelectenerg-3309	1	1	facta	facta	PROPN
fuelectenerg-3309	1	2	universitatis	universitatis	PROPN
fuelectenerg-3309	1	3	series	series	NOUN
fuelectenerg-3309	1	4	:	:	PUNCT
fuelectenerg-3309	1	5	electronics	electronic	NOUN
fuelectenerg-3309	1	6	and	and	CCONJ
fuelectenerg-3309	1	7	energetics	energetics	NOUN
fuelectenerg-3309	1	8	vol	vol	NOUN
fuelectenerg-3309	1	9	.	.	PUNCT
fuelectenerg-3309	2	1	x	x	X
fuelectenerg-3309	2	2	,	,	PUNCT
fuelectenerg-3309	2	3	no	no	DET
fuelectenerg-3309	2	4	x	x	NOUN
fuelectenerg-3309	2	5	,	,	PUNCT
fuelectenerg-3309	2	6	x	x	PROPN
fuelectenerg-3309	2	7	2018	2018	NUM
fuelectenerg-3309	2	8	,	,	PUNCT
fuelectenerg-3309	2	9	pp	pp	ADV
fuelectenerg-3309	2	10	.	.	PUNCT
fuelectenerg-3309	3	1	x	x	PUNCT
fuelectenerg-3309	3	2	energy	energy	NOUN
fuelectenerg-3309	3	3	-	-	PUNCT
fuelectenerg-3309	3	4	efficient	efficient	ADJ
fuelectenerg-3309	3	5	cryptographic	cryptographic	ADJ
fuelectenerg-3309	3	6	primitives	primitive	NOUN
fuelectenerg-3309	3	7	elena	elena	NOUN
fuelectenerg-3309	3	8	dubrova∗	dubrova∗	PROPN
fuelectenerg-3309	3	9	royal	royal	PROPN
fuelectenerg-3309	3	10	institute	institute	PROPN
fuelectenerg-3309	3	11	of	of	ADP
fuelectenerg-3309	3	12	technology	technology	PROPN
fuelectenerg-3309	3	13	(	(	PUNCT
fuelectenerg-3309	3	14	kth	kth	PROPN
fuelectenerg-3309	3	15	)	)	PUNCT
fuelectenerg-3309	3	16	,	,	PUNCT
fuelectenerg-3309	3	17	stockholm	stockholm	PROPN
fuelectenerg-3309	3	18	,	,	PUNCT
fuelectenerg-3309	3	19	sweden	sweden	PROPN
fuelectenerg-3309	3	20	abstract	abstract	NOUN
fuelectenerg-3309	3	21	:	:	PUNCT
fuelectenerg-3309	3	22	our	our	PRON
fuelectenerg-3309	3	23	society	society	NOUN
fuelectenerg-3309	3	24	greatly	greatly	ADV
fuelectenerg-3309	3	25	depends	depend	VERB
fuelectenerg-3309	3	26	on	on	ADP
fuelectenerg-3309	3	27	services	service	NOUN
fuelectenerg-3309	3	28	and	and	CCONJ
fuelectenerg-3309	3	29	applications	application	NOUN
fuelectenerg-3309	3	30	provided	provide	VERB
fuelectenerg-3309	3	31	by	by	ADP
fuelectenerg-3309	3	32	mobile	mobile	ADJ
fuelectenerg-3309	3	33	communication	communication	NOUN
fuelectenerg-3309	3	34	networks	network	NOUN
fuelectenerg-3309	3	35	.	.	PUNCT
fuelectenerg-3309	4	1	as	as	SCONJ
fuelectenerg-3309	4	2	billions	billion	NOUN
fuelectenerg-3309	4	3	of	of	ADP
fuelectenerg-3309	4	4	people	people	NOUN
fuelectenerg-3309	4	5	and	and	CCONJ
fuelectenerg-3309	4	6	devices	device	NOUN
fuelectenerg-3309	4	7	become	become	VERB
fuelectenerg-3309	4	8	connected	connect	VERB
fuelectenerg-3309	4	9	,	,	PUNCT
fuelectenerg-3309	4	10	it	it	PRON
fuelectenerg-3309	4	11	becomes	become	VERB
fuelectenerg-3309	4	12	increasingly	increasingly	ADV
fuelectenerg-3309	4	13	important	important	ADJ
fuelectenerg-3309	4	14	to	to	PART
fuelectenerg-3309	4	15	guarantee	guarantee	VERB
fuelectenerg-3309	4	16	security	security	NOUN
fuelectenerg-3309	4	17	of	of	ADP
fuelectenerg-3309	4	18	interactions	interaction	NOUN
fuelectenerg-3309	4	19	of	of	ADP
fuelectenerg-3309	4	20	all	all	DET
fuelectenerg-3309	4	21	players	player	NOUN
fuelectenerg-3309	4	22	.	.	PUNCT
fuelectenerg-3309	5	1	in	in	ADP
fuelectenerg-3309	5	2	this	this	DET
fuelectenerg-3309	5	3	talk	talk	NOUN
fuelectenerg-3309	5	4	we	we	PRON
fuelectenerg-3309	5	5	address	address	VERB
fuelectenerg-3309	5	6	several	several	ADJ
fuelectenerg-3309	5	7	aspects	aspect	NOUN
fuelectenerg-3309	5	8	of	of	ADP
fuelectenerg-3309	5	9	this	this	DET
fuelectenerg-3309	5	10	important	important	ADJ
fuelectenerg-3309	5	11	,	,	PUNCT
fuelectenerg-3309	5	12	many	many	ADJ
fuelectenerg-3309	5	13	-	-	PUNCT
fuelectenerg-3309	5	14	folded	fold	VERB
fuelectenerg-3309	5	15	problem	problem	NOUN
fuelectenerg-3309	5	16	.	.	PUNCT
fuelectenerg-3309	6	1	first	first	ADV
fuelectenerg-3309	6	2	,	,	PUNCT
fuelectenerg-3309	6	3	we	we	PRON
fuelectenerg-3309	6	4	show	show	VERB
fuelectenerg-3309	6	5	how	how	SCONJ
fuelectenerg-3309	6	6	to	to	PART
fuelectenerg-3309	6	7	design	design	VERB
fuelectenerg-3309	6	8	cryptographic	cryptographic	ADJ
fuelectenerg-3309	6	9	primitives	primitive	NOUN
fuelectenerg-3309	6	10	which	which	PRON
fuelectenerg-3309	6	11	can	can	AUX
fuelectenerg-3309	6	12	assure	assure	VERB
fuelectenerg-3309	6	13	integrity	integrity	NOUN
fuelectenerg-3309	6	14	and	and	CCONJ
fuelectenerg-3309	6	15	confidentiality	confidentiality	NOUN
fuelectenerg-3309	6	16	of	of	ADP
fuelectenerg-3309	6	17	transmitted	transmit	VERB
fuelectenerg-3309	6	18	messages	message	NOUN
fuelectenerg-3309	6	19	while	while	SCONJ
fuelectenerg-3309	6	20	satisfying	satisfy	VERB
fuelectenerg-3309	6	21	resource	resource	NOUN
fuelectenerg-3309	6	22	constrains	constrain	NOUN
fuelectenerg-3309	6	23	of	of	ADP
fuelectenerg-3309	6	24	low	low	ADJ
fuelectenerg-3309	6	25	-	-	PUNCT
fuelectenerg-3309	6	26	end	end	NOUN
fuelectenerg-3309	6	27	low	low	ADJ
fuelectenerg-3309	6	28	-	-	PUNCT
fuelectenerg-3309	6	29	cost	cost	NOUN
fuelectenerg-3309	6	30	wireless	wireless	NOUN
fuelectenerg-3309	6	31	devices	device	NOUN
fuelectenerg-3309	6	32	such	such	ADJ
fuelectenerg-3309	6	33	as	as	ADP
fuelectenerg-3309	6	34	sensors	sensor	NOUN
fuelectenerg-3309	6	35	or	or	CCONJ
fuelectenerg-3309	6	36	rfid	rfid	NOUN
fuelectenerg-3309	6	37	tags	tag	NOUN
fuelectenerg-3309	6	38	.	.	PUNCT
fuelectenerg-3309	7	1	second	second	ADJ
fuelectenerg-3309	7	2	,	,	PUNCT
fuelectenerg-3309	7	3	we	we	PRON
fuelectenerg-3309	7	4	describe	describe	VERB
fuelectenerg-3309	7	5	countermeasures	countermeasure	NOUN
fuelectenerg-3309	7	6	which	which	PRON
fuelectenerg-3309	7	7	can	can	AUX
fuelectenerg-3309	7	8	enhance	enhance	VERB
fuelectenerg-3309	7	9	the	the	DET
fuelectenerg-3309	7	10	resistance	resistance	NOUN
fuelectenerg-3309	7	11	of	of	ADP
fuelectenerg-3309	7	12	hardware	hardware	NOUN
fuelectenerg-3309	7	13	implementing	implement	VERB
fuelectenerg-3309	7	14	cryptographic	cryptographic	ADJ
fuelectenerg-3309	7	15	algorithms	algorithm	NOUN
fuelectenerg-3309	7	16	to	to	ADP
fuelectenerg-3309	7	17	hardware	hardware	NOUN
fuelectenerg-3309	7	18	trojans	trojan	NOUN
fuelectenerg-3309	7	19	.	.	PUNCT
fuelectenerg-3309	8	1	keywords	keyword	NOUN
fuelectenerg-3309	8	2	:	:	PUNCT
fuelectenerg-3309	8	3	security	security	NOUN
fuelectenerg-3309	8	4	,	,	PUNCT
fuelectenerg-3309	8	5	lightweight	lightweight	ADJ
fuelectenerg-3309	8	6	cryptography	cryptography	NOUN
fuelectenerg-3309	8	7	,	,	PUNCT
fuelectenerg-3309	8	8	cryptographic	cryptographic	ADJ
fuelectenerg-3309	8	9	primitive	primitive	ADJ
fuelectenerg-3309	8	10	,	,	PUNCT
fuelectenerg-3309	8	11	encryption	encryption	NOUN
fuelectenerg-3309	8	12	,	,	PUNCT
fuelectenerg-3309	8	13	message	message	NOUN
fuelectenerg-3309	8	14	authentication	authentication	NOUN
fuelectenerg-3309	8	15	,	,	PUNCT
fuelectenerg-3309	8	16	hardware	hardware	NOUN
fuelectenerg-3309	8	17	trojan	trojan	NOUN
fuelectenerg-3309	8	18	.	.	PROPN
fuelectenerg-3309	8	19	1	1	NUM
fuelectenerg-3309	8	20	introduction	introduction	NOUN
fuelectenerg-3309	8	21	today	today	NOUN
fuelectenerg-3309	8	22	minimal	minimal	ADJ
fuelectenerg-3309	8	23	or	or	CCONJ
fuelectenerg-3309	8	24	no	no	DET
fuelectenerg-3309	8	25	security	security	NOUN
fuelectenerg-3309	8	26	is	be	AUX
fuelectenerg-3309	8	27	typically	typically	ADV
fuelectenerg-3309	8	28	provided	provide	VERB
fuelectenerg-3309	8	29	to	to	ADP
fuelectenerg-3309	8	30	low	low	ADJ
fuelectenerg-3309	8	31	-	-	PUNCT
fuelectenerg-3309	8	32	end	end	NOUN
fuelectenerg-3309	8	33	low	low	ADJ
fuelectenerg-3309	8	34	-	-	PUNCT
fuelectenerg-3309	8	35	cost	cost	NOUN
fuelectenerg-3309	8	36	wireless	wireless	NOUN
fuelectenerg-3309	8	37	devices	device	NOUN
fuelectenerg-3309	8	38	such	such	ADJ
fuelectenerg-3309	8	39	as	as	ADP
fuelectenerg-3309	8	40	sensors	sensor	NOUN
fuelectenerg-3309	8	41	or	or	CCONJ
fuelectenerg-3309	8	42	rfid	rfid	VERB
fuelectenerg-3309	8	43	tags	tag	NOUN
fuelectenerg-3309	8	44	in	in	ADP
fuelectenerg-3309	8	45	the	the	DET
fuelectenerg-3309	8	46	conventional	conventional	ADJ
fuelectenerg-3309	8	47	belief	belief	NOUN
fuelectenerg-3309	8	48	that	that	SCONJ
fuelectenerg-3309	8	49	the	the	DET
fuelectenerg-3309	8	50	information	information	NOUN
fuelectenerg-3309	8	51	they	they	PRON
fuelectenerg-3309	8	52	gather	gather	VERB
fuelectenerg-3309	8	53	is	be	AUX
fuelectenerg-3309	8	54	of	of	ADP
fuelectenerg-3309	8	55	little	little	ADJ
fuelectenerg-3309	8	56	concern	concern	NOUN
fuelectenerg-3309	8	57	to	to	ADP
fuelectenerg-3309	8	58	attackers	attacker	NOUN
fuelectenerg-3309	8	59	.	.	PUNCT
fuelectenerg-3309	9	1	however	however	ADV
fuelectenerg-3309	9	2	,	,	PUNCT
fuelectenerg-3309	9	3	case	case	NOUN
fuelectenerg-3309	9	4	studies	study	NOUN
fuelectenerg-3309	9	5	have	have	AUX
fuelectenerg-3309	9	6	shown	show	VERB
fuelectenerg-3309	9	7	that	that	SCONJ
fuelectenerg-3309	9	8	a	a	DET
fuelectenerg-3309	9	9	compromised	compromise	VERB
fuelectenerg-3309	9	10	sensor	sensor	NOUN
fuelectenerg-3309	9	11	can	can	AUX
fuelectenerg-3309	9	12	be	be	AUX
fuelectenerg-3309	9	13	used	use	VERB
fuelectenerg-3309	9	14	as	as	ADP
fuelectenerg-3309	9	15	a	a	DET
fuelectenerg-3309	9	16	stepping	stepping	ADJ
fuelectenerg-3309	9	17	stone	stone	NOUN
fuelectenerg-3309	9	18	to	to	PART
fuelectenerg-3309	9	19	mount	mount	VERB
fuelectenerg-3309	9	20	an	an	DET
fuelectenerg-3309	9	21	attack	attack	NOUN
fuelectenerg-3309	9	22	on	on	ADP
fuelectenerg-3309	9	23	a	a	DET
fuelectenerg-3309	9	24	wireless	wireless	ADJ
fuelectenerg-3309	9	25	network	network	NOUN
fuelectenerg-3309	9	26	.	.	PUNCT
fuelectenerg-3309	10	1	for	for	ADP
fuelectenerg-3309	10	2	example	example	NOUN
fuelectenerg-3309	10	3	,	,	PUNCT
fuelectenerg-3309	10	4	in	in	ADP
fuelectenerg-3309	10	5	the	the	DET
fuelectenerg-3309	10	6	attack	attack	NOUN
fuelectenerg-3309	10	7	manuscript	manuscript	NOUN
fuelectenerg-3309	10	8	received	receive	VERB
fuelectenerg-3309	10	9	x	x	PROPN
fuelectenerg-3309	10	10	x	x	NOUN
fuelectenerg-3309	10	11	,	,	PUNCT
fuelectenerg-3309	10	12	x	x	SYM
fuelectenerg-3309	10	13	corresponding	correspond	VERB
fuelectenerg-3309	10	14	author	author	NOUN
fuelectenerg-3309	10	15	:	:	PUNCT
fuelectenerg-3309	10	16	elena	elena	PROPN
fuelectenerg-3309	10	17	dubrova	dubrova	PROPN
fuelectenerg-3309	10	18	royal	royal	PROPN
fuelectenerg-3309	10	19	institute	institute	PROPN
fuelectenerg-3309	10	20	of	of	ADP
fuelectenerg-3309	10	21	technology	technology	PROPN
fuelectenerg-3309	10	22	(	(	PUNCT
fuelectenerg-3309	10	23	kth	kth	PROPN
fuelectenerg-3309	10	24	)	)	PUNCT
fuelectenerg-3309	10	25	,	,	PUNCT
fuelectenerg-3309	10	26	stockholm	stockholm	PROPN
fuelectenerg-3309	10	27	,	,	PUNCT
fuelectenerg-3309	10	28	sweden	sweden	PROPN
fuelectenerg-3309	10	29	(	(	PUNCT
fuelectenerg-3309	10	30	e	e	NOUN
fuelectenerg-3309	10	31	-	-	NOUN
fuelectenerg-3309	10	32	mail	mail	NOUN
fuelectenerg-3309	10	33	:	:	PUNCT
fuelectenerg-3309	10	34	dubrova@kth.se	dubrova@kth.se	NOUN
fuelectenerg-3309	10	35	)	)	PUNCT
fuelectenerg-3309	10	36	∗an	∗an	PUNCT
fuelectenerg-3309	10	37	earlier	early	ADJ
fuelectenerg-3309	10	38	version	version	NOUN
fuelectenerg-3309	10	39	of	of	ADP
fuelectenerg-3309	10	40	this	this	DET
fuelectenerg-3309	10	41	paper	paper	NOUN
fuelectenerg-3309	10	42	was	be	AUX
fuelectenerg-3309	10	43	presented	present	VERB
fuelectenerg-3309	10	44	as	as	ADP
fuelectenerg-3309	10	45	an	an	DET
fuelectenerg-3309	10	46	invited	invite	VERB
fuelectenerg-3309	10	47	address	address	NOUN
fuelectenerg-3309	10	48	at	at	ADP
fuelectenerg-3309	10	49	the	the	DET
fuelectenerg-3309	10	50	reed	reed	NOUN
fuelectenerg-3309	10	51	-	-	PUNCT
fuelectenerg-3309	10	52	muller	muller	NOUN
fuelectenerg-3309	10	53	2017	2017	NUM
fuelectenerg-3309	10	54	workshop	workshop	NOUN
fuelectenerg-3309	10	55	,	,	PUNCT
fuelectenerg-3309	10	56	novi	novi	PROPN
fuelectenerg-3309	10	57	sad	sad	PROPN
fuelectenerg-3309	10	58	,	,	PUNCT
fuelectenerg-3309	10	59	serbia	serbia	PROPN
fuelectenerg-3309	10	60	,	,	PUNCT
fuelectenerg-3309	10	61	may	may	AUX
fuelectenerg-3309	10	62	24	24	NUM
fuelectenerg-3309	10	63	-	-	SYM
fuelectenerg-3309	10	64	25	25	NUM
fuelectenerg-3309	10	65	,	,	PUNCT
fuelectenerg-3309	10	66	2017	2017	NUM
fuelectenerg-3309	10	67	.	.	PUNCT
fuelectenerg-3309	11	1	1	1	NUM
fuelectenerg-3309	11	2	facta	facta	NOUN
fuelectenerg-3309	11	3	universitatis	universitatis	PROPN
fuelectenerg-3309	11	4	series	series	NOUN
fuelectenerg-3309	11	5	:	:	PUNCT
fuelectenerg-3309	11	6	electronics	electronic	NOUN
fuelectenerg-3309	11	7	and	and	CCONJ
fuelectenerg-3309	11	8	energetics	energetic	NOUN
fuelectenerg-3309	11	9	vol	vol	NOUN
fuelectenerg-3309	11	10	.	.	PUNCT
fuelectenerg-3309	12	1	xx	xx	NUM
fuelectenerg-3309	12	2	,	,	PUNCT
fuelectenerg-3309	12	3	no	no	DET
fuelectenerg-3309	12	4	x	x	ADJ
fuelectenerg-3309	12	5	,	,	PUNCT
fuelectenerg-3309	12	6	xxxx	xxxx	ADJ
fuelectenerg-3309	12	7	,	,	PUNCT
fuelectenerg-3309	12	8	pp	pp	PROPN
fuelectenerg-3309	12	9	.	.	PUNCT
fuelectenerg-3309	13	1	xxx	xxx	NOUN
fuelectenerg-3309	13	2	xxx	xxx	PROPN
fuelectenerg-3309	13	3	enumeration	enumeration	NOUN
fuelectenerg-3309	13	4	and	and	CCONJ
fuelectenerg-3309	13	5	coding	code	VERB
fuelectenerg-3309	13	6	methods	method	NOUN
fuelectenerg-3309	13	7	for	for	ADP
fuelectenerg-3309	13	8	a	a	DET
fuelectenerg-3309	13	9	class	class	NOUN
fuelectenerg-3309	13	10	of	of	ADP
fuelectenerg-3309	13	11	permutations	permutation	NOUN
fuelectenerg-3309	13	12	and	and	CCONJ
fuelectenerg-3309	13	13	reversible	reversible	ADJ
fuelectenerg-3309	13	14	logical	logical	ADJ
fuelectenerg-3309	13	15	gates	gate	NOUN
fuelectenerg-3309	13	16	costas	costa	VERB
fuelectenerg-3309	13	17	karanikas1	karanikas1	PROPN
fuelectenerg-3309	13	18	and	and	CCONJ
fuelectenerg-3309	13	19	nikolaos	nikolaos	PROPN
fuelectenerg-3309	13	20	atreas2	atreas2	VERB
fuelectenerg-3309	13	21	1	1	NUM
fuelectenerg-3309	13	22	school	school	NOUN
fuelectenerg-3309	13	23	of	of	ADP
fuelectenerg-3309	13	24	informatics	informatics	PROPN
fuelectenerg-3309	13	25	,	,	PUNCT
fuelectenerg-3309	13	26	aristotle	aristotle	PROPN
fuelectenerg-3309	13	27	university	university	PROPN
fuelectenerg-3309	13	28	of	of	ADP
fuelectenerg-3309	13	29	thessaloniki	thessaloniki	PROPN
fuelectenerg-3309	13	30	,	,	PUNCT
fuelectenerg-3309	13	31	greece	greece	PROPN
fuelectenerg-3309	13	32	2	2	NUM
fuelectenerg-3309	13	33	school	school	NOUN
fuelectenerg-3309	13	34	of	of	ADP
fuelectenerg-3309	13	35	electrical	electrical	ADJ
fuelectenerg-3309	13	36	and	and	CCONJ
fuelectenerg-3309	13	37	computer	computer	NOUN
fuelectenerg-3309	13	38	engineering	engineering	NOUN
fuelectenerg-3309	13	39	,	,	PUNCT
fuelectenerg-3309	13	40	faculty	faculty	NOUN
fuelectenerg-3309	13	41	of	of	ADP
fuelectenerg-3309	13	42	engineering	engineering	PROPN
fuelectenerg-3309	13	43	,	,	PUNCT
fuelectenerg-3309	13	44	aristotle	aristotle	PROPN
fuelectenerg-3309	13	45	university	university	PROPN
fuelectenerg-3309	13	46	of	of	ADP
fuelectenerg-3309	13	47	thessaloniki	thessaloniki	PROPN
fuelectenerg-3309	13	48	,	,	PUNCT
fuelectenerg-3309	13	49	greece	greece	PROPN
fuelectenerg-3309	13	50	abstract	abstract	PROPN
fuelectenerg-3309	13	51	:	:	PUNCT
fuelectenerg-3309	13	52	we	we	PRON
fuelectenerg-3309	13	53	introduce	introduce	VERB
fuelectenerg-3309	13	54	a	a	DET
fuelectenerg-3309	13	55	great	great	ADJ
fuelectenerg-3309	13	56	variety	variety	NOUN
fuelectenerg-3309	13	57	of	of	ADP
fuelectenerg-3309	13	58	coding	code	VERB
fuelectenerg-3309	13	59	methods	method	NOUN
fuelectenerg-3309	13	60	for	for	ADP
fuelectenerg-3309	13	61	boolean	boolean	ADJ
fuelectenerg-3309	13	62	sparse	sparse	ADJ
fuelectenerg-3309	13	63	invertible	invertible	ADJ
fuelectenerg-3309	13	64	matrices	matrix	NOUN
fuelectenerg-3309	13	65	and	and	CCONJ
fuelectenerg-3309	13	66	we	we	PRON
fuelectenerg-3309	13	67	use	use	VERB
fuelectenerg-3309	13	68	these	these	DET
fuelectenerg-3309	13	69	methods	method	NOUN
fuelectenerg-3309	13	70	to	to	PART
fuelectenerg-3309	13	71	create	create	VERB
fuelectenerg-3309	13	72	a	a	DET
fuelectenerg-3309	13	73	variety	variety	NOUN
fuelectenerg-3309	13	74	of	of	ADP
fuelectenerg-3309	13	75	bijections	bijection	NOUN
fuelectenerg-3309	13	76	on	on	ADP
fuelectenerg-3309	13	77	the	the	DET
fuelectenerg-3309	13	78	permutation	permutation	NOUN
fuelectenerg-3309	13	79	group	group	NOUN
fuelectenerg-3309	13	80	p	p	PROPN
fuelectenerg-3309	13	81	(	(	PUNCT
fuelectenerg-3309	13	82	m	m	NOUN
fuelectenerg-3309	13	83	)	)	PUNCT
fuelectenerg-3309	13	84	of	of	ADP
fuelectenerg-3309	13	85	the	the	DET
fuelectenerg-3309	13	86	set	set	NOUN
fuelectenerg-3309	13	87	{	{	PUNCT
fuelectenerg-3309	13	88	1	1	NUM
fuelectenerg-3309	13	89	,	,	PUNCT
fuelectenerg-3309	13	90	2	2	NUM
fuelectenerg-3309	13	91	,	,	PUNCT
fuelectenerg-3309	13	92	...	...	PUNCT
fuelectenerg-3309	13	93	,	,	PUNCT
fuelectenerg-3309	13	94	m	m	VERB
fuelectenerg-3309	13	95	}	}	PUNCT
fuelectenerg-3309	13	96	.	.	PUNCT
fuelectenerg-3309	14	1	also	also	ADV
fuelectenerg-3309	14	2	,	,	PUNCT
fuelectenerg-3309	14	3	we	we	PRON
fuelectenerg-3309	14	4	propose	propose	VERB
fuelectenerg-3309	14	5	methods	method	NOUN
fuelectenerg-3309	14	6	for	for	ADP
fuelectenerg-3309	14	7	coding	code	VERB
fuelectenerg-3309	14	8	,	,	PUNCT
fuelectenerg-3309	14	9	enumerating	enumerate	VERB
fuelectenerg-3309	14	10	and	and	CCONJ
fuelectenerg-3309	14	11	shuffling	shuffle	VERB
fuelectenerg-3309	14	12	the	the	DET
fuelectenerg-3309	14	13	set	set	NOUN
fuelectenerg-3309	14	14	{	{	PUNCT
fuelectenerg-3309	14	15	0	0	NUM
fuelectenerg-3309	14	16	,	,	PUNCT
fuelectenerg-3309	14	17	...	...	PUNCT
fuelectenerg-3309	14	18	,	,	PUNCT
fuelectenerg-3309	14	19	2	2	NUM
fuelectenerg-3309	14	20	m	m	NOUN
fuelectenerg-3309	14	21	−	−	NOUN
fuelectenerg-3309	14	22	1	1	NUM
fuelectenerg-3309	14	23	}	}	PUNCT
fuelectenerg-3309	14	24	,	,	PUNCT
fuelectenerg-3309	14	25	i.e.	i.e.	X
fuelectenerg-3309	14	26	the	the	DET
fuelectenerg-3309	14	27	set	set	NOUN
fuelectenerg-3309	14	28	of	of	ADP
fuelectenerg-3309	14	29	all	all	DET
fuelectenerg-3309	14	30	m	m	NOUN
fuelectenerg-3309	14	31	-	-	PUNCT
fuelectenerg-3309	14	32	bit	bit	NOUN
fuelectenerg-3309	14	33	binary	binary	NOUN
fuelectenerg-3309	14	34	arrays	array	NOUN
fuelectenerg-3309	14	35	.	.	PUNCT
fuelectenerg-3309	15	1	moreover	moreover	ADV
fuelectenerg-3309	15	2	we	we	PRON
fuelectenerg-3309	15	3	show	show	VERB
fuelectenerg-3309	15	4	that	that	SCONJ
fuelectenerg-3309	15	5	several	several	ADJ
fuelectenerg-3309	15	6	well	well	ADV
fuelectenerg-3309	15	7	known	know	VERB
fuelectenerg-3309	15	8	reversible	reversible	ADJ
fuelectenerg-3309	15	9	logic	logic	NOUN
fuelectenerg-3309	15	10	gates	gate	NOUN
fuelectenerg-3309	15	11	/	/	SYM
fuelectenerg-3309	15	12	circuits	circuit	NOUN
fuelectenerg-3309	15	13	(	(	PUNCT
fuelectenerg-3309	15	14	on	on	ADP
fuelectenerg-3309	15	15	m	m	ADJ
fuelectenerg-3309	15	16	-	-	PUNCT
fuelectenerg-3309	15	17	bit	bit	NOUN
fuelectenerg-3309	15	18	binary	binary	NOUN
fuelectenerg-3309	15	19	arrays	array	NOUN
fuelectenerg-3309	15	20	)	)	PUNCT
fuelectenerg-3309	15	21	can	can	AUX
fuelectenerg-3309	15	22	be	be	AUX
fuelectenerg-3309	15	23	coded	code	VERB
fuelectenerg-3309	15	24	by	by	ADP
fuelectenerg-3309	15	25	sparse	sparse	ADJ
fuelectenerg-3309	15	26	matrices	matrix	NOUN
fuelectenerg-3309	15	27	.	.	PUNCT
fuelectenerg-3309	16	1	keywords	keyword	NOUN
fuelectenerg-3309	16	2	:	:	PUNCT
fuelectenerg-3309	16	3	permutations	permutation	NOUN
fuelectenerg-3309	16	4	,	,	PUNCT
fuelectenerg-3309	16	5	reversible	reversible	ADJ
fuelectenerg-3309	16	6	logical	logical	ADJ
fuelectenerg-3309	16	7	gates	gate	NOUN
fuelectenerg-3309	16	8	.	.	PUNCT
fuelectenerg-3309	17	1	1	1	NUM
fuelectenerg-3309	17	2	introduction	introduction	NOUN
fuelectenerg-3309	17	3	let	let	VERB
fuelectenerg-3309	17	4	m	m	PRON
fuelectenerg-3309	17	5	≥	≥	NOUN
fuelectenerg-3309	17	6	2	2	NUM
fuelectenerg-3309	17	7	be	be	AUX
fuelectenerg-3309	17	8	a	a	DET
fuelectenerg-3309	17	9	natural	natural	ADJ
fuelectenerg-3309	17	10	number	number	NOUN
fuelectenerg-3309	17	11	and	and	CCONJ
fuelectenerg-3309	17	12	p	p	X
fuelectenerg-3309	17	13	(	(	PUNCT
fuelectenerg-3309	17	14	m	m	NOUN
fuelectenerg-3309	17	15	)	)	PUNCT
fuelectenerg-3309	17	16	be	be	VERB
fuelectenerg-3309	17	17	the	the	DET
fuelectenerg-3309	17	18	group	group	NOUN
fuelectenerg-3309	17	19	of	of	ADP
fuelectenerg-3309	17	20	permutations	permutation	NOUN
fuelectenerg-3309	17	21	of	of	ADP
fuelectenerg-3309	17	22	the	the	DET
fuelectenerg-3309	17	23	set	set	NOUN
fuelectenerg-3309	17	24	{	{	PUNCT
fuelectenerg-3309	17	25	1	1	NUM
fuelectenerg-3309	17	26	,	,	PUNCT
fuelectenerg-3309	17	27	...	...	PUNCT
fuelectenerg-3309	17	28	,	,	PUNCT
fuelectenerg-3309	17	29	m	m	VERB
fuelectenerg-3309	17	30	}	}	PUNCT
fuelectenerg-3309	17	31	.	.	PUNCT
fuelectenerg-3309	18	1	in	in	ADP
fuelectenerg-3309	18	2	this	this	DET
fuelectenerg-3309	18	3	work	work	NOUN
fuelectenerg-3309	18	4	we	we	PRON
fuelectenerg-3309	18	5	introduce	introduce	VERB
fuelectenerg-3309	18	6	a	a	DET
fuelectenerg-3309	18	7	variety	variety	NOUN
fuelectenerg-3309	18	8	of	of	ADP
fuelectenerg-3309	18	9	shuffling	shuffle	VERB
fuelectenerg-3309	18	10	methods	method	NOUN
fuelectenerg-3309	18	11	.	.	PUNCT
fuelectenerg-3309	19	1	more	more	ADV
fuelectenerg-3309	19	2	precisely	precisely	ADV
fuelectenerg-3309	19	3	,	,	PUNCT
fuelectenerg-3309	19	4	each	each	DET
fuelectenerg-3309	19	5	shuffling	shuffle	VERB
fuelectenerg-3309	19	6	method	method	NOUN
fuelectenerg-3309	19	7	is	be	AUX
fuelectenerg-3309	19	8	a	a	DET
fuelectenerg-3309	19	9	bijective	bijective	ADJ
fuelectenerg-3309	19	10	map	map	NOUN
fuelectenerg-3309	19	11	of	of	ADP
fuelectenerg-3309	19	12	a	a	DET
fuelectenerg-3309	19	13	set	set	NOUN
fuelectenerg-3309	19	14	onto	onto	ADP
fuelectenerg-3309	19	15	itself	itself	PRON
fuelectenerg-3309	19	16	,	,	PUNCT
fuelectenerg-3309	19	17	i.e.	i.e.	X
fuelectenerg-3309	19	18	different	different	ADJ
fuelectenerg-3309	19	19	inputs	input	NOUN
fuelectenerg-3309	19	20	yield	yield	VERB
fuelectenerg-3309	19	21	different	different	ADJ
fuelectenerg-3309	19	22	outputs	output	NOUN
fuelectenerg-3309	19	23	and	and	CCONJ
fuelectenerg-3309	19	24	the	the	DET
fuelectenerg-3309	19	25	number	number	NOUN
fuelectenerg-3309	19	26	of	of	ADP
fuelectenerg-3309	19	27	inputs	input	NOUN
fuelectenerg-3309	19	28	and	and	CCONJ
fuelectenerg-3309	19	29	outputs	output	NOUN
fuelectenerg-3309	19	30	are	be	AUX
fuelectenerg-3309	19	31	equal	equal	ADJ
fuelectenerg-3309	19	32	.	.	PUNCT
fuelectenerg-3309	20	1	manuscript	manuscript	NOUN
fuelectenerg-3309	20	2	received	receive	VERB
fuelectenerg-3309	20	3	xx	xx	NUM
fuelectenerg-3309	20	4	,	,	PUNCT
fuelectenerg-3309	20	5	xxxx	xxxx	PROPN
fuelectenerg-3309	20	6	corresponding	correspond	VERB
fuelectenerg-3309	20	7	author	author	NOUN
fuelectenerg-3309	20	8	:	:	PUNCT
fuelectenerg-3309	20	9	nikolaos	nikolaos	PROPN
fuelectenerg-3309	20	10	atreas	atreas	PROPN
fuelectenerg-3309	20	11	school	school	PROPN
fuelectenerg-3309	20	12	of	of	ADP
fuelectenerg-3309	20	13	electrical	electrical	ADJ
fuelectenerg-3309	20	14	and	and	CCONJ
fuelectenerg-3309	20	15	computer	computer	NOUN
fuelectenerg-3309	20	16	engineering	engineering	NOUN
fuelectenerg-3309	20	17	,	,	PUNCT
fuelectenerg-3309	20	18	faculty	faculty	NOUN
fuelectenerg-3309	20	19	of	of	ADP
fuelectenerg-3309	20	20	engineering	engineering	PROPN
fuelectenerg-3309	20	21	,	,	PUNCT
fuelectenerg-3309	20	22	aristotle	aristotle	PROPN
fuelectenerg-3309	20	23	university	university	PROPN
fuelectenerg-3309	20	24	of	of	ADP
fuelectenerg-3309	20	25	thessaloniki	thessaloniki	PROPN
fuelectenerg-3309	20	26	,	,	PUNCT
fuelectenerg-3309	20	27	greece	greece	PROPN
fuelectenerg-3309	20	28	(	(	PUNCT
fuelectenerg-3309	20	29	e	e	NOUN
fuelectenerg-3309	20	30	-	-	NOUN
fuelectenerg-3309	20	31	mail	mail	NOUN
fuelectenerg-3309	20	32	:	:	PUNCT
fuelectenerg-3309	20	33	natreas@ece.auth.gr	natreas@ece.auth.gr	NOUN
fuelectenerg-3309	20	34	)	)	PUNCT
fuelectenerg-3309	20	35	an	an	DET
fuelectenerg-3309	20	36	earlier	early	ADJ
fuelectenerg-3309	20	37	version	version	NOUN
fuelectenerg-3309	20	38	of	of	ADP
fuelectenerg-3309	20	39	this	this	DET
fuelectenerg-3309	20	40	paper	paper	NOUN
fuelectenerg-3309	20	41	was	be	AUX
fuelectenerg-3309	20	42	presented	present	VERB
fuelectenerg-3309	20	43	as	as	ADP
fuelectenerg-3309	20	44	an	an	DET
fuelectenerg-3309	20	45	invited	invite	VERB
fuelectenerg-3309	20	46	address	address	NOUN
fuelectenerg-3309	20	47	at	at	ADP
fuelectenerg-3309	20	48	the	the	DET
fuelectenerg-3309	20	49	reed	reed	NOUN
fuelectenerg-3309	20	50	-	-	PUNCT
fuelectenerg-3309	20	51	muller	muller	NOUN
fuelectenerg-3309	20	52	2017	2017	NUM
fuelectenerg-3309	20	53	workshop	workshop	NOUN
fuelectenerg-3309	20	54	,	,	PUNCT
fuelectenerg-3309	20	55	novi	novi	PROPN
fuelectenerg-3309	20	56	sad	sad	PROPN
fuelectenerg-3309	20	57	,	,	PUNCT
fuelectenerg-3309	20	58	serbia	serbia	PROPN
fuelectenerg-3309	20	59	,	,	PUNCT
fuelectenerg-3309	20	60	may	may	AUX
fuelectenerg-3309	20	61	24	24	NUM
fuelectenerg-3309	20	62	-	-	SYM
fuelectenerg-3309	20	63	25	25	NUM
fuelectenerg-3309	20	64	,	,	PUNCT
fuelectenerg-3309	20	65	2017	2017	NUM
fuelectenerg-3309	20	66	1	1	NUM
fuelectenerg-3309	20	67	2	2	NUM
fuelectenerg-3309	20	68	n.	n.	NOUN
fuelectenerg-3309	20	69	atreas	atreas	PROPN
fuelectenerg-3309	20	70	and	and	CCONJ
fuelectenerg-3309	20	71	c.	c.	PROPN
fuelectenerg-3309	20	72	karanikas	karanikas	PROPN
fuelectenerg-3309	20	73	our	our	PRON
fuelectenerg-3309	20	74	main	main	ADJ
fuelectenerg-3309	20	75	theorem	theorem	NOUN
fuelectenerg-3309	20	76	2	2	NUM
fuelectenerg-3309	20	77	in	in	ADP
fuelectenerg-3309	20	78	section	section	NOUN
fuelectenerg-3309	20	79	3	3	NUM
fuelectenerg-3309	20	80	or	or	CCONJ
fuelectenerg-3309	20	81	its	its	PRON
fuelectenerg-3309	20	82	”	"	PUNCT
fuelectenerg-3309	20	83	binary	binary	ADJ
fuelectenerg-3309	20	84	”	"	PUNCT
fuelectenerg-3309	20	85	version	version	NOUN
fuelectenerg-3309	20	86	(	(	PUNCT
fuelectenerg-3309	20	87	see	see	VERB
fuelectenerg-3309	20	88	theorem	theorem	NOUN
fuelectenerg-3309	20	89	3	3	NUM
fuelectenerg-3309	20	90	in	in	ADP
fuelectenerg-3309	20	91	section	section	NOUN
fuelectenerg-3309	20	92	4	4	NUM
fuelectenerg-3309	20	93	)	)	PUNCT
fuelectenerg-3309	20	94	,	,	PUNCT
fuelectenerg-3309	20	95	states	state	VERB
fuelectenerg-3309	20	96	that	that	SCONJ
fuelectenerg-3309	20	97	any	any	DET
fuelectenerg-3309	20	98	pair	pair	NOUN
fuelectenerg-3309	20	99	(	(	PUNCT
fuelectenerg-3309	20	100	ρ	ρ	PROPN
fuelectenerg-3309	20	101	,	,	PUNCT
fuelectenerg-3309	20	102	s	s	NOUN
fuelectenerg-3309	20	103	)	)	PUNCT
fuelectenerg-3309	20	104	of	of	ADP
fuelectenerg-3309	20	105	permutations	permutation	NOUN
fuelectenerg-3309	20	106	in	in	ADP
fuelectenerg-3309	20	107	p	p	PROPN
fuelectenerg-3309	20	108	(	(	PUNCT
fuelectenerg-3309	20	109	m	m	NOUN
fuelectenerg-3309	20	110	)	)	PUNCT
fuelectenerg-3309	20	111	determines	determine	VERB
fuelectenerg-3309	20	112	a	a	DET
fuelectenerg-3309	20	113	bijective	bijective	ADJ
fuelectenerg-3309	20	114	map	map	NOUN
fuelectenerg-3309	21	1	tρ	tρ	ADP
fuelectenerg-3309	21	2	,	,	PUNCT
fuelectenerg-3309	21	3	s	s	PART
fuelectenerg-3309	21	4	:	:	PUNCT
fuelectenerg-3309	21	5	{	{	PUNCT
fuelectenerg-3309	21	6	0	0	NUM
fuelectenerg-3309	21	7	,	,	PUNCT
fuelectenerg-3309	21	8	1	1	NUM
fuelectenerg-3309	21	9	,	,	PUNCT
fuelectenerg-3309	21	10	....	....	PUNCT
fuelectenerg-3309	21	11	,	,	PUNCT
fuelectenerg-3309	21	12	2	2	NUM
fuelectenerg-3309	21	13	m	m	NOUN
fuelectenerg-3309	21	14	−	−	NOUN
fuelectenerg-3309	21	15	1	1	NUM
fuelectenerg-3309	21	16	}	}	PUNCT
fuelectenerg-3309	21	17	→	→	SYM
fuelectenerg-3309	21	18	{	{	PUNCT
fuelectenerg-3309	21	19	0	0	NUM
fuelectenerg-3309	21	20	,	,	PUNCT
fuelectenerg-3309	21	21	1	1	NUM
fuelectenerg-3309	21	22	,	,	PUNCT
fuelectenerg-3309	21	23	....	....	PUNCT
fuelectenerg-3309	21	24	,	,	PUNCT
fuelectenerg-3309	21	25	2	2	NUM
fuelectenerg-3309	21	26	m	m	NOUN
fuelectenerg-3309	21	27	−	−	NOUN
fuelectenerg-3309	21	28	1	1	NUM
fuelectenerg-3309	21	29	}	}	PUNCT
fuelectenerg-3309	21	30	.	.	PUNCT
fuelectenerg-3309	22	1	since	since	SCONJ
fuelectenerg-3309	22	2	every	every	DET
fuelectenerg-3309	22	3	non	non	PRON
fuelectenerg-3309	22	4	negative	negative	ADJ
fuelectenerg-3309	22	5	integer	integer	NOUN
fuelectenerg-3309	22	6	n	n	PRON
fuelectenerg-3309	22	7	∈	∈	PROPN
fuelectenerg-3309	22	8	{	{	PUNCT
fuelectenerg-3309	22	9	0	0	NUM
fuelectenerg-3309	22	10	,	,	PUNCT
fuelectenerg-3309	22	11	1	1	NUM
fuelectenerg-3309	22	12	,	,	PUNCT
fuelectenerg-3309	22	13	....	....	PUNCT
fuelectenerg-3309	22	14	,	,	PUNCT
fuelectenerg-3309	22	15	2	2	NUM
fuelectenerg-3309	22	16	m	m	NOUN
fuelectenerg-3309	22	17	−	−	NUM
fuelectenerg-3309	22	18	1	1	NUM
fuelectenerg-3309	22	19	}	}	PUNCT
fuelectenerg-3309	22	20	can	can	AUX
fuelectenerg-3309	22	21	be	be	AUX
fuelectenerg-3309	22	22	expressed	express	VERB
fuelectenerg-3309	22	23	either	either	CCONJ
fuelectenerg-3309	22	24	as	as	ADP
fuelectenerg-3309	22	25	an	an	DET
fuelectenerg-3309	22	26	m	m	NOUN
fuelectenerg-3309	22	27	-	-	PUNCT
fuelectenerg-3309	22	28	bit	bit	NOUN
fuelectenerg-3309	22	29	binary	binary	ADJ
fuelectenerg-3309	22	30	array	array	NOUN
fuelectenerg-3309	22	31	en	en	X
fuelectenerg-3309	22	32	=	=	SYM
fuelectenerg-3309	22	33	(	(	PUNCT
fuelectenerg-3309	22	34	ε0(n	ε0(n	NOUN
fuelectenerg-3309	22	35	)	)	PUNCT
fuelectenerg-3309	22	36	,	,	PUNCT
fuelectenerg-3309	22	37	ε1(n	ε1(n	NOUN
fuelectenerg-3309	22	38	)	)	PUNCT
fuelectenerg-3309	22	39	,	,	PUNCT
fuelectenerg-3309	22	40	...	...	PUNCT
fuelectenerg-3309	22	41	,	,	PUNCT
fuelectenerg-3309	22	42	εm−1(n	εm−1(n	PROPN
fuelectenerg-3309	22	43	)	)	PUNCT
fuelectenerg-3309	22	44	)	)	PUNCT
fuelectenerg-3309	22	45	,	,	PUNCT
fuelectenerg-3309	22	46	εj	εj	NOUN
fuelectenerg-3309	22	47	∈	∈	PROPN
fuelectenerg-3309	22	48	{	{	PUNCT
fuelectenerg-3309	22	49	0	0	NUM
fuelectenerg-3309	22	50	,	,	PUNCT
fuelectenerg-3309	22	51	1	1	NUM
fuelectenerg-3309	22	52	}	}	PUNCT
fuelectenerg-3309	22	53	,	,	PUNCT
fuelectenerg-3309	22	54	or	or	CCONJ
fuelectenerg-3309	22	55	by	by	ADP
fuelectenerg-3309	22	56	its	its	PRON
fuelectenerg-3309	22	57	dyadic	dyadic	ADJ
fuelectenerg-3309	22	58	expansion	expansion	NOUN
fuelectenerg-3309	22	59	n	n	NOUN
fuelectenerg-3309	22	60	=	=	PUNCT
fuelectenerg-3309	22	61	m∑	m∑	PROPN
fuelectenerg-3309	22	62	j=1	j=1	PROPN
fuelectenerg-3309	22	63	εj(n)2	εj(n)2	PROPN
fuelectenerg-3309	22	64	j−1	j−1	PROPN
fuelectenerg-3309	22	65	,	,	PUNCT
fuelectenerg-3309	22	66	the	the	DET
fuelectenerg-3309	22	67	above	above	ADJ
fuelectenerg-3309	22	68	map	map	NOUN
fuelectenerg-3309	22	69	tρ	tρ	ADP
fuelectenerg-3309	22	70	,	,	PUNCT
fuelectenerg-3309	22	71	s	s	PART
fuelectenerg-3309	22	72	can	can	AUX
fuelectenerg-3309	22	73	be	be	AUX
fuelectenerg-3309	22	74	considered	consider	VERB
fuelectenerg-3309	22	75	as	as	ADP
fuelectenerg-3309	22	76	a	a	DET
fuelectenerg-3309	22	77	reversible	reversible	ADJ
fuelectenerg-3309	22	78	map	map	NOUN
fuelectenerg-3309	22	79	on	on	ADP
fuelectenerg-3309	22	80	the	the	DET
fuelectenerg-3309	22	81	set	set	NOUN
fuelectenerg-3309	22	82	of	of	ADP
fuelectenerg-3309	22	83	all	all	DET
fuelectenerg-3309	22	84	m	m	NOUN
fuelectenerg-3309	22	85	-	-	PUNCT
fuelectenerg-3309	22	86	bit	bit	NOUN
fuelectenerg-3309	22	87	binary	binary	NOUN
fuelectenerg-3309	22	88	arrays	array	NOUN
fuelectenerg-3309	22	89	.	.	PUNCT
fuelectenerg-3309	23	1	in	in	ADP
fuelectenerg-3309	23	2	a	a	DET
fuelectenerg-3309	23	3	different	different	ADJ
fuelectenerg-3309	23	4	terminology	terminology	NOUN
fuelectenerg-3309	23	5	,	,	PUNCT
fuelectenerg-3309	23	6	we	we	PRON
fuelectenerg-3309	23	7	can	can	AUX
fuelectenerg-3309	23	8	say	say	VERB
fuelectenerg-3309	23	9	that	that	SCONJ
fuelectenerg-3309	23	10	in	in	ADP
fuelectenerg-3309	23	11	theorem	theorem	NOUN
fuelectenerg-3309	23	12	3	3	NUM
fuelectenerg-3309	23	13	we	we	PRON
fuelectenerg-3309	23	14	introduce	introduce	VERB
fuelectenerg-3309	23	15	reversible	reversible	ADJ
fuelectenerg-3309	23	16	logic	logic	NOUN
fuelectenerg-3309	23	17	gates	gate	NOUN
fuelectenerg-3309	23	18	,	,	PUNCT
fuelectenerg-3309	23	19	i.e	i.e	DET
fuelectenerg-3309	23	20	bijective	bijective	ADJ
fuelectenerg-3309	23	21	maps	map	NOUN
fuelectenerg-3309	23	22	on	on	ADP
fuelectenerg-3309	23	23	the	the	DET
fuelectenerg-3309	23	24	set	set	NOUN
fuelectenerg-3309	23	25	of	of	ADP
fuelectenerg-3309	23	26	m	m	NOUN
fuelectenerg-3309	23	27	-	-	PUNCT
fuelectenerg-3309	23	28	bit	bit	NOUN
fuelectenerg-3309	23	29	binary	binary	NOUN
fuelectenerg-3309	23	30	arrays	array	NOUN
fuelectenerg-3309	23	31	,	,	PUNCT
fuelectenerg-3309	23	32	(	(	PUNCT
fuelectenerg-3309	23	33	see	see	VERB
fuelectenerg-3309	23	34	[	[	X
fuelectenerg-3309	23	35	1	1	NUM
fuelectenerg-3309	23	36	]	]	NUM
fuelectenerg-3309	23	37	)	)	PUNCT
fuelectenerg-3309	23	38	.	.	PUNCT
fuelectenerg-3309	24	1	an	an	DET
fuelectenerg-3309	24	2	example	example	NOUN
fuelectenerg-3309	24	3	of	of	ADP
fuelectenerg-3309	24	4	a	a	DET
fuelectenerg-3309	24	5	reversible	reversible	ADJ
fuelectenerg-3309	24	6	gate	gate	NOUN
fuelectenerg-3309	24	7	is	be	AUX
fuelectenerg-3309	24	8	the	the	DET
fuelectenerg-3309	24	9	not	not	PART
fuelectenerg-3309	24	10	gate	gate	NOUN
fuelectenerg-3309	24	11	,	,	PUNCT
fuelectenerg-3309	24	12	whereas	whereas	SCONJ
fuelectenerg-3309	24	13	the	the	PRON
fuelectenerg-3309	24	14	and	and	CCONJ
fuelectenerg-3309	24	15	,	,	PUNCT
fuelectenerg-3309	24	16	or	or	CCONJ
fuelectenerg-3309	24	17	,	,	PUNCT
fuelectenerg-3309	24	18	xor	xor	PROPN
fuelectenerg-3309	24	19	gates	gate	NOUN
fuelectenerg-3309	24	20	are	be	AUX
fuelectenerg-3309	24	21	irreversible	irreversible	ADJ
fuelectenerg-3309	24	22	(	(	PUNCT
fuelectenerg-3309	24	23	not	not	PART
fuelectenerg-3309	24	24	reversible	reversible	ADJ
fuelectenerg-3309	24	25	)	)	PUNCT
fuelectenerg-3309	24	26	,	,	PUNCT
fuelectenerg-3309	24	27	because	because	SCONJ
fuelectenerg-3309	24	28	they	they	PRON
fuelectenerg-3309	24	29	map	map	VERB
fuelectenerg-3309	24	30	4	4	NUM
fuelectenerg-3309	24	31	=	=	SYM
fuelectenerg-3309	24	32	22	22	NUM
fuelectenerg-3309	24	33	input	input	NOUN
fuelectenerg-3309	24	34	states	state	NOUN
fuelectenerg-3309	24	35	into	into	ADP
fuelectenerg-3309	24	36	2	2	NUM
fuelectenerg-3309	24	37	=	=	SYM
fuelectenerg-3309	24	38	21	21	NUM
fuelectenerg-3309	24	39	output	output	NOUN
fuelectenerg-3309	24	40	states	state	NOUN
fuelectenerg-3309	24	41	,	,	PUNCT
fuelectenerg-3309	24	42	so	so	CCONJ
fuelectenerg-3309	24	43	information	information	NOUN
fuelectenerg-3309	24	44	is	be	AUX
fuelectenerg-3309	24	45	lost	lose	VERB
fuelectenerg-3309	24	46	in	in	ADP
fuelectenerg-3309	24	47	the	the	DET
fuelectenerg-3309	24	48	merging	merging	NOUN
fuelectenerg-3309	24	49	of	of	ADP
fuelectenerg-3309	24	50	paths	path	NOUN
fuelectenerg-3309	24	51	.	.	PUNCT
fuelectenerg-3309	25	1	a	a	DET
fuelectenerg-3309	25	2	second	second	ADJ
fuelectenerg-3309	25	3	target	target	NOUN
fuelectenerg-3309	25	4	of	of	ADP
fuelectenerg-3309	25	5	this	this	DET
fuelectenerg-3309	25	6	work	work	NOUN
fuelectenerg-3309	25	7	is	be	AUX
fuelectenerg-3309	25	8	to	to	PART
fuelectenerg-3309	25	9	enumerate	enumerate	VERB
fuelectenerg-3309	25	10	and	and	CCONJ
fuelectenerg-3309	25	11	code	code	NOUN
fuelectenerg-3309	25	12	permutations	permutation	NOUN
fuelectenerg-3309	25	13	in	in	ADP
fuelectenerg-3309	25	14	p	p	PROPN
fuelectenerg-3309	25	15	(	(	PUNCT
fuelectenerg-3309	25	16	m	m	NOUN
fuelectenerg-3309	25	17	)	)	PUNCT
fuelectenerg-3309	25	18	of	of	ADP
fuelectenerg-3309	25	19	large	large	ADJ
fuelectenerg-3309	25	20	length	length	NOUN
fuelectenerg-3309	25	21	(	(	PUNCT
fuelectenerg-3309	25	22	note	note	VERB
fuelectenerg-3309	25	23	that	that	SCONJ
fuelectenerg-3309	25	24	the	the	DET
fuelectenerg-3309	25	25	cardinality	cardinality	NOUN
fuelectenerg-3309	25	26	of	of	ADP
fuelectenerg-3309	25	27	the	the	DET
fuelectenerg-3309	25	28	set	set	NOUN
fuelectenerg-3309	25	29	p	p	PROPN
fuelectenerg-3309	25	30	(	(	PUNCT
fuelectenerg-3309	25	31	m	m	NOUN
fuelectenerg-3309	25	32	)	)	PUNCT
fuelectenerg-3309	25	33	is	be	AUX
fuelectenerg-3309	25	34	m	m	PRON
fuelectenerg-3309	25	35	!	!	PUNCT
fuelectenerg-3309	25	36	)	)	PUNCT
fuelectenerg-3309	25	37	.	.	PUNCT
fuelectenerg-3309	26	1	therefore	therefore	ADV
fuelectenerg-3309	26	2	,	,	PUNCT
fuelectenerg-3309	26	3	a	a	DET
fuelectenerg-3309	26	4	reversible	reversible	ADJ
fuelectenerg-3309	26	5	map	map	NOUN
fuelectenerg-3309	26	6	tρ	tρ	NOUN
fuelectenerg-3309	26	7	,	,	PUNCT
fuelectenerg-3309	26	8	s	s	AUX
fuelectenerg-3309	26	9	associated	associate	VERB
fuelectenerg-3309	26	10	with	with	ADP
fuelectenerg-3309	26	11	the	the	DET
fuelectenerg-3309	26	12	pair	pair	NOUN
fuelectenerg-3309	26	13	(	(	PUNCT
fuelectenerg-3309	26	14	ρ	ρ	PROPN
fuelectenerg-3309	26	15	,	,	PUNCT
fuelectenerg-3309	26	16	s	s	PART
fuelectenerg-3309	26	17	)	)	PUNCT
fuelectenerg-3309	26	18	can	can	AUX
fuelectenerg-3309	26	19	be	be	AUX
fuelectenerg-3309	26	20	coded	code	VERB
fuelectenerg-3309	26	21	either	either	ADV
fuelectenerg-3309	26	22	by	by	ADP
fuelectenerg-3309	26	23	the	the	DET
fuelectenerg-3309	26	24	pair	pair	NOUN
fuelectenerg-3309	26	25	(	(	PUNCT
fuelectenerg-3309	26	26	ρ	ρ	PROPN
fuelectenerg-3309	26	27	,	,	PUNCT
fuelectenerg-3309	26	28	s	s	PART
fuelectenerg-3309	26	29	)	)	PUNCT
fuelectenerg-3309	26	30	or	or	CCONJ
fuelectenerg-3309	26	31	by	by	ADP
fuelectenerg-3309	26	32	an	an	DET
fuelectenerg-3309	26	33	enumeration	enumeration	NOUN
fuelectenerg-3309	26	34	of	of	ADP
fuelectenerg-3309	26	35	p	p	PROPN
fuelectenerg-3309	26	36	(	(	PUNCT
fuelectenerg-3309	26	37	m)×p	m)×p	NOUN
fuelectenerg-3309	26	38	(	(	PUNCT
fuelectenerg-3309	26	39	m	m	NOUN
fuelectenerg-3309	26	40	)	)	PUNCT
fuelectenerg-3309	26	41	as	as	ADP
fuelectenerg-3309	26	42	in	in	ADP
fuelectenerg-3309	26	43	section	section	NOUN
fuelectenerg-3309	26	44	2	2	NUM
fuelectenerg-3309	26	45	.	.	PUNCT
fuelectenerg-3309	27	1	this	this	DET
fuelectenerg-3309	27	2	coding	code	VERB
fuelectenerg-3309	27	3	method	method	NOUN
fuelectenerg-3309	27	4	is	be	AUX
fuelectenerg-3309	27	5	associated	associate	VERB
fuelectenerg-3309	27	6	with	with	ADP
fuelectenerg-3309	27	7	a	a	DET
fuelectenerg-3309	27	8	particular	particular	ADJ
fuelectenerg-3309	27	9	class	class	NOUN
fuelectenerg-3309	27	10	of	of	ADP
fuelectenerg-3309	27	11	sparse	sparse	ADJ
fuelectenerg-3309	27	12	boolean	boolean	ADJ
fuelectenerg-3309	27	13	invertible	invertible	ADJ
fuelectenerg-3309	27	14	matrices	matrix	NOUN
fuelectenerg-3309	27	15	introduced	introduce	VERB
fuelectenerg-3309	27	16	in	in	ADP
fuelectenerg-3309	27	17	[	[	X
fuelectenerg-3309	27	18	2	2	NUM
fuelectenerg-3309	27	19	]	]	PUNCT
fuelectenerg-3309	27	20	(	(	PUNCT
fuelectenerg-3309	27	21	see	see	VERB
fuelectenerg-3309	27	22	also	also	ADV
fuelectenerg-3309	27	23	[	[	X
fuelectenerg-3309	27	24	3–6	3–6	NUM
fuelectenerg-3309	27	25	]	]	X
fuelectenerg-3309	27	26	)	)	PUNCT
fuelectenerg-3309	27	27	.	.	PUNCT
fuelectenerg-3309	28	1	notice	notice	VERB
fuelectenerg-3309	28	2	that	that	SCONJ
fuelectenerg-3309	28	3	sparse	sparse	ADJ
fuelectenerg-3309	28	4	matrices	matrix	NOUN
fuelectenerg-3309	28	5	are	be	AUX
fuelectenerg-3309	28	6	very	very	ADV
fuelectenerg-3309	28	7	useful	useful	ADJ
fuelectenerg-3309	28	8	for	for	ADP
fuelectenerg-3309	28	9	fast	fast	ADJ
fuelectenerg-3309	28	10	processing	processing	NOUN
fuelectenerg-3309	28	11	/	/	SYM
fuelectenerg-3309	28	12	transmission	transmission	NOUN
fuelectenerg-3309	28	13	of	of	ADP
fuelectenerg-3309	28	14	data	datum	NOUN
fuelectenerg-3309	28	15	and	and	CCONJ
fuelectenerg-3309	28	16	they	they	PRON
fuelectenerg-3309	28	17	have	have	AUX
fuelectenerg-3309	28	18	been	be	AUX
fuelectenerg-3309	28	19	effectively	effectively	ADV
fuelectenerg-3309	28	20	used	use	VERB
fuelectenerg-3309	28	21	in	in	ADP
fuelectenerg-3309	28	22	[	[	X
fuelectenerg-3309	28	23	6	6	NUM
fuelectenerg-3309	28	24	]	]	PUNCT
fuelectenerg-3309	28	25	for	for	ADP
fuelectenerg-3309	28	26	detecting	detect	VERB
fuelectenerg-3309	28	27	specific	specific	ADJ
fuelectenerg-3309	28	28	characteristics	characteristic	NOUN
fuelectenerg-3309	28	29	on	on	ADP
fuelectenerg-3309	28	30	finite	finite	ADJ
fuelectenerg-3309	28	31	data	datum	NOUN
fuelectenerg-3309	28	32	.	.	PUNCT
fuelectenerg-3309	29	1	the	the	DET
fuelectenerg-3309	29	2	paper	paper	NOUN
fuelectenerg-3309	29	3	is	be	AUX
fuelectenerg-3309	29	4	organized	organize	VERB
fuelectenerg-3309	29	5	in	in	ADP
fuelectenerg-3309	29	6	the	the	DET
fuelectenerg-3309	29	7	following	follow	VERB
fuelectenerg-3309	29	8	sections	section	NOUN
fuelectenerg-3309	29	9	:	:	PUNCT
fuelectenerg-3309	29	10	in	in	ADP
fuelectenerg-3309	29	11	section	section	NOUN
fuelectenerg-3309	29	12	2	2	NUM
fuelectenerg-3309	29	13	we	we	PRON
fuelectenerg-3309	29	14	introduce	introduce	VERB
fuelectenerg-3309	29	15	our	our	PRON
fuelectenerg-3309	29	16	main	main	ADJ
fuelectenerg-3309	29	17	tool	tool	NOUN
fuelectenerg-3309	29	18	,	,	PUNCT
fuelectenerg-3309	29	19	the	the	DET
fuelectenerg-3309	29	20	invertible	invertible	ADJ
fuelectenerg-3309	29	21	map	map	NOUN
fuelectenerg-3309	29	22	p	p	X
fuelectenerg-3309	29	23	(	(	PUNCT
fuelectenerg-3309	29	24	m	m	NOUN
fuelectenerg-3309	29	25	)	)	PUNCT
fuelectenerg-3309	29	26	→	→	SYM
fuelectenerg-3309	29	27	s(m	s(m	PROPN
fuelectenerg-3309	29	28	)	)	PUNCT
fuelectenerg-3309	29	29	(	(	PUNCT
fuelectenerg-3309	29	30	see	see	VERB
fuelectenerg-3309	29	31	(	(	PUNCT
fuelectenerg-3309	29	32	2	2	NUM
fuelectenerg-3309	29	33	)	)	PUNCT
fuelectenerg-3309	29	34	and	and	CCONJ
fuelectenerg-3309	29	35	(	(	PUNCT
fuelectenerg-3309	29	36	3	3	NUM
fuelectenerg-3309	29	37	)	)	PUNCT
fuelectenerg-3309	29	38	)	)	PUNCT
fuelectenerg-3309	29	39	and	and	CCONJ
fuelectenerg-3309	29	40	in	in	ADP
fuelectenerg-3309	29	41	proposition	proposition	NOUN
fuelectenerg-3309	29	42	1	1	NUM
fuelectenerg-3309	29	43	,	,	PUNCT
fuelectenerg-3309	29	44	we	we	PRON
fuelectenerg-3309	29	45	see	see	VERB
fuelectenerg-3309	29	46	that	that	SCONJ
fuelectenerg-3309	29	47	this	this	DET
fuelectenerg-3309	29	48	map	map	NOUN
fuelectenerg-3309	29	49	induces	induce	VERB
fuelectenerg-3309	29	50	the	the	DET
fuelectenerg-3309	29	51	lexicographic	lexicographic	ADJ
fuelectenerg-3309	29	52	order	order	NOUN
fuelectenerg-3309	29	53	of	of	ADP
fuelectenerg-3309	29	54	the	the	DET
fuelectenerg-3309	29	55	enumeration	enumeration	NOUN
fuelectenerg-3309	29	56	of	of	ADP
fuelectenerg-3309	29	57	p	p	PROPN
fuelectenerg-3309	29	58	(	(	PUNCT
fuelectenerg-3309	29	59	m	m	NOUN
fuelectenerg-3309	29	60	)	)	PUNCT
fuelectenerg-3309	29	61	.	.	PUNCT
fuelectenerg-3309	30	1	moreover	moreover	ADV
fuelectenerg-3309	30	2	we	we	PRON
fuelectenerg-3309	30	3	consider	consider	VERB
fuelectenerg-3309	30	4	the	the	DET
fuelectenerg-3309	30	5	cartesian	cartesian	ADJ
fuelectenerg-3309	30	6	product	product	NOUN
fuelectenerg-3309	30	7	r(m	r(m	NOUN
fuelectenerg-3309	30	8	)	)	PUNCT
fuelectenerg-3309	30	9	=	=	SYM
fuelectenerg-3309	30	10	p	p	X
fuelectenerg-3309	30	11	(	(	PUNCT
fuelectenerg-3309	30	12	1)×p	1)×p	NUM
fuelectenerg-3309	30	13	(	(	PUNCT
fuelectenerg-3309	30	14	2)×	2)×	NUM
fuelectenerg-3309	30	15	...	...	PUNCT
fuelectenerg-3309	30	16	×p	×p	PRON
fuelectenerg-3309	30	17	(	(	PUNCT
fuelectenerg-3309	30	18	m	m	NOUN
fuelectenerg-3309	30	19	)	)	PUNCT
fuelectenerg-3309	30	20	of	of	ADP
fuelectenerg-3309	30	21	permutations	permutation	NOUN
fuelectenerg-3309	30	22	to	to	PART
fuelectenerg-3309	30	23	show	show	VERB
fuelectenerg-3309	30	24	in	in	ADP
fuelectenerg-3309	30	25	theorem	theorem	NOUN
fuelectenerg-3309	30	26	1	1	NUM
fuelectenerg-3309	30	27	that	that	SCONJ
fuelectenerg-3309	30	28	each	each	DET
fuelectenerg-3309	30	29	fixed	fix	VERB
fuelectenerg-3309	30	30	element	element	NOUN
fuelectenerg-3309	30	31	of	of	ADP
fuelectenerg-3309	30	32	r(m	r(m	PROPN
fuelectenerg-3309	30	33	)	)	PUNCT
fuelectenerg-3309	30	34	provides	provide	VERB
fuelectenerg-3309	30	35	an	an	DET
fuelectenerg-3309	30	36	enumeration	enumeration	NOUN
fuelectenerg-3309	30	37	of	of	ADP
fuelectenerg-3309	30	38	p	p	PROPN
fuelectenerg-3309	30	39	(	(	PUNCT
fuelectenerg-3309	30	40	m	m	NOUN
fuelectenerg-3309	30	41	)	)	PUNCT
fuelectenerg-3309	30	42	.	.	PUNCT
fuelectenerg-3309	31	1	in	in	ADP
fuelectenerg-3309	31	2	section	section	NOUN
fuelectenerg-3309	31	3	3	3	NUM
fuelectenerg-3309	31	4	we	we	PRON
fuelectenerg-3309	31	5	define	define	VERB
fuelectenerg-3309	31	6	a	a	DET
fuelectenerg-3309	31	7	class	class	NOUN
fuelectenerg-3309	31	8	of	of	ADP
fuelectenerg-3309	31	9	sparse	sparse	ADJ
fuelectenerg-3309	31	10	m×m	m×m	ADJ
fuelectenerg-3309	31	11	boolean	boolean	ADJ
fuelectenerg-3309	31	12	invertible	invertible	ADJ
fuelectenerg-3309	31	13	matrices	matrix	NOUN
fuelectenerg-3309	31	14	zm	zm	PROPN
fuelectenerg-3309	31	15	identified	identify	VERB
fuelectenerg-3309	31	16	by	by	ADP
fuelectenerg-3309	31	17	a	a	DET
fuelectenerg-3309	31	18	pair	pair	NOUN
fuelectenerg-3309	31	19	(	(	PUNCT
fuelectenerg-3309	31	20	ρ	ρ	PROPN
fuelectenerg-3309	31	21	,	,	PUNCT
fuelectenerg-3309	31	22	s	s	PART
fuelectenerg-3309	31	23	)	)	PUNCT
fuelectenerg-3309	31	24	∈	∈	PROPN
fuelectenerg-3309	31	25	p	p	NOUN
fuelectenerg-3309	31	26	(	(	PUNCT
fuelectenerg-3309	31	27	m)×s(m	m)×s(m	NOUN
fuelectenerg-3309	31	28	)	)	PUNCT
fuelectenerg-3309	31	29	and	and	CCONJ
fuelectenerg-3309	31	30	we	we	PRON
fuelectenerg-3309	31	31	use	use	VERB
fuelectenerg-3309	31	32	this	this	DET
fuelectenerg-3309	31	33	class	class	NOUN
fuelectenerg-3309	31	34	of	of	ADP
fuelectenerg-3309	31	35	matrices	matrix	NOUN
fuelectenerg-3309	31	36	facta	facta	PROPN
fuelectenerg-3309	31	37	universitatis	universitatis	PROPN
fuelectenerg-3309	31	38	series	series	NOUN
fuelectenerg-3309	31	39	:	:	PUNCT
fuelectenerg-3309	31	40	electronics	electronic	NOUN
fuelectenerg-3309	31	41	and	and	CCONJ
fuelectenerg-3309	31	42	energetics	energetics	NOUN
fuelectenerg-3309	31	43	vol	vol	NOUN
fuelectenerg-3309	31	44	.	.	PUNCT
fuelectenerg-3309	32	1	31	31	NUM
fuelectenerg-3309	32	2	,	,	PUNCT
fuelectenerg-3309	32	3	no	no	DET
fuelectenerg-3309	32	4	2	2	NUM
fuelectenerg-3309	32	5	,	,	PUNCT
fuelectenerg-3309	32	6	june	june	PROPN
fuelectenerg-3309	32	7	2018	2018	NUM
fuelectenerg-3309	32	8	,	,	PUNCT
fuelectenerg-3309	32	9	pp	pp	ADV
fuelectenerg-3309	32	10	.	.	PUNCT
fuelectenerg-3309	33	1	241	241	NUM
fuelectenerg-3309	33	2	255	255	NUM
fuelectenerg-3309	33	3	https://doi.org/10.2298/fuee1802241k	https://doi.org/10.2298/fuee1802241k	PROPN
fuelectenerg-3309	33	4	costas	costas	PROPN
fuelectenerg-3309	33	5	karanikas1	karanikas1	PROPN
fuelectenerg-3309	33	6	,	,	PUNCT
fuelectenerg-3309	33	7	nikolaos	nikolaos	PROPN
fuelectenerg-3309	33	8	atreas2	atreas2	PROPN
fuelectenerg-3309	33	9	received	receive	VERB
fuelectenerg-3309	33	10	october	october	PROPN
fuelectenerg-3309	33	11	22	22	NUM
fuelectenerg-3309	33	12	,	,	PUNCT
fuelectenerg-3309	33	13	2017	2017	NUM
fuelectenerg-3309	33	14	;	;	PUNCT
fuelectenerg-3309	33	15	received	receive	VERB
fuelectenerg-3309	33	16	in	in	ADP
fuelectenerg-3309	33	17	revised	revise	VERB
fuelectenerg-3309	33	18	form	form	NOUN
fuelectenerg-3309	33	19	january	january	PROPN
fuelectenerg-3309	33	20	24	24	NUM
fuelectenerg-3309	33	21	,	,	PUNCT
fuelectenerg-3309	33	22	2018	2018	NUM
fuelectenerg-3309	33	23	corresponding	correspond	VERB
fuelectenerg-3309	33	24	author	author	NOUN
fuelectenerg-3309	33	25	:	:	PUNCT
fuelectenerg-3309	33	26	nikolaos	nikolaos	PROPN
fuelectenerg-3309	33	27	atreas	atreas	PROPN
fuelectenerg-3309	33	28	school	school	PROPN
fuelectenerg-3309	33	29	of	of	ADP
fuelectenerg-3309	33	30	electrical	electrical	ADJ
fuelectenerg-3309	33	31	and	and	CCONJ
fuelectenerg-3309	33	32	computer	computer	NOUN
fuelectenerg-3309	33	33	engineering	engineering	NOUN
fuelectenerg-3309	33	34	,	,	PUNCT
fuelectenerg-3309	33	35	dpt	dpt	PROPN
fuelectenerg-3309	33	36	of	of	ADP
fuelectenerg-3309	33	37	telecommunications	telecommunication	NOUN
fuelectenerg-3309	33	38	,	,	PUNCT
fuelectenerg-3309	33	39	faculty	faculty	NOUN
fuelectenerg-3309	33	40	of	of	ADP
fuelectenerg-3309	33	41	engineering	engineering	PROPN
fuelectenerg-3309	33	42	,	,	PUNCT
fuelectenerg-3309	33	43	aristotle	aristotle	PROPN
fuelectenerg-3309	33	44	university	university	PROPN
fuelectenerg-3309	33	45	of	of	ADP
fuelectenerg-3309	33	46	thessaloniki	thessaloniki	PROPN
fuelectenerg-3309	33	47	,	,	PUNCT
fuelectenerg-3309	33	48	54124	54124	NUM
fuelectenerg-3309	33	49	,	,	PUNCT
fuelectenerg-3309	33	50	thessaloniki	thessaloniki	PROPN
fuelectenerg-3309	33	51	,	,	PUNCT
fuelectenerg-3309	33	52	greece	greece	PROPN
fuelectenerg-3309	33	53	(	(	PUNCT
fuelectenerg-3309	33	54	e	e	NOUN
fuelectenerg-3309	33	55	-	-	NOUN
fuelectenerg-3309	33	56	mail	mail	NOUN
fuelectenerg-3309	33	57	:	:	PUNCT
fuelectenerg-3309	33	58	natreas@auth.gr	natreas@auth.gr	NUM
fuelectenerg-3309	33	59	)	)	PUNCT
fuelectenerg-3309	34	1	*	*	PUNCT
fuelectenerg-3309	34	2	an	an	DET
fuelectenerg-3309	34	3	earlier	early	ADJ
fuelectenerg-3309	34	4	version	version	NOUN
fuelectenerg-3309	34	5	of	of	ADP
fuelectenerg-3309	34	6	this	this	DET
fuelectenerg-3309	34	7	paper	paper	NOUN
fuelectenerg-3309	34	8	was	be	AUX
fuelectenerg-3309	34	9	presented	present	VERB
fuelectenerg-3309	34	10	as	as	ADP
fuelectenerg-3309	34	11	an	an	DET
fuelectenerg-3309	34	12	invited	invite	VERB
fuelectenerg-3309	34	13	address	address	NOUN
fuelectenerg-3309	34	14	at	at	ADP
fuelectenerg-3309	34	15	the	the	DET
fuelectenerg-3309	34	16	reed	reed	NOUN
fuelectenerg-3309	34	17	-	-	PUNCT
fuelectenerg-3309	34	18	muller	muller	NOUN
fuelectenerg-3309	34	19	2017	2017	NUM
fuelectenerg-3309	34	20	workshop	workshop	NOUN
fuelectenerg-3309	34	21	,	,	PUNCT
fuelectenerg-3309	34	22	novi	novi	PROPN
fuelectenerg-3309	34	23	sad	sad	PROPN
fuelectenerg-3309	34	24	,	,	PUNCT
fuelectenerg-3309	34	25	serbia	serbia	PROPN
fuelectenerg-3309	34	26	,	,	PUNCT
fuelectenerg-3309	34	27	may	may	AUX
fuelectenerg-3309	34	28	24	24	NUM
fuelectenerg-3309	34	29	-	-	SYM
fuelectenerg-3309	34	30	25	25	NUM
fuelectenerg-3309	34	31	,	,	PUNCT
fuelectenerg-3309	34	32	2017	2017	NUM
fuelectenerg-3309	34	33	facta	facta	NOUN
fuelectenerg-3309	34	34	universitatis	universitatis	PROPN
fuelectenerg-3309	34	35	series	series	NOUN
fuelectenerg-3309	34	36	:	:	PUNCT
fuelectenerg-3309	34	37	electronics	electronic	NOUN
fuelectenerg-3309	34	38	and	and	CCONJ
fuelectenerg-3309	34	39	energetics	energetics	NOUN
fuelectenerg-3309	34	40	vol	vol	NOUN
fuelectenerg-3309	34	41	.	.	PUNCT
fuelectenerg-3309	35	1	28	28	NUM
fuelectenerg-3309	35	2	,	,	PUNCT
fuelectenerg-3309	35	3	no	no	DET
fuelectenerg-3309	35	4	4	4	NUM
fuelectenerg-3309	35	5	,	,	PUNCT
fuelectenerg-3309	35	6	december	december	PROPN
fuelectenerg-3309	35	7	2015	2015	NUM
fuelectenerg-3309	35	8	,	,	PUNCT
fuelectenerg-3309	35	9	pp	pp	ADJ
fuelectenerg-3309	35	10	.	.	PUNCT
fuelectenerg-3309	36	1	507	507	NUM
fuelectenerg-3309	36	2	525	525	NUM
fuelectenerg-3309	36	3	doi	doi	NOUN
fuelectenerg-3309	36	4	:	:	PUNCT
fuelectenerg-3309	36	5	10.2298	10.2298	NUM
fuelectenerg-3309	36	6	/	/	SYM
fuelectenerg-3309	36	7	fuee1504507s	fuee1504507	VERB
fuelectenerg-3309	36	8	horizontal	horizontal	ADJ
fuelectenerg-3309	36	9	current	current	ADJ
fuelectenerg-3309	36	10	bipolar	bipolar	ADJ
fuelectenerg-3309	36	11	transistor	transistor	NOUN
fuelectenerg-3309	36	12	(	(	PUNCT
fuelectenerg-3309	36	13	hcbt	hcbt	NOUN
fuelectenerg-3309	36	14	)	)	PUNCT
fuelectenerg-3309	36	15	–	–	PUNCT
fuelectenerg-3309	36	16	a	a	DET
fuelectenerg-3309	36	17	low	low	ADJ
fuelectenerg-3309	36	18	-	-	PUNCT
fuelectenerg-3309	36	19	cost	cost	NOUN
fuelectenerg-3309	36	20	,	,	PUNCT
fuelectenerg-3309	36	21	high	high	ADJ
fuelectenerg-3309	36	22	-	-	PUNCT
fuelectenerg-3309	36	23	performance	performance	NOUN
fuelectenerg-3309	36	24	flexible	flexible	ADJ
fuelectenerg-3309	36	25	bicmos	bicmos	PROPN
fuelectenerg-3309	36	26	technology	technology	PROPN
fuelectenerg-3309	36	27	for	for	ADP
fuelectenerg-3309	36	28	rf	rf	NOUN
fuelectenerg-3309	36	29	communication	communication	NOUN
fuelectenerg-3309	36	30	applications	applications	X
fuelectenerg-3309	36	31	tomislav	tomislav	PROPN
fuelectenerg-3309	36	32	suligoj1	suligoj1	PROPN
fuelectenerg-3309	36	33	,	,	PUNCT
fuelectenerg-3309	36	34	marko	marko	PROPN
fuelectenerg-3309	36	35	koričić1	koričić1	PROPN
fuelectenerg-3309	36	36	,	,	PUNCT
fuelectenerg-3309	36	37	josip	josip	PROPN
fuelectenerg-3309	36	38	žilak1	žilak1	PROPN
fuelectenerg-3309	36	39	,	,	PUNCT
fuelectenerg-3309	36	40	hidenori	hidenori	PROPN
fuelectenerg-3309	36	41	mochizuki2	mochizuki2	PROPN
fuelectenerg-3309	36	42	,	,	PUNCT
fuelectenerg-3309	36	43	so	so	ADV
fuelectenerg-3309	36	44	-	-	PUNCT
fuelectenerg-3309	36	45	ichi	ichi	ADJ
fuelectenerg-3309	36	46	morita2	morita2	NOUN
fuelectenerg-3309	36	47	,	,	PUNCT
fuelectenerg-3309	36	48	katsumi	katsumi	PROPN
fuelectenerg-3309	36	49	shinomura2	shinomura2	PROPN
fuelectenerg-3309	36	50	,	,	PUNCT
fuelectenerg-3309	36	51	hisaya	hisaya	NOUN
fuelectenerg-3309	36	52	imai2	imai2	PROPN
fuelectenerg-3309	36	53	1university	1university	NUM
fuelectenerg-3309	36	54	of	of	ADP
fuelectenerg-3309	36	55	zagreb	zagreb	PROPN
fuelectenerg-3309	36	56	,	,	PUNCT
fuelectenerg-3309	36	57	faculty	faculty	NOUN
fuelectenerg-3309	36	58	of	of	ADP
fuelectenerg-3309	36	59	electrical	electrical	ADJ
fuelectenerg-3309	36	60	engineering	engineering	NOUN
fuelectenerg-3309	36	61	and	and	CCONJ
fuelectenerg-3309	36	62	computing	computing	NOUN
fuelectenerg-3309	36	63	,	,	PUNCT
fuelectenerg-3309	36	64	department	department	NOUN
fuelectenerg-3309	36	65	of	of	ADP
fuelectenerg-3309	36	66	electronics	electronic	NOUN
fuelectenerg-3309	36	67	,	,	PUNCT
fuelectenerg-3309	36	68	microand	microand	NOUN
fuelectenerg-3309	36	69	nano	nano	NOUN
fuelectenerg-3309	36	70	-	-	PUNCT
fuelectenerg-3309	36	71	electronics	electronic	NOUN
fuelectenerg-3309	36	72	laboratory	laboratory	NOUN
fuelectenerg-3309	36	73	,	,	PUNCT
fuelectenerg-3309	36	74	croatia	croatia	PROPN
fuelectenerg-3309	36	75	2asahi	2asahi	PROPN
fuelectenerg-3309	36	76	kasei	kasei	PROPN
fuelectenerg-3309	36	77	microdevices	microdevices	PROPN
fuelectenerg-3309	36	78	co.	co.	PROPN
fuelectenerg-3309	36	79	5	5	NUM
fuelectenerg-3309	36	80	-	-	SYM
fuelectenerg-3309	36	81	4960	4960	NUM
fuelectenerg-3309	36	82	,	,	PUNCT
fuelectenerg-3309	36	83	nobeoka	nobeoka	NOUN
fuelectenerg-3309	36	84	,	,	PUNCT
fuelectenerg-3309	36	85	miyazaki	miyazaki	PROPN
fuelectenerg-3309	36	86	,	,	PUNCT
fuelectenerg-3309	36	87	882	882	NUM
fuelectenerg-3309	36	88	-	-	SYM
fuelectenerg-3309	36	89	0031	0031	NUM
fuelectenerg-3309	36	90	,	,	PUNCT
fuelectenerg-3309	36	91	japan	japan	PROPN
fuelectenerg-3309	36	92	abstract	abstract	PROPN
fuelectenerg-3309	36	93	.	.	PUNCT
fuelectenerg-3309	37	1	in	in	ADP
fuelectenerg-3309	37	2	an	an	DET
fuelectenerg-3309	37	3	overview	overview	NOUN
fuelectenerg-3309	37	4	of	of	ADP
fuelectenerg-3309	37	5	horizontal	horizontal	ADJ
fuelectenerg-3309	37	6	current	current	ADJ
fuelectenerg-3309	37	7	bipolar	bipolar	ADJ
fuelectenerg-3309	37	8	transistor	transistor	NOUN
fuelectenerg-3309	37	9	(	(	PUNCT
fuelectenerg-3309	37	10	hcbt	hcbt	NOUN
fuelectenerg-3309	37	11	)	)	PUNCT
fuelectenerg-3309	37	12	technology	technology	NOUN
fuelectenerg-3309	37	13	,	,	PUNCT
fuelectenerg-3309	37	14	the	the	DET
fuelectenerg-3309	37	15	state	state	NOUN
fuelectenerg-3309	37	16	-	-	PUNCT
fuelectenerg-3309	37	17	of	of	ADP
fuelectenerg-3309	37	18	-	-	PUNCT
fuelectenerg-3309	37	19	the	the	DET
fuelectenerg-3309	37	20	-	-	PUNCT
fuelectenerg-3309	37	21	art	art	NOUN
fuelectenerg-3309	37	22	integrated	integrate	VERB
fuelectenerg-3309	37	23	silicon	silicon	NOUN
fuelectenerg-3309	37	24	bipolar	bipolar	ADJ
fuelectenerg-3309	37	25	transistors	transistor	NOUN
fuelectenerg-3309	37	26	are	be	AUX
fuelectenerg-3309	37	27	described	describe	VERB
fuelectenerg-3309	37	28	which	which	PRON
fuelectenerg-3309	37	29	exhibit	exhibit	VERB
fuelectenerg-3309	37	30	ft	ft	PROPN
fuelectenerg-3309	37	31	and	and	CCONJ
fuelectenerg-3309	37	32	fmax	fmax	PROPN
fuelectenerg-3309	37	33	of	of	ADP
fuelectenerg-3309	37	34	51	51	NUM
fuelectenerg-3309	37	35	ghz	ghz	NOUN
fuelectenerg-3309	37	36	and	and	CCONJ
fuelectenerg-3309	37	37	61	61	NUM
fuelectenerg-3309	37	38	ghz	ghz	NOUN
fuelectenerg-3309	37	39	and	and	CCONJ
fuelectenerg-3309	37	40	ftbvceo	ftbvceo	ADJ
fuelectenerg-3309	37	41	product	product	NOUN
fuelectenerg-3309	37	42	of	of	ADP
fuelectenerg-3309	37	43	173	173	NUM
fuelectenerg-3309	37	44	ghzv	ghzv	NOUN
fuelectenerg-3309	37	45	that	that	PRON
fuelectenerg-3309	37	46	are	be	AUX
fuelectenerg-3309	37	47	among	among	ADP
fuelectenerg-3309	37	48	the	the	DET
fuelectenerg-3309	37	49	highest	high	ADJ
fuelectenerg-3309	37	50	-	-	PUNCT
fuelectenerg-3309	37	51	performance	performance	NOUN
fuelectenerg-3309	37	52	implanted	implant	VERB
fuelectenerg-3309	37	53	-	-	PUNCT
fuelectenerg-3309	37	54	base	base	NOUN
fuelectenerg-3309	37	55	,	,	PUNCT
fuelectenerg-3309	37	56	silicon	silicon	NOUN
fuelectenerg-3309	37	57	bipolar	bipolar	ADJ
fuelectenerg-3309	37	58	transistors	transistor	NOUN
fuelectenerg-3309	37	59	.	.	PUNCT
fuelectenerg-3309	38	1	hbct	hbct	ADV
fuelectenerg-3309	38	2	is	be	AUX
fuelectenerg-3309	38	3	integrated	integrate	VERB
fuelectenerg-3309	38	4	with	with	ADP
fuelectenerg-3309	38	5	cmos	cmos	PROPN
fuelectenerg-3309	38	6	in	in	ADP
fuelectenerg-3309	38	7	a	a	DET
fuelectenerg-3309	38	8	considerably	considerably	ADV
fuelectenerg-3309	38	9	lower	low	ADJ
fuelectenerg-3309	38	10	-	-	PUNCT
fuelectenerg-3309	38	11	cost	cost	NOUN
fuelectenerg-3309	38	12	fabrication	fabrication	NOUN
fuelectenerg-3309	38	13	sequence	sequence	NOUN
fuelectenerg-3309	38	14	as	as	ADP
fuelectenerg-3309	38	15	compared	compare	VERB
fuelectenerg-3309	38	16	to	to	ADP
fuelectenerg-3309	38	17	standard	standard	ADJ
fuelectenerg-3309	38	18	vertical	vertical	ADJ
fuelectenerg-3309	38	19	-	-	PUNCT
fuelectenerg-3309	38	20	current	current	ADJ
fuelectenerg-3309	38	21	bipolar	bipolar	ADJ
fuelectenerg-3309	38	22	transistors	transistor	NOUN
fuelectenerg-3309	38	23	with	with	ADP
fuelectenerg-3309	38	24	only	only	ADV
fuelectenerg-3309	38	25	2	2	NUM
fuelectenerg-3309	38	26	or	or	CCONJ
fuelectenerg-3309	38	27	3	3	NUM
fuelectenerg-3309	38	28	additional	additional	ADJ
fuelectenerg-3309	38	29	masks	mask	NOUN
fuelectenerg-3309	38	30	and	and	CCONJ
fuelectenerg-3309	38	31	fewer	few	ADJ
fuelectenerg-3309	38	32	process	process	NOUN
fuelectenerg-3309	38	33	steps	step	NOUN
fuelectenerg-3309	38	34	.	.	PUNCT
fuelectenerg-3309	39	1	due	due	ADP
fuelectenerg-3309	39	2	to	to	ADP
fuelectenerg-3309	39	3	its	its	PRON
fuelectenerg-3309	39	4	specific	specific	ADJ
fuelectenerg-3309	39	5	structure	structure	NOUN
fuelectenerg-3309	39	6	,	,	PUNCT
fuelectenerg-3309	39	7	the	the	DET
fuelectenerg-3309	39	8	charge	charge	NOUN
fuelectenerg-3309	39	9	sharing	sharing	NOUN
fuelectenerg-3309	39	10	effect	effect	NOUN
fuelectenerg-3309	39	11	can	can	AUX
fuelectenerg-3309	39	12	be	be	AUX
fuelectenerg-3309	39	13	employed	employ	VERB
fuelectenerg-3309	39	14	to	to	PART
fuelectenerg-3309	39	15	increase	increase	VERB
fuelectenerg-3309	39	16	bvceo	bvceo	ADV
fuelectenerg-3309	39	17	without	without	ADP
fuelectenerg-3309	39	18	sacrificing	sacrifice	VERB
fuelectenerg-3309	39	19	ft	ft	X
fuelectenerg-3309	39	20	and	and	CCONJ
fuelectenerg-3309	39	21	fmax	fmax	PROPN
fuelectenerg-3309	39	22	.	.	PUNCT
fuelectenerg-3309	40	1	moreover	moreover	ADV
fuelectenerg-3309	40	2	,	,	PUNCT
fuelectenerg-3309	40	3	the	the	DET
fuelectenerg-3309	40	4	electric	electric	ADJ
fuelectenerg-3309	40	5	field	field	NOUN
fuelectenerg-3309	40	6	can	can	AUX
fuelectenerg-3309	40	7	be	be	AUX
fuelectenerg-3309	40	8	engineered	engineer	VERB
fuelectenerg-3309	40	9	just	just	ADV
fuelectenerg-3309	40	10	by	by	ADP
fuelectenerg-3309	40	11	manipulating	manipulate	VERB
fuelectenerg-3309	40	12	the	the	DET
fuelectenerg-3309	40	13	lithography	lithography	NOUN
fuelectenerg-3309	40	14	masks	mask	NOUN
fuelectenerg-3309	40	15	achieving	achieve	VERB
fuelectenerg-3309	40	16	the	the	DET
fuelectenerg-3309	40	17	high	high	ADJ
fuelectenerg-3309	40	18	-	-	PUNCT
fuelectenerg-3309	40	19	voltage	voltage	NOUN
fuelectenerg-3309	40	20	hcbts	hcbt	NOUN
fuelectenerg-3309	40	21	with	with	ADP
fuelectenerg-3309	40	22	breakdowns	breakdown	NOUN
fuelectenerg-3309	40	23	up	up	ADP
fuelectenerg-3309	40	24	to	to	PART
fuelectenerg-3309	40	25	36	36	NUM
fuelectenerg-3309	40	26	v	v	NOUN
fuelectenerg-3309	40	27	integrated	integrate	VERB
fuelectenerg-3309	40	28	in	in	ADP
fuelectenerg-3309	40	29	the	the	DET
fuelectenerg-3309	40	30	same	same	ADJ
fuelectenerg-3309	40	31	process	process	NOUN
fuelectenerg-3309	40	32	flow	flow	NOUN
fuelectenerg-3309	40	33	with	with	ADP
fuelectenerg-3309	40	34	high	high	ADJ
fuelectenerg-3309	40	35	-	-	PUNCT
fuelectenerg-3309	40	36	speed	speed	NOUN
fuelectenerg-3309	40	37	devices	device	NOUN
fuelectenerg-3309	40	38	,	,	PUNCT
fuelectenerg-3309	40	39	i.e.	i.e.	X
fuelectenerg-3309	40	40	at	at	ADP
fuelectenerg-3309	40	41	zero	zero	NUM
fuelectenerg-3309	40	42	additional	additional	ADJ
fuelectenerg-3309	40	43	costs	cost	NOUN
fuelectenerg-3309	40	44	.	.	PUNCT
fuelectenerg-3309	41	1	double	double	ADJ
fuelectenerg-3309	41	2	-	-	PUNCT
fuelectenerg-3309	41	3	balanced	balanced	ADJ
fuelectenerg-3309	41	4	active	active	ADJ
fuelectenerg-3309	41	5	mixer	mixer	NOUN
fuelectenerg-3309	41	6	circuit	circuit	NOUN
fuelectenerg-3309	41	7	is	be	AUX
fuelectenerg-3309	41	8	designed	design	VERB
fuelectenerg-3309	41	9	and	and	CCONJ
fuelectenerg-3309	41	10	fabricated	fabricate	VERB
fuelectenerg-3309	41	11	in	in	ADP
fuelectenerg-3309	41	12	hcbt	hcbt	NOUN
fuelectenerg-3309	41	13	technology	technology	NOUN
fuelectenerg-3309	41	14	.	.	PUNCT
fuelectenerg-3309	42	1	the	the	DET
fuelectenerg-3309	42	2	maximum	maximum	ADJ
fuelectenerg-3309	42	3	iip3	iip3	NOUN
fuelectenerg-3309	42	4	of	of	ADP
fuelectenerg-3309	42	5	17.7	17.7	NUM
fuelectenerg-3309	42	6	dbm	dbm	NOUN
fuelectenerg-3309	42	7	at	at	ADP
fuelectenerg-3309	42	8	mixer	mixer	PROPN
fuelectenerg-3309	42	9	current	current	ADJ
fuelectenerg-3309	42	10	of	of	ADP
fuelectenerg-3309	42	11	9.2	9.2	NUM
fuelectenerg-3309	42	12	ma	ma	PROPN
fuelectenerg-3309	42	13	and	and	CCONJ
fuelectenerg-3309	42	14	conversion	conversion	NOUN
fuelectenerg-3309	42	15	gain	gain	NOUN
fuelectenerg-3309	42	16	of	of	ADP
fuelectenerg-3309	42	17	-5	-5	INTJ
fuelectenerg-3309	42	18	db	db	PROPN
fuelectenerg-3309	42	19	are	be	AUX
fuelectenerg-3309	42	20	achieved	achieve	VERB
fuelectenerg-3309	42	21	.	.	PUNCT
fuelectenerg-3309	43	1	key	key	ADJ
fuelectenerg-3309	43	2	words	word	NOUN
fuelectenerg-3309	43	3	:	:	PUNCT
fuelectenerg-3309	43	4	bicmos	bicmos	ADJ
fuelectenerg-3309	43	5	technology	technology	NOUN
fuelectenerg-3309	43	6	,	,	PUNCT
fuelectenerg-3309	43	7	bipolar	bipolar	ADJ
fuelectenerg-3309	43	8	transistors	transistor	NOUN
fuelectenerg-3309	43	9	,	,	PUNCT
fuelectenerg-3309	43	10	horizontal	horizontal	ADJ
fuelectenerg-3309	43	11	current	current	ADJ
fuelectenerg-3309	43	12	bipolar	bipolar	ADJ
fuelectenerg-3309	43	13	transistor	transistor	NOUN
fuelectenerg-3309	43	14	,	,	PUNCT
fuelectenerg-3309	43	15	radio	radio	NOUN
fuelectenerg-3309	43	16	frequency	frequency	NOUN
fuelectenerg-3309	43	17	integrated	integrate	VERB
fuelectenerg-3309	43	18	circuits	circuit	NOUN
fuelectenerg-3309	43	19	,	,	PUNCT
fuelectenerg-3309	43	20	mixer	mixer	NOUN
fuelectenerg-3309	43	21	,	,	PUNCT
fuelectenerg-3309	43	22	high	high	ADJ
fuelectenerg-3309	43	23	-	-	PUNCT
fuelectenerg-3309	43	24	voltage	voltage	NOUN
fuelectenerg-3309	43	25	bipolar	bipolar	ADJ
fuelectenerg-3309	43	26	transistors	transistor	NOUN
fuelectenerg-3309	43	27	.	.	PUNCT
fuelectenerg-3309	44	1	1	1	X
fuelectenerg-3309	44	2	.	.	X
fuelectenerg-3309	44	3	introduction	introduction	NOUN
fuelectenerg-3309	44	4	in	in	ADP
fuelectenerg-3309	44	5	the	the	DET
fuelectenerg-3309	44	6	highly	highly	ADV
fuelectenerg-3309	44	7	competitive	competitive	ADJ
fuelectenerg-3309	44	8	wireless	wireless	ADJ
fuelectenerg-3309	44	9	communication	communication	NOUN
fuelectenerg-3309	44	10	markets	market	NOUN
fuelectenerg-3309	44	11	,	,	PUNCT
fuelectenerg-3309	44	12	the	the	DET
fuelectenerg-3309	44	13	rf	rf	ADJ
fuelectenerg-3309	44	14	circuits	circuit	NOUN
fuelectenerg-3309	44	15	and	and	CCONJ
fuelectenerg-3309	44	16	systems	system	NOUN
fuelectenerg-3309	44	17	are	be	AUX
fuelectenerg-3309	44	18	fabricated	fabricate	VERB
fuelectenerg-3309	44	19	in	in	ADP
fuelectenerg-3309	44	20	the	the	DET
fuelectenerg-3309	44	21	technologies	technology	NOUN
fuelectenerg-3309	44	22	that	that	PRON
fuelectenerg-3309	44	23	are	be	AUX
fuelectenerg-3309	44	24	very	very	ADV
fuelectenerg-3309	44	25	cost	cost	NOUN
fuelectenerg-3309	44	26	-	-	PUNCT
fuelectenerg-3309	44	27	sensitive	sensitive	ADJ
fuelectenerg-3309	44	28	.	.	PUNCT
fuelectenerg-3309	45	1	in	in	ADP
fuelectenerg-3309	45	2	order	order	NOUN
fuelectenerg-3309	45	3	to	to	PART
fuelectenerg-3309	45	4	minimize	minimize	VERB
fuelectenerg-3309	45	5	the	the	DET
fuelectenerg-3309	45	6	fabrication	fabrication	NOUN
fuelectenerg-3309	45	7	costs	cost	NOUN
fuelectenerg-3309	45	8	,	,	PUNCT
fuelectenerg-3309	45	9	the	the	DET
fuelectenerg-3309	45	10	sub-10	sub-10	NUM
fuelectenerg-3309	45	11	ghz	ghz	NOUN
fuelectenerg-3309	45	12	applications	application	NOUN
fuelectenerg-3309	45	13	can	can	AUX
fuelectenerg-3309	45	14	be	be	AUX
fuelectenerg-3309	45	15	processed	process	VERB
fuelectenerg-3309	45	16	by	by	ADP
fuelectenerg-3309	45	17	using	use	VERB
fuelectenerg-3309	45	18	the	the	DET
fuelectenerg-3309	45	19	high	high	ADJ
fuelectenerg-3309	45	20	-	-	PUNCT
fuelectenerg-3309	45	21	volume	volume	NOUN
fuelectenerg-3309	45	22	silicon	silicon	NOUN
fuelectenerg-3309	45	23	technologies	technology	NOUN
fuelectenerg-3309	45	24	.	.	PUNCT
fuelectenerg-3309	46	1	it	it	PRON
fuelectenerg-3309	46	2	has	have	AUX
fuelectenerg-3309	46	3	been	be	AUX
fuelectenerg-3309	46	4	identified	identify	VERB
fuelectenerg-3309	46	5	that	that	SCONJ
fuelectenerg-3309	46	6	the	the	DET
fuelectenerg-3309	46	7	optimum	optimum	ADJ
fuelectenerg-3309	46	8	solution	solution	NOUN
fuelectenerg-3309	46	9	might	might	AUX
fuelectenerg-3309	46	10	received	receive	VERB
fuelectenerg-3309	46	11	march	march	PROPN
fuelectenerg-3309	46	12	9	9	NUM
fuelectenerg-3309	46	13	,	,	PUNCT
fuelectenerg-3309	46	14	2015	2015	NUM
fuelectenerg-3309	46	15	corresponding	correspond	VERB
fuelectenerg-3309	46	16	author	author	NOUN
fuelectenerg-3309	46	17	:	:	PUNCT
fuelectenerg-3309	46	18	tomislav	tomislav	PROPN
fuelectenerg-3309	46	19	suligoj	suligoj	PROPN
fuelectenerg-3309	46	20	university	university	PROPN
fuelectenerg-3309	46	21	of	of	ADP
fuelectenerg-3309	46	22	zagreb	zagreb	PROPN
fuelectenerg-3309	46	23	,	,	PUNCT
fuelectenerg-3309	46	24	faculty	faculty	NOUN
fuelectenerg-3309	46	25	of	of	ADP
fuelectenerg-3309	46	26	electrical	electrical	ADJ
fuelectenerg-3309	46	27	engineering	engineering	NOUN
fuelectenerg-3309	46	28	and	and	CCONJ
fuelectenerg-3309	46	29	computing	computing	NOUN
fuelectenerg-3309	46	30	,	,	PUNCT
fuelectenerg-3309	46	31	department	department	NOUN
fuelectenerg-3309	46	32	of	of	ADP
fuelectenerg-3309	46	33	electronics	electronic	NOUN
fuelectenerg-3309	46	34	,	,	PUNCT
fuelectenerg-3309	46	35	microand	microand	NOUN
fuelectenerg-3309	46	36	nano	nano	NOUN
fuelectenerg-3309	46	37	-	-	PUNCT
fuelectenerg-3309	46	38	electronics	electronic	NOUN
fuelectenerg-3309	46	39	laboratory	laboratory	NOUN
fuelectenerg-3309	46	40	,	,	PUNCT
fuelectenerg-3309	46	41	croatia	croatia	PROPN
fuelectenerg-3309	46	42	(	(	PUNCT
fuelectenerg-3309	46	43	e	e	NOUN
fuelectenerg-3309	46	44	-	-	NOUN
fuelectenerg-3309	46	45	mail	mail	NOUN
fuelectenerg-3309	46	46	:	:	PUNCT
fuelectenerg-3309	46	47	tom@zemris.fer.hr	tom@zemris.fer.hr	X
fuelectenerg-3309	46	48	)	)	PUNCT
fuelectenerg-3309	46	49	enumeration	enumeration	NOUN
fuelectenerg-3309	46	50	and	and	CCONJ
fuelectenerg-3309	46	51	coding	code	VERB
fuelectenerg-3309	46	52	methods	method	NOUN
fuelectenerg-3309	46	53	for	for	ADP
fuelectenerg-3309	46	54	a	a	DET
fuelectenerg-3309	46	55	class	class	NOUN
fuelectenerg-3309	46	56	of	of	ADP
fuelectenerg-3309	46	57	permutations	permutation	NOUN
fuelectenerg-3309	46	58	and	and	CCONJ
fuelectenerg-3309	46	59	reversible	reversible	ADJ
fuelectenerg-3309	46	60	logical	logical	ADJ
fuelectenerg-3309	46	61	gates	gate	NOUN
fuelectenerg-3309	46	62	*	*	PROPN
fuelectenerg-3309	46	63	1school	1school	NUM
fuelectenerg-3309	46	64	of	of	ADP
fuelectenerg-3309	46	65	informatics	informatic	NOUN
fuelectenerg-3309	46	66	,	,	PUNCT
fuelectenerg-3309	46	67	aristotle	aristotle	PROPN
fuelectenerg-3309	46	68	university	university	PROPN
fuelectenerg-3309	46	69	of	of	ADP
fuelectenerg-3309	46	70	thessaloniki	thessaloniki	PROPN
fuelectenerg-3309	46	71	,	,	PUNCT
fuelectenerg-3309	46	72	greece	greece	PROPN
fuelectenerg-3309	46	73	2school	2school	NUM
fuelectenerg-3309	46	74	of	of	ADP
fuelectenerg-3309	46	75	electrical	electrical	ADJ
fuelectenerg-3309	46	76	and	and	CCONJ
fuelectenerg-3309	46	77	computer	computer	NOUN
fuelectenerg-3309	46	78	engineering	engineering	NOUN
fuelectenerg-3309	46	79	,	,	PUNCT
fuelectenerg-3309	46	80	faculty	faculty	NOUN
fuelectenerg-3309	46	81	of	of	ADP
fuelectenerg-3309	46	82	engineering	engineering	PROPN
fuelectenerg-3309	46	83	,	,	PUNCT
fuelectenerg-3309	46	84	aristotle	aristotle	PROPN
fuelectenerg-3309	46	85	university	university	PROPN
fuelectenerg-3309	46	86	of	of	ADP
fuelectenerg-3309	46	87	thessaloniki	thessaloniki	PROPN
fuelectenerg-3309	46	88	,	,	PUNCT
fuelectenerg-3309	46	89	greece	greece	PROPN
fuelectenerg-3309	46	90	abstract	abstract	PROPN
fuelectenerg-3309	46	91	.	.	PUNCT
fuelectenerg-3309	47	1	we	we	PRON
fuelectenerg-3309	47	2	introduce	introduce	VERB
fuelectenerg-3309	47	3	a	a	DET
fuelectenerg-3309	47	4	great	great	ADJ
fuelectenerg-3309	47	5	variety	variety	NOUN
fuelectenerg-3309	47	6	of	of	ADP
fuelectenerg-3309	47	7	coding	code	VERB
fuelectenerg-3309	47	8	methods	method	NOUN
fuelectenerg-3309	47	9	for	for	ADP
fuelectenerg-3309	47	10	boolean	boolean	ADJ
fuelectenerg-3309	47	11	sparse	sparse	ADJ
fuelectenerg-3309	47	12	invertible	invertible	ADJ
fuelectenerg-3309	47	13	matrices	matrix	NOUN
fuelectenerg-3309	47	14	and	and	CCONJ
fuelectenerg-3309	47	15	we	we	PRON
fuelectenerg-3309	47	16	use	use	VERB
fuelectenerg-3309	47	17	these	these	DET
fuelectenerg-3309	47	18	methods	method	NOUN
fuelectenerg-3309	47	19	to	to	PART
fuelectenerg-3309	47	20	create	create	VERB
fuelectenerg-3309	47	21	a	a	DET
fuelectenerg-3309	47	22	variety	variety	NOUN
fuelectenerg-3309	47	23	of	of	ADP
fuelectenerg-3309	47	24	bijections	bijection	NOUN
fuelectenerg-3309	47	25	on	on	ADP
fuelectenerg-3309	47	26	the	the	DET
fuelectenerg-3309	47	27	permutation	permutation	NOUN
fuelectenerg-3309	47	28	group	group	NOUN
fuelectenerg-3309	47	29	p(m	p(m	NOUN
fuelectenerg-3309	47	30	)	)	PUNCT
fuelectenerg-3309	47	31	of	of	ADP
fuelectenerg-3309	47	32	the	the	DET
fuelectenerg-3309	47	33	set	set	NOUN
fuelectenerg-3309	47	34	{	{	PUNCT
fuelectenerg-3309	47	35	1,2,	1,2,	NUM
fuelectenerg-3309	47	36	...	...	PUNCT
fuelectenerg-3309	47	37	,m	,m	PUNCT
fuelectenerg-3309	47	38	}	}	PUNCT
fuelectenerg-3309	47	39	.	.	PUNCT
fuelectenerg-3309	48	1	also	also	ADV
fuelectenerg-3309	48	2	,	,	PUNCT
fuelectenerg-3309	48	3	we	we	PRON
fuelectenerg-3309	48	4	propose	propose	VERB
fuelectenerg-3309	48	5	methods	method	NOUN
fuelectenerg-3309	48	6	for	for	ADP
fuelectenerg-3309	48	7	coding	code	VERB
fuelectenerg-3309	48	8	,	,	PUNCT
fuelectenerg-3309	48	9	enumerating	enumerate	VERB
fuelectenerg-3309	48	10	and	and	CCONJ
fuelectenerg-3309	48	11	shuffling	shuffle	VERB
fuelectenerg-3309	48	12	the	the	DET
fuelectenerg-3309	48	13	set{0,	set{0,	NOUN
fuelectenerg-3309	48	14	...	...	PUNCT
fuelectenerg-3309	48	15	,2m−1	,2m−1	PUNCT
fuelectenerg-3309	48	16	}	}	PUNCT
fuelectenerg-3309	48	17	,	,	PUNCT
fuelectenerg-3309	48	18	i.e.	i.e.	X
fuelectenerg-3309	48	19	the	the	DET
fuelectenerg-3309	48	20	set	set	NOUN
fuelectenerg-3309	48	21	of	of	ADP
fuelectenerg-3309	48	22	all	all	DET
fuelectenerg-3309	48	23	m	m	NOUN
fuelectenerg-3309	48	24	-	-	PUNCT
fuelectenerg-3309	48	25	bit	bit	NOUN
fuelectenerg-3309	48	26	binary	binary	NOUN
fuelectenerg-3309	48	27	arrays	array	NOUN
fuelectenerg-3309	48	28	.	.	PUNCT
fuelectenerg-3309	49	1	moreover	moreover	ADV
fuelectenerg-3309	49	2	we	we	PRON
fuelectenerg-3309	49	3	show	show	VERB
fuelectenerg-3309	49	4	that	that	SCONJ
fuelectenerg-3309	49	5	several	several	ADJ
fuelectenerg-3309	49	6	well	well	ADV
fuelectenerg-3309	49	7	known	know	VERB
fuelectenerg-3309	49	8	reversible	reversible	ADJ
fuelectenerg-3309	49	9	logic	logic	NOUN
fuelectenerg-3309	49	10	gates	gate	NOUN
fuelectenerg-3309	49	11	/	/	SYM
fuelectenerg-3309	49	12	circuits	circuit	NOUN
fuelectenerg-3309	49	13	(	(	PUNCT
fuelectenerg-3309	49	14	on	on	ADP
fuelectenerg-3309	49	15	m	m	ADJ
fuelectenerg-3309	49	16	-	-	PUNCT
fuelectenerg-3309	49	17	bit	bit	NOUN
fuelectenerg-3309	49	18	binary	binary	NOUN
fuelectenerg-3309	49	19	arrays	array	NOUN
fuelectenerg-3309	49	20	)	)	PUNCT
fuelectenerg-3309	49	21	can	can	AUX
fuelectenerg-3309	49	22	be	be	AUX
fuelectenerg-3309	49	23	coded	code	VERB
fuelectenerg-3309	49	24	by	by	ADP
fuelectenerg-3309	49	25	sparse	sparse	ADJ
fuelectenerg-3309	49	26	matrices	matrix	NOUN
fuelectenerg-3309	49	27	.	.	PUNCT
fuelectenerg-3309	50	1	key	key	ADJ
fuelectenerg-3309	50	2	words	word	NOUN
fuelectenerg-3309	50	3	:	:	PUNCT
fuelectenerg-3309	50	4	permutations	permutation	NOUN
fuelectenerg-3309	50	5	,	,	PUNCT
fuelectenerg-3309	50	6	reversible	reversible	ADJ
fuelectenerg-3309	50	7	logical	logical	ADJ
fuelectenerg-3309	50	8	gates	gate	NOUN
fuelectenerg-3309	50	9	.	.	PUNCT
fuelectenerg-3309	51	1	2	2	NUM
fuelectenerg-3309	51	2	n.	n.	NOUN
fuelectenerg-3309	51	3	atreas	atreas	PROPN
fuelectenerg-3309	51	4	and	and	CCONJ
fuelectenerg-3309	51	5	c.	c.	PROPN
fuelectenerg-3309	51	6	karanikas	karanikas	PROPN
fuelectenerg-3309	51	7	our	our	PRON
fuelectenerg-3309	51	8	main	main	ADJ
fuelectenerg-3309	51	9	theorem	theorem	NOUN
fuelectenerg-3309	51	10	2	2	NUM
fuelectenerg-3309	51	11	in	in	ADP
fuelectenerg-3309	51	12	section	section	NOUN
fuelectenerg-3309	51	13	3	3	NUM
fuelectenerg-3309	51	14	or	or	CCONJ
fuelectenerg-3309	51	15	its	its	PRON
fuelectenerg-3309	51	16	”	"	PUNCT
fuelectenerg-3309	51	17	binary	binary	ADJ
fuelectenerg-3309	51	18	”	"	PUNCT
fuelectenerg-3309	51	19	version	version	NOUN
fuelectenerg-3309	51	20	(	(	PUNCT
fuelectenerg-3309	51	21	see	see	VERB
fuelectenerg-3309	51	22	theorem	theorem	NOUN
fuelectenerg-3309	51	23	3	3	NUM
fuelectenerg-3309	51	24	in	in	ADP
fuelectenerg-3309	51	25	section	section	NOUN
fuelectenerg-3309	51	26	4	4	NUM
fuelectenerg-3309	51	27	)	)	PUNCT
fuelectenerg-3309	51	28	,	,	PUNCT
fuelectenerg-3309	51	29	states	state	VERB
fuelectenerg-3309	51	30	that	that	SCONJ
fuelectenerg-3309	51	31	any	any	DET
fuelectenerg-3309	51	32	pair	pair	NOUN
fuelectenerg-3309	51	33	(	(	PUNCT
fuelectenerg-3309	51	34	ρ	ρ	PROPN
fuelectenerg-3309	51	35	,	,	PUNCT
fuelectenerg-3309	51	36	s	s	NOUN
fuelectenerg-3309	51	37	)	)	PUNCT
fuelectenerg-3309	51	38	of	of	ADP
fuelectenerg-3309	51	39	permutations	permutation	NOUN
fuelectenerg-3309	51	40	in	in	ADP
fuelectenerg-3309	51	41	p	p	PROPN
fuelectenerg-3309	51	42	(	(	PUNCT
fuelectenerg-3309	51	43	m	m	NOUN
fuelectenerg-3309	51	44	)	)	PUNCT
fuelectenerg-3309	51	45	determines	determine	VERB
fuelectenerg-3309	51	46	a	a	DET
fuelectenerg-3309	51	47	bijective	bijective	ADJ
fuelectenerg-3309	51	48	map	map	NOUN
fuelectenerg-3309	51	49	tρ	tρ	ADP
fuelectenerg-3309	51	50	,	,	PUNCT
fuelectenerg-3309	51	51	s	s	PART
fuelectenerg-3309	51	52	:	:	PUNCT
fuelectenerg-3309	51	53	{	{	PUNCT
fuelectenerg-3309	51	54	0	0	NUM
fuelectenerg-3309	51	55	,	,	PUNCT
fuelectenerg-3309	51	56	1	1	NUM
fuelectenerg-3309	51	57	,	,	PUNCT
fuelectenerg-3309	51	58	....	....	PUNCT
fuelectenerg-3309	51	59	,	,	PUNCT
fuelectenerg-3309	51	60	2	2	NUM
fuelectenerg-3309	51	61	m	m	NOUN
fuelectenerg-3309	51	62	−	−	NOUN
fuelectenerg-3309	51	63	1	1	NUM
fuelectenerg-3309	51	64	}	}	PUNCT
fuelectenerg-3309	51	65	→	→	SYM
fuelectenerg-3309	51	66	{	{	PUNCT
fuelectenerg-3309	51	67	0	0	NUM
fuelectenerg-3309	51	68	,	,	PUNCT
fuelectenerg-3309	51	69	1	1	NUM
fuelectenerg-3309	51	70	,	,	PUNCT
fuelectenerg-3309	51	71	....	....	PUNCT
fuelectenerg-3309	51	72	,	,	PUNCT
fuelectenerg-3309	51	73	2	2	NUM
fuelectenerg-3309	51	74	m	m	NOUN
fuelectenerg-3309	51	75	−	−	NOUN
fuelectenerg-3309	51	76	1	1	NUM
fuelectenerg-3309	51	77	}	}	PUNCT
fuelectenerg-3309	51	78	.	.	PUNCT
fuelectenerg-3309	52	1	since	since	SCONJ
fuelectenerg-3309	52	2	every	every	DET
fuelectenerg-3309	52	3	non	non	PRON
fuelectenerg-3309	52	4	negative	negative	ADJ
fuelectenerg-3309	52	5	integer	integer	NOUN
fuelectenerg-3309	52	6	n	n	PRON
fuelectenerg-3309	52	7	∈	∈	PROPN
fuelectenerg-3309	52	8	{	{	PUNCT
fuelectenerg-3309	52	9	0	0	NUM
fuelectenerg-3309	52	10	,	,	PUNCT
fuelectenerg-3309	52	11	1	1	NUM
fuelectenerg-3309	52	12	,	,	PUNCT
fuelectenerg-3309	52	13	....	....	PUNCT
fuelectenerg-3309	52	14	,	,	PUNCT
fuelectenerg-3309	52	15	2	2	NUM
fuelectenerg-3309	52	16	m	m	NOUN
fuelectenerg-3309	52	17	−	−	NUM
fuelectenerg-3309	52	18	1	1	NUM
fuelectenerg-3309	52	19	}	}	PUNCT
fuelectenerg-3309	52	20	can	can	AUX
fuelectenerg-3309	52	21	be	be	AUX
fuelectenerg-3309	52	22	expressed	express	VERB
fuelectenerg-3309	52	23	either	either	CCONJ
fuelectenerg-3309	52	24	as	as	ADP
fuelectenerg-3309	52	25	an	an	DET
fuelectenerg-3309	52	26	m	m	NOUN
fuelectenerg-3309	52	27	-	-	PUNCT
fuelectenerg-3309	52	28	bit	bit	NOUN
fuelectenerg-3309	52	29	binary	binary	ADJ
fuelectenerg-3309	52	30	array	array	NOUN
fuelectenerg-3309	52	31	en	en	X
fuelectenerg-3309	52	32	=	=	SYM
fuelectenerg-3309	52	33	(	(	PUNCT
fuelectenerg-3309	52	34	ε0(n	ε0(n	NOUN
fuelectenerg-3309	52	35	)	)	PUNCT
fuelectenerg-3309	52	36	,	,	PUNCT
fuelectenerg-3309	52	37	ε1(n	ε1(n	NOUN
fuelectenerg-3309	52	38	)	)	PUNCT
fuelectenerg-3309	52	39	,	,	PUNCT
fuelectenerg-3309	52	40	...	...	PUNCT
fuelectenerg-3309	52	41	,	,	PUNCT
fuelectenerg-3309	52	42	εm−1(n	εm−1(n	PROPN
fuelectenerg-3309	52	43	)	)	PUNCT
fuelectenerg-3309	52	44	)	)	PUNCT
fuelectenerg-3309	52	45	,	,	PUNCT
fuelectenerg-3309	52	46	εj	εj	NOUN
fuelectenerg-3309	52	47	∈	∈	PROPN
fuelectenerg-3309	52	48	{	{	PUNCT
fuelectenerg-3309	52	49	0	0	NUM
fuelectenerg-3309	52	50	,	,	PUNCT
fuelectenerg-3309	52	51	1	1	NUM
fuelectenerg-3309	52	52	}	}	PUNCT
fuelectenerg-3309	52	53	,	,	PUNCT
fuelectenerg-3309	52	54	or	or	CCONJ
fuelectenerg-3309	52	55	by	by	ADP
fuelectenerg-3309	52	56	its	its	PRON
fuelectenerg-3309	52	57	dyadic	dyadic	ADJ
fuelectenerg-3309	52	58	expansion	expansion	NOUN
fuelectenerg-3309	52	59	n	n	NOUN
fuelectenerg-3309	52	60	=	=	PUNCT
fuelectenerg-3309	52	61	m∑	m∑	PROPN
fuelectenerg-3309	52	62	j=1	j=1	PROPN
fuelectenerg-3309	52	63	εj(n)2	εj(n)2	PROPN
fuelectenerg-3309	52	64	j−1	j−1	PROPN
fuelectenerg-3309	52	65	,	,	PUNCT
fuelectenerg-3309	52	66	the	the	DET
fuelectenerg-3309	52	67	above	above	ADJ
fuelectenerg-3309	52	68	map	map	NOUN
fuelectenerg-3309	52	69	tρ	tρ	ADP
fuelectenerg-3309	52	70	,	,	PUNCT
fuelectenerg-3309	52	71	s	s	PART
fuelectenerg-3309	52	72	can	can	AUX
fuelectenerg-3309	52	73	be	be	AUX
fuelectenerg-3309	52	74	considered	consider	VERB
fuelectenerg-3309	52	75	as	as	ADP
fuelectenerg-3309	52	76	a	a	DET
fuelectenerg-3309	52	77	reversible	reversible	ADJ
fuelectenerg-3309	52	78	map	map	NOUN
fuelectenerg-3309	52	79	on	on	ADP
fuelectenerg-3309	52	80	the	the	DET
fuelectenerg-3309	52	81	set	set	NOUN
fuelectenerg-3309	52	82	of	of	ADP
fuelectenerg-3309	52	83	all	all	DET
fuelectenerg-3309	52	84	m	m	NOUN
fuelectenerg-3309	52	85	-	-	PUNCT
fuelectenerg-3309	52	86	bit	bit	NOUN
fuelectenerg-3309	52	87	binary	binary	NOUN
fuelectenerg-3309	52	88	arrays	array	NOUN
fuelectenerg-3309	52	89	.	.	PUNCT
fuelectenerg-3309	53	1	in	in	ADP
fuelectenerg-3309	53	2	a	a	DET
fuelectenerg-3309	53	3	different	different	ADJ
fuelectenerg-3309	53	4	terminology	terminology	NOUN
fuelectenerg-3309	53	5	,	,	PUNCT
fuelectenerg-3309	53	6	we	we	PRON
fuelectenerg-3309	53	7	can	can	AUX
fuelectenerg-3309	53	8	say	say	VERB
fuelectenerg-3309	53	9	that	that	SCONJ
fuelectenerg-3309	53	10	in	in	ADP
fuelectenerg-3309	53	11	theorem	theorem	NOUN
fuelectenerg-3309	53	12	3	3	NUM
fuelectenerg-3309	53	13	we	we	PRON
fuelectenerg-3309	53	14	introduce	introduce	VERB
fuelectenerg-3309	53	15	reversible	reversible	ADJ
fuelectenerg-3309	53	16	logic	logic	NOUN
fuelectenerg-3309	53	17	gates	gate	NOUN
fuelectenerg-3309	53	18	,	,	PUNCT
fuelectenerg-3309	53	19	i.e	i.e	DET
fuelectenerg-3309	53	20	bijective	bijective	ADJ
fuelectenerg-3309	53	21	maps	map	NOUN
fuelectenerg-3309	53	22	on	on	ADP
fuelectenerg-3309	53	23	the	the	DET
fuelectenerg-3309	53	24	set	set	NOUN
fuelectenerg-3309	53	25	of	of	ADP
fuelectenerg-3309	53	26	m	m	NOUN
fuelectenerg-3309	53	27	-	-	PUNCT
fuelectenerg-3309	53	28	bit	bit	NOUN
fuelectenerg-3309	53	29	binary	binary	NOUN
fuelectenerg-3309	53	30	arrays	array	NOUN
fuelectenerg-3309	53	31	,	,	PUNCT
fuelectenerg-3309	53	32	(	(	PUNCT
fuelectenerg-3309	53	33	see	see	VERB
fuelectenerg-3309	53	34	[	[	X
fuelectenerg-3309	53	35	1	1	NUM
fuelectenerg-3309	53	36	]	]	NUM
fuelectenerg-3309	53	37	)	)	PUNCT
fuelectenerg-3309	53	38	.	.	PUNCT
fuelectenerg-3309	54	1	an	an	DET
fuelectenerg-3309	54	2	example	example	NOUN
fuelectenerg-3309	54	3	of	of	ADP
fuelectenerg-3309	54	4	a	a	DET
fuelectenerg-3309	54	5	reversible	reversible	ADJ
fuelectenerg-3309	54	6	gate	gate	NOUN
fuelectenerg-3309	54	7	is	be	AUX
fuelectenerg-3309	54	8	the	the	DET
fuelectenerg-3309	54	9	not	not	PART
fuelectenerg-3309	54	10	gate	gate	NOUN
fuelectenerg-3309	54	11	,	,	PUNCT
fuelectenerg-3309	54	12	whereas	whereas	SCONJ
fuelectenerg-3309	54	13	the	the	PRON
fuelectenerg-3309	54	14	and	and	CCONJ
fuelectenerg-3309	54	15	,	,	PUNCT
fuelectenerg-3309	54	16	or	or	CCONJ
fuelectenerg-3309	54	17	,	,	PUNCT
fuelectenerg-3309	54	18	xor	xor	PROPN
fuelectenerg-3309	54	19	gates	gate	NOUN
fuelectenerg-3309	54	20	are	be	AUX
fuelectenerg-3309	54	21	irreversible	irreversible	ADJ
fuelectenerg-3309	54	22	(	(	PUNCT
fuelectenerg-3309	54	23	not	not	PART
fuelectenerg-3309	54	24	reversible	reversible	ADJ
fuelectenerg-3309	54	25	)	)	PUNCT
fuelectenerg-3309	54	26	,	,	PUNCT
fuelectenerg-3309	54	27	because	because	SCONJ
fuelectenerg-3309	54	28	they	they	PRON
fuelectenerg-3309	54	29	map	map	VERB
fuelectenerg-3309	54	30	4	4	NUM
fuelectenerg-3309	54	31	=	=	SYM
fuelectenerg-3309	54	32	22	22	NUM
fuelectenerg-3309	54	33	input	input	NOUN
fuelectenerg-3309	54	34	states	state	NOUN
fuelectenerg-3309	54	35	into	into	ADP
fuelectenerg-3309	54	36	2	2	NUM
fuelectenerg-3309	54	37	=	=	SYM
fuelectenerg-3309	54	38	21	21	NUM
fuelectenerg-3309	54	39	output	output	NOUN
fuelectenerg-3309	54	40	states	state	NOUN
fuelectenerg-3309	54	41	,	,	PUNCT
fuelectenerg-3309	54	42	so	so	CCONJ
fuelectenerg-3309	54	43	information	information	NOUN
fuelectenerg-3309	54	44	is	be	AUX
fuelectenerg-3309	54	45	lost	lose	VERB
fuelectenerg-3309	54	46	in	in	ADP
fuelectenerg-3309	54	47	the	the	DET
fuelectenerg-3309	54	48	merging	merging	NOUN
fuelectenerg-3309	54	49	of	of	ADP
fuelectenerg-3309	54	50	paths	path	NOUN
fuelectenerg-3309	54	51	.	.	PUNCT
fuelectenerg-3309	55	1	a	a	DET
fuelectenerg-3309	55	2	second	second	ADJ
fuelectenerg-3309	55	3	target	target	NOUN
fuelectenerg-3309	55	4	of	of	ADP
fuelectenerg-3309	55	5	this	this	DET
fuelectenerg-3309	55	6	work	work	NOUN
fuelectenerg-3309	55	7	is	be	AUX
fuelectenerg-3309	55	8	to	to	PART
fuelectenerg-3309	55	9	enumerate	enumerate	VERB
fuelectenerg-3309	55	10	and	and	CCONJ
fuelectenerg-3309	55	11	code	code	NOUN
fuelectenerg-3309	55	12	permutations	permutation	NOUN
fuelectenerg-3309	55	13	in	in	ADP
fuelectenerg-3309	55	14	p	p	PROPN
fuelectenerg-3309	55	15	(	(	PUNCT
fuelectenerg-3309	55	16	m	m	NOUN
fuelectenerg-3309	55	17	)	)	PUNCT
fuelectenerg-3309	55	18	of	of	ADP
fuelectenerg-3309	55	19	large	large	ADJ
fuelectenerg-3309	55	20	length	length	NOUN
fuelectenerg-3309	55	21	(	(	PUNCT
fuelectenerg-3309	55	22	note	note	VERB
fuelectenerg-3309	55	23	that	that	SCONJ
fuelectenerg-3309	55	24	the	the	DET
fuelectenerg-3309	55	25	cardinality	cardinality	NOUN
fuelectenerg-3309	55	26	of	of	ADP
fuelectenerg-3309	55	27	the	the	DET
fuelectenerg-3309	55	28	set	set	NOUN
fuelectenerg-3309	55	29	p	p	PROPN
fuelectenerg-3309	55	30	(	(	PUNCT
fuelectenerg-3309	55	31	m	m	NOUN
fuelectenerg-3309	55	32	)	)	PUNCT
fuelectenerg-3309	55	33	is	be	AUX
fuelectenerg-3309	55	34	m	m	PRON
fuelectenerg-3309	55	35	!	!	PUNCT
fuelectenerg-3309	55	36	)	)	PUNCT
fuelectenerg-3309	55	37	.	.	PUNCT
fuelectenerg-3309	56	1	therefore	therefore	ADV
fuelectenerg-3309	56	2	,	,	PUNCT
fuelectenerg-3309	56	3	a	a	DET
fuelectenerg-3309	56	4	reversible	reversible	ADJ
fuelectenerg-3309	56	5	map	map	NOUN
fuelectenerg-3309	56	6	tρ	tρ	NOUN
fuelectenerg-3309	56	7	,	,	PUNCT
fuelectenerg-3309	56	8	s	s	AUX
fuelectenerg-3309	56	9	associated	associate	VERB
fuelectenerg-3309	56	10	with	with	ADP
fuelectenerg-3309	56	11	the	the	DET
fuelectenerg-3309	56	12	pair	pair	NOUN
fuelectenerg-3309	56	13	(	(	PUNCT
fuelectenerg-3309	56	14	ρ	ρ	PROPN
fuelectenerg-3309	56	15	,	,	PUNCT
fuelectenerg-3309	56	16	s	s	PART
fuelectenerg-3309	56	17	)	)	PUNCT
fuelectenerg-3309	56	18	can	can	AUX
fuelectenerg-3309	56	19	be	be	AUX
fuelectenerg-3309	56	20	coded	code	VERB
fuelectenerg-3309	56	21	either	either	ADV
fuelectenerg-3309	56	22	by	by	ADP
fuelectenerg-3309	56	23	the	the	DET
fuelectenerg-3309	56	24	pair	pair	NOUN
fuelectenerg-3309	56	25	(	(	PUNCT
fuelectenerg-3309	56	26	ρ	ρ	PROPN
fuelectenerg-3309	56	27	,	,	PUNCT
fuelectenerg-3309	56	28	s	s	PART
fuelectenerg-3309	56	29	)	)	PUNCT
fuelectenerg-3309	56	30	or	or	CCONJ
fuelectenerg-3309	56	31	by	by	ADP
fuelectenerg-3309	56	32	an	an	DET
fuelectenerg-3309	56	33	enumeration	enumeration	NOUN
fuelectenerg-3309	56	34	of	of	ADP
fuelectenerg-3309	56	35	p	p	PROPN
fuelectenerg-3309	56	36	(	(	PUNCT
fuelectenerg-3309	56	37	m)×p	m)×p	NOUN
fuelectenerg-3309	56	38	(	(	PUNCT
fuelectenerg-3309	56	39	m	m	NOUN
fuelectenerg-3309	56	40	)	)	PUNCT
fuelectenerg-3309	56	41	as	as	ADP
fuelectenerg-3309	56	42	in	in	ADP
fuelectenerg-3309	56	43	section	section	NOUN
fuelectenerg-3309	56	44	2	2	NUM
fuelectenerg-3309	56	45	.	.	PUNCT
fuelectenerg-3309	57	1	this	this	DET
fuelectenerg-3309	57	2	coding	code	VERB
fuelectenerg-3309	57	3	method	method	NOUN
fuelectenerg-3309	57	4	is	be	AUX
fuelectenerg-3309	57	5	associated	associate	VERB
fuelectenerg-3309	57	6	with	with	ADP
fuelectenerg-3309	57	7	a	a	DET
fuelectenerg-3309	57	8	particular	particular	ADJ
fuelectenerg-3309	57	9	class	class	NOUN
fuelectenerg-3309	57	10	of	of	ADP
fuelectenerg-3309	57	11	sparse	sparse	ADJ
fuelectenerg-3309	57	12	boolean	boolean	ADJ
fuelectenerg-3309	57	13	invertible	invertible	ADJ
fuelectenerg-3309	57	14	matrices	matrix	NOUN
fuelectenerg-3309	57	15	introduced	introduce	VERB
fuelectenerg-3309	57	16	in	in	ADP
fuelectenerg-3309	57	17	[	[	X
fuelectenerg-3309	57	18	2	2	NUM
fuelectenerg-3309	57	19	]	]	PUNCT
fuelectenerg-3309	57	20	(	(	PUNCT
fuelectenerg-3309	57	21	see	see	VERB
fuelectenerg-3309	57	22	also	also	ADV
fuelectenerg-3309	57	23	[	[	X
fuelectenerg-3309	57	24	3–6	3–6	NUM
fuelectenerg-3309	57	25	]	]	X
fuelectenerg-3309	57	26	)	)	PUNCT
fuelectenerg-3309	57	27	.	.	PUNCT
fuelectenerg-3309	58	1	notice	notice	VERB
fuelectenerg-3309	58	2	that	that	SCONJ
fuelectenerg-3309	58	3	sparse	sparse	ADJ
fuelectenerg-3309	58	4	matrices	matrix	NOUN
fuelectenerg-3309	58	5	are	be	AUX
fuelectenerg-3309	58	6	very	very	ADV
fuelectenerg-3309	58	7	useful	useful	ADJ
fuelectenerg-3309	58	8	for	for	ADP
fuelectenerg-3309	58	9	fast	fast	ADJ
fuelectenerg-3309	58	10	processing	processing	NOUN
fuelectenerg-3309	58	11	/	/	SYM
fuelectenerg-3309	58	12	transmission	transmission	NOUN
fuelectenerg-3309	58	13	of	of	ADP
fuelectenerg-3309	58	14	data	datum	NOUN
fuelectenerg-3309	58	15	and	and	CCONJ
fuelectenerg-3309	58	16	they	they	PRON
fuelectenerg-3309	58	17	have	have	AUX
fuelectenerg-3309	58	18	been	be	AUX
fuelectenerg-3309	58	19	effectively	effectively	ADV
fuelectenerg-3309	58	20	used	use	VERB
fuelectenerg-3309	58	21	in	in	ADP
fuelectenerg-3309	58	22	[	[	X
fuelectenerg-3309	58	23	6	6	NUM
fuelectenerg-3309	58	24	]	]	PUNCT
fuelectenerg-3309	58	25	for	for	ADP
fuelectenerg-3309	58	26	detecting	detect	VERB
fuelectenerg-3309	58	27	specific	specific	ADJ
fuelectenerg-3309	58	28	characteristics	characteristic	NOUN
fuelectenerg-3309	58	29	on	on	ADP
fuelectenerg-3309	58	30	finite	finite	ADJ
fuelectenerg-3309	58	31	data	datum	NOUN
fuelectenerg-3309	58	32	.	.	PUNCT
fuelectenerg-3309	59	1	the	the	DET
fuelectenerg-3309	59	2	paper	paper	NOUN
fuelectenerg-3309	59	3	is	be	AUX
fuelectenerg-3309	59	4	organized	organize	VERB
fuelectenerg-3309	59	5	in	in	ADP
fuelectenerg-3309	59	6	the	the	DET
fuelectenerg-3309	59	7	following	follow	VERB
fuelectenerg-3309	59	8	sections	section	NOUN
fuelectenerg-3309	59	9	:	:	PUNCT
fuelectenerg-3309	59	10	in	in	ADP
fuelectenerg-3309	59	11	section	section	NOUN
fuelectenerg-3309	59	12	2	2	NUM
fuelectenerg-3309	59	13	we	we	PRON
fuelectenerg-3309	59	14	introduce	introduce	VERB
fuelectenerg-3309	59	15	our	our	PRON
fuelectenerg-3309	59	16	main	main	ADJ
fuelectenerg-3309	59	17	tool	tool	NOUN
fuelectenerg-3309	59	18	,	,	PUNCT
fuelectenerg-3309	59	19	the	the	DET
fuelectenerg-3309	59	20	invertible	invertible	ADJ
fuelectenerg-3309	59	21	map	map	NOUN
fuelectenerg-3309	59	22	p	p	X
fuelectenerg-3309	59	23	(	(	PUNCT
fuelectenerg-3309	59	24	m	m	NOUN
fuelectenerg-3309	59	25	)	)	PUNCT
fuelectenerg-3309	59	26	→	→	SYM
fuelectenerg-3309	59	27	s(m	s(m	PROPN
fuelectenerg-3309	59	28	)	)	PUNCT
fuelectenerg-3309	59	29	(	(	PUNCT
fuelectenerg-3309	59	30	see	see	VERB
fuelectenerg-3309	59	31	(	(	PUNCT
fuelectenerg-3309	59	32	2	2	NUM
fuelectenerg-3309	59	33	)	)	PUNCT
fuelectenerg-3309	59	34	and	and	CCONJ
fuelectenerg-3309	59	35	(	(	PUNCT
fuelectenerg-3309	59	36	3	3	NUM
fuelectenerg-3309	59	37	)	)	PUNCT
fuelectenerg-3309	59	38	)	)	PUNCT
fuelectenerg-3309	59	39	and	and	CCONJ
fuelectenerg-3309	59	40	in	in	ADP
fuelectenerg-3309	59	41	proposition	proposition	NOUN
fuelectenerg-3309	59	42	1	1	NUM
fuelectenerg-3309	59	43	,	,	PUNCT
fuelectenerg-3309	59	44	we	we	PRON
fuelectenerg-3309	59	45	see	see	VERB
fuelectenerg-3309	59	46	that	that	SCONJ
fuelectenerg-3309	59	47	this	this	DET
fuelectenerg-3309	59	48	map	map	NOUN
fuelectenerg-3309	59	49	induces	induce	VERB
fuelectenerg-3309	59	50	the	the	DET
fuelectenerg-3309	59	51	lexicographic	lexicographic	ADJ
fuelectenerg-3309	59	52	order	order	NOUN
fuelectenerg-3309	59	53	of	of	ADP
fuelectenerg-3309	59	54	the	the	DET
fuelectenerg-3309	59	55	enumeration	enumeration	NOUN
fuelectenerg-3309	59	56	of	of	ADP
fuelectenerg-3309	59	57	p	p	PROPN
fuelectenerg-3309	59	58	(	(	PUNCT
fuelectenerg-3309	59	59	m	m	NOUN
fuelectenerg-3309	59	60	)	)	PUNCT
fuelectenerg-3309	59	61	.	.	PUNCT
fuelectenerg-3309	60	1	moreover	moreover	ADV
fuelectenerg-3309	60	2	we	we	PRON
fuelectenerg-3309	60	3	consider	consider	VERB
fuelectenerg-3309	60	4	the	the	DET
fuelectenerg-3309	60	5	cartesian	cartesian	ADJ
fuelectenerg-3309	60	6	product	product	NOUN
fuelectenerg-3309	60	7	r(m	r(m	NOUN
fuelectenerg-3309	60	8	)	)	PUNCT
fuelectenerg-3309	60	9	=	=	SYM
fuelectenerg-3309	60	10	p	p	X
fuelectenerg-3309	60	11	(	(	PUNCT
fuelectenerg-3309	60	12	1)×p	1)×p	NUM
fuelectenerg-3309	60	13	(	(	PUNCT
fuelectenerg-3309	60	14	2)×	2)×	NUM
fuelectenerg-3309	60	15	...	...	PUNCT
fuelectenerg-3309	60	16	×p	×p	PRON
fuelectenerg-3309	60	17	(	(	PUNCT
fuelectenerg-3309	60	18	m	m	NOUN
fuelectenerg-3309	60	19	)	)	PUNCT
fuelectenerg-3309	60	20	of	of	ADP
fuelectenerg-3309	60	21	permutations	permutation	NOUN
fuelectenerg-3309	60	22	to	to	PART
fuelectenerg-3309	60	23	show	show	VERB
fuelectenerg-3309	60	24	in	in	ADP
fuelectenerg-3309	60	25	theorem	theorem	NOUN
fuelectenerg-3309	60	26	1	1	NUM
fuelectenerg-3309	60	27	that	that	SCONJ
fuelectenerg-3309	60	28	each	each	DET
fuelectenerg-3309	60	29	fixed	fix	VERB
fuelectenerg-3309	60	30	element	element	NOUN
fuelectenerg-3309	60	31	of	of	ADP
fuelectenerg-3309	60	32	r(m	r(m	PROPN
fuelectenerg-3309	60	33	)	)	PUNCT
fuelectenerg-3309	60	34	provides	provide	VERB
fuelectenerg-3309	60	35	an	an	DET
fuelectenerg-3309	60	36	enumeration	enumeration	NOUN
fuelectenerg-3309	60	37	of	of	ADP
fuelectenerg-3309	60	38	p	p	PROPN
fuelectenerg-3309	60	39	(	(	PUNCT
fuelectenerg-3309	60	40	m	m	NOUN
fuelectenerg-3309	60	41	)	)	PUNCT
fuelectenerg-3309	60	42	.	.	PUNCT
fuelectenerg-3309	61	1	in	in	ADP
fuelectenerg-3309	61	2	section	section	NOUN
fuelectenerg-3309	61	3	3	3	NUM
fuelectenerg-3309	61	4	we	we	PRON
fuelectenerg-3309	61	5	define	define	VERB
fuelectenerg-3309	61	6	a	a	DET
fuelectenerg-3309	61	7	class	class	NOUN
fuelectenerg-3309	61	8	of	of	ADP
fuelectenerg-3309	61	9	sparse	sparse	ADJ
fuelectenerg-3309	61	10	m×m	m×m	ADJ
fuelectenerg-3309	61	11	boolean	boolean	ADJ
fuelectenerg-3309	61	12	invertible	invertible	ADJ
fuelectenerg-3309	61	13	matrices	matrix	NOUN
fuelectenerg-3309	61	14	zm	zm	PROPN
fuelectenerg-3309	61	15	identified	identify	VERB
fuelectenerg-3309	61	16	by	by	ADP
fuelectenerg-3309	61	17	a	a	DET
fuelectenerg-3309	61	18	pair	pair	NOUN
fuelectenerg-3309	61	19	(	(	PUNCT
fuelectenerg-3309	61	20	ρ	ρ	PROPN
fuelectenerg-3309	61	21	,	,	PUNCT
fuelectenerg-3309	61	22	s	s	PART
fuelectenerg-3309	61	23	)	)	PUNCT
fuelectenerg-3309	61	24	∈	∈	PROPN
fuelectenerg-3309	61	25	p	p	NOUN
fuelectenerg-3309	61	26	(	(	PUNCT
fuelectenerg-3309	61	27	m)×s(m	m)×s(m	NOUN
fuelectenerg-3309	61	28	)	)	PUNCT
fuelectenerg-3309	61	29	and	and	CCONJ
fuelectenerg-3309	61	30	we	we	PRON
fuelectenerg-3309	61	31	use	use	VERB
fuelectenerg-3309	61	32	this	this	DET
fuelectenerg-3309	61	33	class	class	NOUN
fuelectenerg-3309	61	34	of	of	ADP
fuelectenerg-3309	61	35	matrices	matrix	NOUN
fuelectenerg-3309	61	36	enumeration	enumeration	NOUN
fuelectenerg-3309	61	37	and	and	CCONJ
fuelectenerg-3309	61	38	coding	code	VERB
fuelectenerg-3309	61	39	permutations	permutation	NOUN
fuelectenerg-3309	61	40	and	and	CCONJ
fuelectenerg-3309	61	41	reversible	reversible	ADJ
fuelectenerg-3309	61	42	logical	logical	ADJ
fuelectenerg-3309	61	43	circuits	circuit	NOUN
fuelectenerg-3309	61	44	3	3	NUM
fuelectenerg-3309	61	45	to	to	PART
fuelectenerg-3309	61	46	produce	produce	VERB
fuelectenerg-3309	61	47	a	a	DET
fuelectenerg-3309	61	48	class	class	NOUN
fuelectenerg-3309	61	49	of	of	ADP
fuelectenerg-3309	61	50	non	non	ADJ
fuelectenerg-3309	61	51	-	-	ADJ
fuelectenerg-3309	61	52	linear	linear	ADJ
fuelectenerg-3309	61	53	bijection	bijection	NOUN
fuelectenerg-3309	61	54	maps	map	NOUN
fuelectenerg-3309	61	55	tq	tq	ADP
fuelectenerg-3309	61	56	,	,	PUNCT
fuelectenerg-3309	61	57	ρ	ρ	PROPN
fuelectenerg-3309	61	58	,	,	PUNCT
fuelectenerg-3309	61	59	s	s	PART
fuelectenerg-3309	61	60	:	:	PUNCT
fuelectenerg-3309	61	61	{	{	PUNCT
fuelectenerg-3309	61	62	0	0	NUM
fuelectenerg-3309	61	63	,	,	PUNCT
fuelectenerg-3309	61	64	...	...	PUNCT
fuelectenerg-3309	61	65	,	,	PUNCT
fuelectenerg-3309	61	66	qm	qm	PROPN
fuelectenerg-3309	61	67	−	−	PROPN
fuelectenerg-3309	61	68	1	1	NUM
fuelectenerg-3309	61	69	}	}	PUNCT
fuelectenerg-3309	61	70	→	→	SYM
fuelectenerg-3309	61	71	{	{	PUNCT
fuelectenerg-3309	61	72	0	0	NUM
fuelectenerg-3309	61	73	,	,	PUNCT
fuelectenerg-3309	61	74	...	...	PUNCT
fuelectenerg-3309	61	75	,	,	PUNCT
fuelectenerg-3309	61	76	qm	qm	PROPN
fuelectenerg-3309	61	77	−	−	PROPN
fuelectenerg-3309	61	78	1	1	NUM
fuelectenerg-3309	61	79	}	}	PUNCT
fuelectenerg-3309	61	80	,	,	PUNCT
fuelectenerg-3309	61	81	see	see	VERB
fuelectenerg-3309	61	82	our	our	PRON
fuelectenerg-3309	61	83	main	main	ADJ
fuelectenerg-3309	61	84	theorem	theorem	NOUN
fuelectenerg-3309	61	85	2	2	NUM
fuelectenerg-3309	61	86	.	.	PUNCT
fuelectenerg-3309	62	1	in	in	ADP
fuelectenerg-3309	62	2	section	section	NOUN
fuelectenerg-3309	62	3	4	4	NUM
fuelectenerg-3309	62	4	we	we	PRON
fuelectenerg-3309	62	5	show	show	VERB
fuelectenerg-3309	62	6	that	that	SCONJ
fuelectenerg-3309	62	7	any	any	PRON
fuelectenerg-3309	62	8	triple	triple	ADJ
fuelectenerg-3309	62	9	(	(	PUNCT
fuelectenerg-3309	62	10	ρ	ρ	PROPN
fuelectenerg-3309	62	11	,	,	PUNCT
fuelectenerg-3309	62	12	s	s	PROPN
fuelectenerg-3309	62	13	,	,	PUNCT
fuelectenerg-3309	62	14	τ	τ	X
fuelectenerg-3309	62	15	)	)	PUNCT
fuelectenerg-3309	62	16	of	of	ADP
fuelectenerg-3309	62	17	permutations	permutation	NOUN
fuelectenerg-3309	62	18	in	in	ADP
fuelectenerg-3309	62	19	p	p	PROPN
fuelectenerg-3309	62	20	(	(	PUNCT
fuelectenerg-3309	62	21	m	m	NOUN
fuelectenerg-3309	62	22	)	)	PUNCT
fuelectenerg-3309	62	23	provides	provide	VERB
fuelectenerg-3309	62	24	a	a	DET
fuelectenerg-3309	62	25	variety	variety	NOUN
fuelectenerg-3309	62	26	of	of	ADP
fuelectenerg-3309	62	27	maps	map	NOUN
fuelectenerg-3309	62	28	from	from	ADP
fuelectenerg-3309	62	29	{	{	PUNCT
fuelectenerg-3309	62	30	0	0	NUM
fuelectenerg-3309	62	31	,	,	PUNCT
fuelectenerg-3309	62	32	...	...	PUNCT
fuelectenerg-3309	62	33	,	,	PUNCT
fuelectenerg-3309	62	34	2	2	NUM
fuelectenerg-3309	62	35	m	m	NOUN
fuelectenerg-3309	62	36	−	−	NOUN
fuelectenerg-3309	62	37	1	1	NUM
fuelectenerg-3309	62	38	}	}	PUNCT
fuelectenerg-3309	62	39	onto	onto	ADP
fuelectenerg-3309	62	40	{	{	PUNCT
fuelectenerg-3309	62	41	0	0	NUM
fuelectenerg-3309	62	42	,	,	PUNCT
fuelectenerg-3309	62	43	...	...	PUNCT
fuelectenerg-3309	62	44	,	,	PUNCT
fuelectenerg-3309	62	45	2	2	NUM
fuelectenerg-3309	62	46	m	m	NOUN
fuelectenerg-3309	62	47	−	−	NOUN
fuelectenerg-3309	62	48	1	1	NUM
fuelectenerg-3309	62	49	}	}	PUNCT
fuelectenerg-3309	62	50	and	and	CCONJ
fuelectenerg-3309	62	51	we	we	PRON
fuelectenerg-3309	62	52	see	see	VERB
fuelectenerg-3309	62	53	that	that	SCONJ
fuelectenerg-3309	62	54	several	several	ADJ
fuelectenerg-3309	62	55	reversible	reversible	ADJ
fuelectenerg-3309	62	56	logic	logic	NOUN
fuelectenerg-3309	62	57	gates	gate	NOUN
fuelectenerg-3309	62	58	can	can	AUX
fuelectenerg-3309	62	59	be	be	AUX
fuelectenerg-3309	62	60	determined	determine	VERB
fuelectenerg-3309	62	61	by	by	ADP
fuelectenerg-3309	62	62	this	this	DET
fuelectenerg-3309	62	63	triple	triple	NOUN
fuelectenerg-3309	62	64	.	.	PUNCT
fuelectenerg-3309	63	1	finally	finally	ADV
fuelectenerg-3309	63	2	,	,	PUNCT
fuelectenerg-3309	63	3	in	in	ADP
fuelectenerg-3309	63	4	section	section	NOUN
fuelectenerg-3309	63	5	5	5	NUM
fuelectenerg-3309	63	6	we	we	PRON
fuelectenerg-3309	63	7	apply	apply	VERB
fuelectenerg-3309	63	8	theorems	theorem	NOUN
fuelectenerg-3309	63	9	1	1	NUM
fuelectenerg-3309	63	10	and	and	CCONJ
fuelectenerg-3309	63	11	2	2	NUM
fuelectenerg-3309	63	12	,	,	PUNCT
fuelectenerg-3309	63	13	to	to	PART
fuelectenerg-3309	63	14	see	see	VERB
fuelectenerg-3309	63	15	with	with	ADP
fuelectenerg-3309	63	16	an	an	DET
fuelectenerg-3309	63	17	example	example	NOUN
fuelectenerg-3309	63	18	that	that	SCONJ
fuelectenerg-3309	63	19	for	for	ADP
fuelectenerg-3309	63	20	any	any	DET
fuelectenerg-3309	63	21	pair	pair	NOUN
fuelectenerg-3309	63	22	(	(	PUNCT
fuelectenerg-3309	63	23	ρ	ρ	PROPN
fuelectenerg-3309	63	24	,	,	PUNCT
fuelectenerg-3309	63	25	s	s	PART
fuelectenerg-3309	63	26	)	)	PUNCT
fuelectenerg-3309	63	27	∈	∈	PROPN
fuelectenerg-3309	63	28	p	p	X
fuelectenerg-3309	63	29	(	(	PUNCT
fuelectenerg-3309	63	30	m	m	NOUN
fuelectenerg-3309	63	31	)	)	PUNCT
fuelectenerg-3309	63	32	×	×	PROPN
fuelectenerg-3309	63	33	s(m	s(m	PROPN
fuelectenerg-3309	63	34	)	)	PUNCT
fuelectenerg-3309	63	35	and	and	CCONJ
fuelectenerg-3309	63	36	any	any	DET
fuelectenerg-3309	63	37	fixed	fix	VERB
fuelectenerg-3309	63	38	r	r	NOUN
fuelectenerg-3309	63	39	∈	∈	PROPN
fuelectenerg-3309	63	40	r(2	r(2	PROPN
fuelectenerg-3309	63	41	m	m	NOUN
fuelectenerg-3309	63	42	)	)	PUNCT
fuelectenerg-3309	63	43	we	we	PRON
fuelectenerg-3309	63	44	shuffle	shuffle	VERB
fuelectenerg-3309	63	45	the	the	DET
fuelectenerg-3309	63	46	elements	element	NOUN
fuelectenerg-3309	63	47	of	of	ADP
fuelectenerg-3309	63	48	the	the	DET
fuelectenerg-3309	63	49	set	set	NOUN
fuelectenerg-3309	63	50	{	{	PUNCT
fuelectenerg-3309	63	51	0	0	NUM
fuelectenerg-3309	63	52	,	,	PUNCT
fuelectenerg-3309	63	53	...	...	PUNCT
fuelectenerg-3309	63	54	,	,	PUNCT
fuelectenerg-3309	63	55	2m−1	2m−1	NUM
fuelectenerg-3309	63	56	}	}	PUNCT
fuelectenerg-3309	63	57	and	and	CCONJ
fuelectenerg-3309	63	58	we	we	PRON
fuelectenerg-3309	63	59	discus	discus	VERB
fuelectenerg-3309	63	60	the	the	DET
fuelectenerg-3309	63	61	random	random	ADJ
fuelectenerg-3309	63	62	permutation	permutation	NOUN
fuelectenerg-3309	63	63	generation	generation	NOUN
fuelectenerg-3309	63	64	problem	problem	NOUN
fuelectenerg-3309	63	65	.	.	PUNCT
fuelectenerg-3309	64	1	2	2	NUM
fuelectenerg-3309	64	2	enumeration	enumeration	NOUN
fuelectenerg-3309	64	3	methods	method	NOUN
fuelectenerg-3309	64	4	for	for	ADP
fuelectenerg-3309	64	5	p	p	PROPN
fuelectenerg-3309	64	6	(	(	PUNCT
fuelectenerg-3309	64	7	m	m	NOUN
fuelectenerg-3309	64	8	)	)	PUNCT
fuelectenerg-3309	64	9	let	let	VERB
fuelectenerg-3309	64	10	m	m	PRON
fuelectenerg-3309	64	11	≥	≥	NOUN
fuelectenerg-3309	64	12	2	2	NUM
fuelectenerg-3309	64	13	be	be	AUX
fuelectenerg-3309	64	14	a	a	DET
fuelectenerg-3309	64	15	natural	natural	ADJ
fuelectenerg-3309	64	16	number	number	NOUN
fuelectenerg-3309	64	17	.	.	PUNCT
fuelectenerg-3309	65	1	first	first	ADV
fuelectenerg-3309	65	2	we	we	PRON
fuelectenerg-3309	65	3	review	review	VERB
fuelectenerg-3309	65	4	the	the	DET
fuelectenerg-3309	65	5	lexicographical	lexicographical	ADJ
fuelectenerg-3309	65	6	order	order	NOUN
fuelectenerg-3309	65	7	of	of	ADP
fuelectenerg-3309	65	8	the	the	DET
fuelectenerg-3309	65	9	set	set	NOUN
fuelectenerg-3309	65	10	s(m	s(m	PROPN
fuelectenerg-3309	65	11	)	)	PUNCT
fuelectenerg-3309	66	1	=	=	PRON
fuelectenerg-3309	66	2	{	{	PUNCT
fuelectenerg-3309	66	3	s	s	NOUN
fuelectenerg-3309	66	4	=	=	PUNCT
fuelectenerg-3309	66	5	(	(	PUNCT
fuelectenerg-3309	66	6	s1	s1	PROPN
fuelectenerg-3309	66	7	,	,	PUNCT
fuelectenerg-3309	66	8	...	...	PUNCT
fuelectenerg-3309	66	9	,	,	PUNCT
fuelectenerg-3309	66	10	sm	sm	PROPN
fuelectenerg-3309	66	11	)	)	PUNCT
fuelectenerg-3309	66	12	:	:	PUNCT
fuelectenerg-3309	66	13	si	si	PROPN
fuelectenerg-3309	66	14	∈	∈	PROPN
fuelectenerg-3309	66	15	{	{	PUNCT
fuelectenerg-3309	66	16	1	1	NUM
fuelectenerg-3309	66	17	,	,	PUNCT
fuelectenerg-3309	66	18	2	2	NUM
fuelectenerg-3309	66	19	,	,	PUNCT
fuelectenerg-3309	66	20	...	...	PUNCT
fuelectenerg-3309	66	21	,	,	PUNCT
fuelectenerg-3309	66	22	i	i	PRON
fuelectenerg-3309	66	23	}	}	PUNCT
fuelectenerg-3309	66	24	}	}	PUNCT
fuelectenerg-3309	66	25	.	.	PUNCT
fuelectenerg-3309	67	1	(	(	PUNCT
fuelectenerg-3309	67	2	1	1	X
fuelectenerg-3309	67	3	)	)	PUNCT
fuelectenerg-3309	67	4	obviously	obviously	ADV
fuelectenerg-3309	67	5	,	,	PUNCT
fuelectenerg-3309	67	6	the	the	DET
fuelectenerg-3309	67	7	map	map	NOUN
fuelectenerg-3309	67	8	u	u	NOUN
fuelectenerg-3309	67	9	:	:	PUNCT
fuelectenerg-3309	67	10	s(m	s(m	PROPN
fuelectenerg-3309	67	11	)	)	PUNCT
fuelectenerg-3309	67	12	→	→	SYM
fuelectenerg-3309	67	13	{	{	PUNCT
fuelectenerg-3309	67	14	0	0	NUM
fuelectenerg-3309	67	15	,	,	PUNCT
fuelectenerg-3309	67	16	...	...	PUNCT
fuelectenerg-3309	67	17	,	,	PUNCT
fuelectenerg-3309	67	18	m!−	m!−	VERB
fuelectenerg-3309	67	19	1	1	NUM
fuelectenerg-3309	67	20	}	}	PUNCT
fuelectenerg-3309	67	21	:	:	PUNCT
fuelectenerg-3309	67	22	u(s	u(s	X
fuelectenerg-3309	67	23	)	)	PUNCT
fuelectenerg-3309	67	24	=	=	PUNCT
fuelectenerg-3309	68	1	m	m	PROPN
fuelectenerg-3309	68	2	!	!	PUNCT
fuelectenerg-3309	68	3	m∑	m∑	X
fuelectenerg-3309	69	1	i=1	i=1	PROPN
fuelectenerg-3309	69	2	si	si	PROPN
fuelectenerg-3309	70	1	−	−	PROPN
fuelectenerg-3309	70	2	1	1	NUM
fuelectenerg-3309	70	3	i	i	PRON
fuelectenerg-3309	70	4	!	!	PUNCT
fuelectenerg-3309	71	1	(	(	PUNCT
fuelectenerg-3309	71	2	2	2	X
fuelectenerg-3309	71	3	)	)	PUNCT
fuelectenerg-3309	71	4	is	be	AUX
fuelectenerg-3309	71	5	a	a	DET
fuelectenerg-3309	71	6	bijection	bijection	NOUN
fuelectenerg-3309	71	7	and	and	CCONJ
fuelectenerg-3309	71	8	the	the	DET
fuelectenerg-3309	71	9	elements	element	NOUN
fuelectenerg-3309	71	10	si	si	X
fuelectenerg-3309	71	11	∈	∈	PROPN
fuelectenerg-3309	71	12	{	{	PUNCT
fuelectenerg-3309	71	13	1	1	NUM
fuelectenerg-3309	71	14	,	,	PUNCT
fuelectenerg-3309	71	15	...	...	PUNCT
fuelectenerg-3309	71	16	,	,	PUNCT
fuelectenerg-3309	71	17	i	i	PRON
fuelectenerg-3309	71	18	}	}	PUNCT
fuelectenerg-3309	71	19	can	can	AUX
fuelectenerg-3309	71	20	be	be	AUX
fuelectenerg-3309	71	21	thought	think	VERB
fuelectenerg-3309	71	22	of	of	ADP
fuelectenerg-3309	71	23	digits	digit	NOUN
fuelectenerg-3309	71	24	of	of	ADP
fuelectenerg-3309	71	25	the	the	DET
fuelectenerg-3309	71	26	number	number	NOUN
fuelectenerg-3309	71	27	u(s	u(s	PUNCT
fuelectenerg-3309	71	28	)	)	PUNCT
fuelectenerg-3309	71	29	with	with	ADP
fuelectenerg-3309	71	30	respect	respect	NOUN
fuelectenerg-3309	71	31	to	to	ADP
fuelectenerg-3309	71	32	the	the	DET
fuelectenerg-3309	71	33	factorial	factorial	ADJ
fuelectenerg-3309	71	34	number	number	NOUN
fuelectenerg-3309	71	35	system	system	NOUN
fuelectenerg-3309	71	36	.	.	PUNCT
fuelectenerg-3309	72	1	inversely	inversely	ADV
fuelectenerg-3309	72	2	,	,	PUNCT
fuelectenerg-3309	72	3	for	for	ADP
fuelectenerg-3309	72	4	any	any	DET
fuelectenerg-3309	72	5	n	n	ADV
fuelectenerg-3309	72	6	∈	∈	PROPN
fuelectenerg-3309	72	7	{	{	PUNCT
fuelectenerg-3309	72	8	0	0	NUM
fuelectenerg-3309	72	9	,	,	PUNCT
fuelectenerg-3309	72	10	...	...	PUNCT
fuelectenerg-3309	72	11	,	,	PUNCT
fuelectenerg-3309	72	12	m!−	m!−	VERB
fuelectenerg-3309	72	13	1	1	NUM
fuelectenerg-3309	72	14	}	}	PUNCT
fuelectenerg-3309	72	15	,	,	PUNCT
fuelectenerg-3309	72	16	its	its	PRON
fuelectenerg-3309	72	17	digits	digit	NOUN
fuelectenerg-3309	72	18	si(n	si(n	NOUN
fuelectenerg-3309	72	19	)	)	PUNCT
fuelectenerg-3309	72	20	,	,	PUNCT
fuelectenerg-3309	72	21	i	i	PRON
fuelectenerg-3309	72	22	=	=	NOUN
fuelectenerg-3309	72	23	1	1	NUM
fuelectenerg-3309	72	24	,	,	PUNCT
fuelectenerg-3309	72	25	...	...	PUNCT
fuelectenerg-3309	72	26	,	,	PUNCT
fuelectenerg-3309	72	27	m	m	VERB
fuelectenerg-3309	72	28	are	be	AUX
fuelectenerg-3309	72	29	computed	compute	VERB
fuelectenerg-3309	72	30	by	by	ADP
fuelectenerg-3309	72	31	the	the	DET
fuelectenerg-3309	72	32	formula	formula	NOUN
fuelectenerg-3309	72	33	si(n	si(n	NOUN
fuelectenerg-3309	72	34	)	)	PUNCT
fuelectenerg-3309	73	1	=	=	SYM
fuelectenerg-3309	73	2	mod	mod	NOUN
fuelectenerg-3309	73	3	(	(	PUNCT
fuelectenerg-3309	73	4	[	[	X
fuelectenerg-3309	73	5	n	n	X
fuelectenerg-3309	73	6	i	i	PRON
fuelectenerg-3309	73	7	!	!	PUNCT
fuelectenerg-3309	74	1	m	m	VERB
fuelectenerg-3309	74	2	!	!	PUNCT
fuelectenerg-3309	74	3	]	]	PUNCT
fuelectenerg-3309	75	1	,	,	PUNCT
fuelectenerg-3309	75	2	i	i	PRON
fuelectenerg-3309	75	3	)	)	PUNCT
fuelectenerg-3309	76	1	+	+	CCONJ
fuelectenerg-3309	76	2	1	1	NUM
fuelectenerg-3309	76	3	describing	describe	VERB
fuelectenerg-3309	76	4	the	the	DET
fuelectenerg-3309	76	5	inverse	inverse	NOUN
fuelectenerg-3309	76	6	map	map	NOUN
fuelectenerg-3309	76	7	u−1	u−1	PROPN
fuelectenerg-3309	76	8	.	.	PUNCT
fuelectenerg-3309	77	1	here	here	ADV
fuelectenerg-3309	77	2	,	,	PUNCT
fuelectenerg-3309	77	3	[	[	X
fuelectenerg-3309	77	4	x	x	X
fuelectenerg-3309	77	5	]	]	X
fuelectenerg-3309	77	6	is	be	AUX
fuelectenerg-3309	77	7	the	the	DET
fuelectenerg-3309	77	8	floor	floor	NOUN
fuelectenerg-3309	77	9	of	of	ADP
fuelectenerg-3309	77	10	x.	x.	NOUN
fuelectenerg-3309	77	11	from	from	ADP
fuelectenerg-3309	77	12	now	now	ADV
fuelectenerg-3309	77	13	on	on	ADV
fuelectenerg-3309	77	14	we	we	PRON
fuelectenerg-3309	77	15	say	say	VERB
fuelectenerg-3309	77	16	that	that	SCONJ
fuelectenerg-3309	77	17	u	u	PRON
fuelectenerg-3309	77	18	provides	provide	VERB
fuelectenerg-3309	77	19	the	the	DET
fuelectenerg-3309	77	20	lexicographical	lexicographical	ADJ
fuelectenerg-3309	77	21	order	order	NOUN
fuelectenerg-3309	77	22	of	of	ADP
fuelectenerg-3309	77	23	s(m	s(m	PROPN
fuelectenerg-3309	77	24	)	)	PUNCT
fuelectenerg-3309	77	25	.	.	PUNCT
fuelectenerg-3309	78	1	using	use	VERB
fuelectenerg-3309	78	2	the	the	DET
fuelectenerg-3309	78	3	lexicographical	lexicographical	ADJ
fuelectenerg-3309	78	4	order	order	NOUN
fuelectenerg-3309	78	5	of	of	ADP
fuelectenerg-3309	78	6	s(m	s(m	PROPN
fuelectenerg-3309	78	7	)	)	PUNCT
fuelectenerg-3309	78	8	we	we	PRON
fuelectenerg-3309	78	9	may	may	AUX
fuelectenerg-3309	78	10	obtain	obtain	VERB
fuelectenerg-3309	78	11	an	an	DET
fuelectenerg-3309	78	12	enumeration	enumeration	NOUN
fuelectenerg-3309	78	13	of	of	ADP
fuelectenerg-3309	78	14	the	the	DET
fuelectenerg-3309	78	15	group	group	NOUN
fuelectenerg-3309	78	16	of	of	ADP
fuelectenerg-3309	78	17	permutations	permutation	NOUN
fuelectenerg-3309	78	18	p	p	X
fuelectenerg-3309	78	19	(	(	PUNCT
fuelectenerg-3309	78	20	m	m	NOUN
fuelectenerg-3309	78	21	)	)	PUNCT
fuelectenerg-3309	78	22	of	of	ADP
fuelectenerg-3309	78	23	the	the	DET
fuelectenerg-3309	78	24	set	set	NOUN
fuelectenerg-3309	78	25	{	{	PUNCT
fuelectenerg-3309	78	26	1	1	NUM
fuelectenerg-3309	78	27	,	,	PUNCT
fuelectenerg-3309	78	28	...	...	PUNCT
fuelectenerg-3309	78	29	,	,	PUNCT
fuelectenerg-3309	78	30	m	m	VERB
fuelectenerg-3309	78	31	}	}	PUNCT
fuelectenerg-3309	78	32	as	as	ADV
fuelectenerg-3309	78	33	well	well	ADV
fuelectenerg-3309	78	34	.	.	PUNCT
fuelectenerg-3309	79	1	in	in	ADP
fuelectenerg-3309	79	2	fact	fact	NOUN
fuelectenerg-3309	79	3	,	,	PUNCT
fuelectenerg-3309	79	4	let	let	VERB
fuelectenerg-3309	79	5	us	we	PRON
fuelectenerg-3309	79	6	define	define	VERB
fuelectenerg-3309	79	7	the	the	DET
fuelectenerg-3309	79	8	map	map	NOUN
fuelectenerg-3309	79	9	q	q	NOUN
fuelectenerg-3309	79	10	:	:	PUNCT
fuelectenerg-3309	79	11	p	p	X
fuelectenerg-3309	79	12	(	(	PUNCT
fuelectenerg-3309	79	13	m	m	NOUN
fuelectenerg-3309	79	14	)	)	PUNCT
fuelectenerg-3309	79	15	→	→	SYM
fuelectenerg-3309	79	16	s(m	s(m	PROPN
fuelectenerg-3309	79	17	)	)	PUNCT
fuelectenerg-3309	79	18	:	:	PUNCT
fuelectenerg-3309	80	1	q(ρ	q(ρ	X
fuelectenerg-3309	80	2	)	)	PUNCT
fuelectenerg-3309	80	3	=	=	SYM
fuelectenerg-3309	80	4	s	s	NOUN
fuelectenerg-3309	80	5	=	=	PUNCT
fuelectenerg-3309	80	6	(	(	PUNCT
fuelectenerg-3309	80	7	s1	s1	PROPN
fuelectenerg-3309	80	8	,	,	PUNCT
fuelectenerg-3309	80	9	...	...	PUNCT
fuelectenerg-3309	80	10	,	,	PUNCT
fuelectenerg-3309	80	11	sm	sm	PROPN
fuelectenerg-3309	80	12	)	)	PUNCT
fuelectenerg-3309	80	13	,	,	PUNCT
fuelectenerg-3309	80	14	(	(	PUNCT
fuelectenerg-3309	80	15	3	3	X
fuelectenerg-3309	80	16	)	)	PUNCT
fuelectenerg-3309	80	17	where	where	SCONJ
fuelectenerg-3309	80	18	each	each	DET
fuelectenerg-3309	80	19	element	element	NOUN
fuelectenerg-3309	80	20	si	si	PROPN
fuelectenerg-3309	80	21	∈	∈	PROPN
fuelectenerg-3309	80	22	s(m	s(m	PROPN
fuelectenerg-3309	80	23	)	)	PUNCT
fuelectenerg-3309	80	24	is	be	AUX
fuelectenerg-3309	80	25	defined	define	VERB
fuelectenerg-3309	80	26	by	by	ADP
fuelectenerg-3309	80	27	using	use	VERB
fuelectenerg-3309	80	28	the	the	DET
fuelectenerg-3309	80	29	following	follow	VERB
fuelectenerg-3309	80	30	iteration	iteration	NOUN
fuelectenerg-3309	80	31	scheme	scheme	NOUN
fuelectenerg-3309	80	32	:	:	PUNCT
fuelectenerg-3309	80	33	242	242	NUM
fuelectenerg-3309	80	34	c.	c.	PROPN
fuelectenerg-3309	80	35	karanikas	karanikas	PROPN
fuelectenerg-3309	80	36	,	,	PUNCT
fuelectenerg-3309	80	37	n.	n.	PROPN
fuelectenerg-3309	80	38	atreas	atreas	PROPN
fuelectenerg-3309	80	39	enumeration	enumeration	PROPN
fuelectenerg-3309	80	40	and	and	CCONJ
fuelectenerg-3309	80	41	coding	code	VERB
fuelectenerg-3309	80	42	permutations	permutation	NOUN
fuelectenerg-3309	80	43	and	and	CCONJ
fuelectenerg-3309	80	44	reversible	reversible	ADJ
fuelectenerg-3309	80	45	logical	logical	ADJ
fuelectenerg-3309	80	46	circuits	circuit	NOUN
fuelectenerg-3309	80	47	243	243	NUM
fuelectenerg-3309	80	48	2	2	NUM
fuelectenerg-3309	80	49	n.	n.	NOUN
fuelectenerg-3309	80	50	atreas	atreas	PROPN
fuelectenerg-3309	80	51	and	and	CCONJ
fuelectenerg-3309	80	52	c.	c.	PROPN
fuelectenerg-3309	80	53	karanikas	karanikas	PROPN
fuelectenerg-3309	80	54	our	our	PRON
fuelectenerg-3309	80	55	main	main	ADJ
fuelectenerg-3309	80	56	theorem	theorem	NOUN
fuelectenerg-3309	80	57	2	2	NUM
fuelectenerg-3309	80	58	in	in	ADP
fuelectenerg-3309	80	59	section	section	NOUN
fuelectenerg-3309	80	60	3	3	NUM
fuelectenerg-3309	80	61	or	or	CCONJ
fuelectenerg-3309	80	62	its	its	PRON
fuelectenerg-3309	80	63	”	"	PUNCT
fuelectenerg-3309	80	64	binary	binary	ADJ
fuelectenerg-3309	80	65	”	"	PUNCT
fuelectenerg-3309	80	66	version	version	NOUN
fuelectenerg-3309	80	67	(	(	PUNCT
fuelectenerg-3309	80	68	see	see	VERB
fuelectenerg-3309	80	69	theorem	theorem	NOUN
fuelectenerg-3309	80	70	3	3	NUM
fuelectenerg-3309	80	71	in	in	ADP
fuelectenerg-3309	80	72	section	section	NOUN
fuelectenerg-3309	80	73	4	4	NUM
fuelectenerg-3309	80	74	)	)	PUNCT
fuelectenerg-3309	80	75	,	,	PUNCT
fuelectenerg-3309	80	76	states	state	VERB
fuelectenerg-3309	80	77	that	that	SCONJ
fuelectenerg-3309	80	78	any	any	DET
fuelectenerg-3309	80	79	pair	pair	NOUN
fuelectenerg-3309	80	80	(	(	PUNCT
fuelectenerg-3309	80	81	ρ	ρ	PROPN
fuelectenerg-3309	80	82	,	,	PUNCT
fuelectenerg-3309	80	83	s	s	NOUN
fuelectenerg-3309	80	84	)	)	PUNCT
fuelectenerg-3309	80	85	of	of	ADP
fuelectenerg-3309	80	86	permutations	permutation	NOUN
fuelectenerg-3309	80	87	in	in	ADP
fuelectenerg-3309	80	88	p	p	PROPN
fuelectenerg-3309	80	89	(	(	PUNCT
fuelectenerg-3309	80	90	m	m	NOUN
fuelectenerg-3309	80	91	)	)	PUNCT
fuelectenerg-3309	80	92	determines	determine	VERB
fuelectenerg-3309	80	93	a	a	DET
fuelectenerg-3309	80	94	bijective	bijective	ADJ
fuelectenerg-3309	80	95	map	map	NOUN
fuelectenerg-3309	80	96	tρ	tρ	ADP
fuelectenerg-3309	80	97	,	,	PUNCT
fuelectenerg-3309	80	98	s	s	PART
fuelectenerg-3309	80	99	:	:	PUNCT
fuelectenerg-3309	80	100	{	{	PUNCT
fuelectenerg-3309	80	101	0	0	NUM
fuelectenerg-3309	80	102	,	,	PUNCT
fuelectenerg-3309	80	103	1	1	NUM
fuelectenerg-3309	80	104	,	,	PUNCT
fuelectenerg-3309	80	105	....	....	PUNCT
fuelectenerg-3309	80	106	,	,	PUNCT
fuelectenerg-3309	80	107	2	2	NUM
fuelectenerg-3309	80	108	m	m	NOUN
fuelectenerg-3309	80	109	−	−	NOUN
fuelectenerg-3309	80	110	1	1	NUM
fuelectenerg-3309	80	111	}	}	PUNCT
fuelectenerg-3309	80	112	→	→	SYM
fuelectenerg-3309	80	113	{	{	PUNCT
fuelectenerg-3309	80	114	0	0	NUM
fuelectenerg-3309	80	115	,	,	PUNCT
fuelectenerg-3309	80	116	1	1	NUM
fuelectenerg-3309	80	117	,	,	PUNCT
fuelectenerg-3309	80	118	....	....	PUNCT
fuelectenerg-3309	80	119	,	,	PUNCT
fuelectenerg-3309	80	120	2	2	NUM
fuelectenerg-3309	80	121	m	m	NOUN
fuelectenerg-3309	80	122	−	−	NOUN
fuelectenerg-3309	80	123	1	1	NUM
fuelectenerg-3309	80	124	}	}	PUNCT
fuelectenerg-3309	80	125	.	.	PUNCT
fuelectenerg-3309	81	1	since	since	SCONJ
fuelectenerg-3309	81	2	every	every	DET
fuelectenerg-3309	81	3	non	non	PRON
fuelectenerg-3309	81	4	negative	negative	ADJ
fuelectenerg-3309	81	5	integer	integer	NOUN
fuelectenerg-3309	81	6	n	n	PRON
fuelectenerg-3309	81	7	∈	∈	PROPN
fuelectenerg-3309	81	8	{	{	PUNCT
fuelectenerg-3309	81	9	0	0	NUM
fuelectenerg-3309	81	10	,	,	PUNCT
fuelectenerg-3309	81	11	1	1	NUM
fuelectenerg-3309	81	12	,	,	PUNCT
fuelectenerg-3309	81	13	....	....	PUNCT
fuelectenerg-3309	81	14	,	,	PUNCT
fuelectenerg-3309	81	15	2	2	NUM
fuelectenerg-3309	81	16	m	m	NOUN
fuelectenerg-3309	81	17	−	−	NUM
fuelectenerg-3309	81	18	1	1	NUM
fuelectenerg-3309	81	19	}	}	PUNCT
fuelectenerg-3309	81	20	can	can	AUX
fuelectenerg-3309	81	21	be	be	AUX
fuelectenerg-3309	81	22	expressed	express	VERB
fuelectenerg-3309	81	23	either	either	CCONJ
fuelectenerg-3309	81	24	as	as	ADP
fuelectenerg-3309	81	25	an	an	DET
fuelectenerg-3309	81	26	m	m	NOUN
fuelectenerg-3309	81	27	-	-	PUNCT
fuelectenerg-3309	81	28	bit	bit	NOUN
fuelectenerg-3309	81	29	binary	binary	ADJ
fuelectenerg-3309	81	30	array	array	NOUN
fuelectenerg-3309	81	31	en	en	X
fuelectenerg-3309	81	32	=	=	SYM
fuelectenerg-3309	81	33	(	(	PUNCT
fuelectenerg-3309	81	34	ε0(n	ε0(n	NOUN
fuelectenerg-3309	81	35	)	)	PUNCT
fuelectenerg-3309	81	36	,	,	PUNCT
fuelectenerg-3309	81	37	ε1(n	ε1(n	NOUN
fuelectenerg-3309	81	38	)	)	PUNCT
fuelectenerg-3309	81	39	,	,	PUNCT
fuelectenerg-3309	81	40	...	...	PUNCT
fuelectenerg-3309	81	41	,	,	PUNCT
fuelectenerg-3309	81	42	εm−1(n	εm−1(n	PROPN
fuelectenerg-3309	81	43	)	)	PUNCT
fuelectenerg-3309	81	44	)	)	PUNCT
fuelectenerg-3309	81	45	,	,	PUNCT
fuelectenerg-3309	81	46	εj	εj	NOUN
fuelectenerg-3309	81	47	∈	∈	PROPN
fuelectenerg-3309	81	48	{	{	PUNCT
fuelectenerg-3309	81	49	0	0	NUM
fuelectenerg-3309	81	50	,	,	PUNCT
fuelectenerg-3309	81	51	1	1	NUM
fuelectenerg-3309	81	52	}	}	PUNCT
fuelectenerg-3309	81	53	,	,	PUNCT
fuelectenerg-3309	81	54	or	or	CCONJ
fuelectenerg-3309	81	55	by	by	ADP
fuelectenerg-3309	81	56	its	its	PRON
fuelectenerg-3309	81	57	dyadic	dyadic	ADJ
fuelectenerg-3309	81	58	expansion	expansion	NOUN
fuelectenerg-3309	81	59	n	n	NOUN
fuelectenerg-3309	81	60	=	=	PUNCT
fuelectenerg-3309	81	61	m∑	m∑	PROPN
fuelectenerg-3309	81	62	j=1	j=1	PROPN
fuelectenerg-3309	81	63	εj(n)2	εj(n)2	PROPN
fuelectenerg-3309	81	64	j−1	j−1	PROPN
fuelectenerg-3309	81	65	,	,	PUNCT
fuelectenerg-3309	81	66	the	the	DET
fuelectenerg-3309	81	67	above	above	ADJ
fuelectenerg-3309	81	68	map	map	NOUN
fuelectenerg-3309	81	69	tρ	tρ	ADP
fuelectenerg-3309	81	70	,	,	PUNCT
fuelectenerg-3309	81	71	s	s	PART
fuelectenerg-3309	81	72	can	can	AUX
fuelectenerg-3309	81	73	be	be	AUX
fuelectenerg-3309	81	74	considered	consider	VERB
fuelectenerg-3309	81	75	as	as	ADP
fuelectenerg-3309	81	76	a	a	DET
fuelectenerg-3309	81	77	reversible	reversible	ADJ
fuelectenerg-3309	81	78	map	map	NOUN
fuelectenerg-3309	81	79	on	on	ADP
fuelectenerg-3309	81	80	the	the	DET
fuelectenerg-3309	81	81	set	set	NOUN
fuelectenerg-3309	81	82	of	of	ADP
fuelectenerg-3309	81	83	all	all	DET
fuelectenerg-3309	81	84	m	m	NOUN
fuelectenerg-3309	81	85	-	-	PUNCT
fuelectenerg-3309	81	86	bit	bit	NOUN
fuelectenerg-3309	81	87	binary	binary	NOUN
fuelectenerg-3309	81	88	arrays	array	NOUN
fuelectenerg-3309	81	89	.	.	PUNCT
fuelectenerg-3309	82	1	in	in	ADP
fuelectenerg-3309	82	2	a	a	DET
fuelectenerg-3309	82	3	different	different	ADJ
fuelectenerg-3309	82	4	terminology	terminology	NOUN
fuelectenerg-3309	82	5	,	,	PUNCT
fuelectenerg-3309	82	6	we	we	PRON
fuelectenerg-3309	82	7	can	can	AUX
fuelectenerg-3309	82	8	say	say	VERB
fuelectenerg-3309	82	9	that	that	SCONJ
fuelectenerg-3309	82	10	in	in	ADP
fuelectenerg-3309	82	11	theorem	theorem	NOUN
fuelectenerg-3309	82	12	3	3	NUM
fuelectenerg-3309	82	13	we	we	PRON
fuelectenerg-3309	82	14	introduce	introduce	VERB
fuelectenerg-3309	82	15	reversible	reversible	ADJ
fuelectenerg-3309	82	16	logic	logic	NOUN
fuelectenerg-3309	82	17	gates	gate	NOUN
fuelectenerg-3309	82	18	,	,	PUNCT
fuelectenerg-3309	82	19	i.e	i.e	DET
fuelectenerg-3309	82	20	bijective	bijective	ADJ
fuelectenerg-3309	82	21	maps	map	NOUN
fuelectenerg-3309	82	22	on	on	ADP
fuelectenerg-3309	82	23	the	the	DET
fuelectenerg-3309	82	24	set	set	NOUN
fuelectenerg-3309	82	25	of	of	ADP
fuelectenerg-3309	82	26	m	m	NOUN
fuelectenerg-3309	82	27	-	-	PUNCT
fuelectenerg-3309	82	28	bit	bit	NOUN
fuelectenerg-3309	82	29	binary	binary	NOUN
fuelectenerg-3309	82	30	arrays	array	NOUN
fuelectenerg-3309	82	31	,	,	PUNCT
fuelectenerg-3309	82	32	(	(	PUNCT
fuelectenerg-3309	82	33	see	see	VERB
fuelectenerg-3309	82	34	[	[	X
fuelectenerg-3309	82	35	1	1	NUM
fuelectenerg-3309	82	36	]	]	NUM
fuelectenerg-3309	82	37	)	)	PUNCT
fuelectenerg-3309	82	38	.	.	PUNCT
fuelectenerg-3309	83	1	an	an	DET
fuelectenerg-3309	83	2	example	example	NOUN
fuelectenerg-3309	83	3	of	of	ADP
fuelectenerg-3309	83	4	a	a	DET
fuelectenerg-3309	83	5	reversible	reversible	ADJ
fuelectenerg-3309	83	6	gate	gate	NOUN
fuelectenerg-3309	83	7	is	be	AUX
fuelectenerg-3309	83	8	the	the	DET
fuelectenerg-3309	83	9	not	not	PART
fuelectenerg-3309	83	10	gate	gate	NOUN
fuelectenerg-3309	83	11	,	,	PUNCT
fuelectenerg-3309	83	12	whereas	whereas	SCONJ
fuelectenerg-3309	83	13	the	the	PRON
fuelectenerg-3309	83	14	and	and	CCONJ
fuelectenerg-3309	83	15	,	,	PUNCT
fuelectenerg-3309	83	16	or	or	CCONJ
fuelectenerg-3309	83	17	,	,	PUNCT
fuelectenerg-3309	83	18	xor	xor	PROPN
fuelectenerg-3309	83	19	gates	gate	NOUN
fuelectenerg-3309	83	20	are	be	AUX
fuelectenerg-3309	83	21	irreversible	irreversible	ADJ
fuelectenerg-3309	83	22	(	(	PUNCT
fuelectenerg-3309	83	23	not	not	PART
fuelectenerg-3309	83	24	reversible	reversible	ADJ
fuelectenerg-3309	83	25	)	)	PUNCT
fuelectenerg-3309	83	26	,	,	PUNCT
fuelectenerg-3309	83	27	because	because	SCONJ
fuelectenerg-3309	83	28	they	they	PRON
fuelectenerg-3309	83	29	map	map	VERB
fuelectenerg-3309	83	30	4	4	NUM
fuelectenerg-3309	83	31	=	=	SYM
fuelectenerg-3309	83	32	22	22	NUM
fuelectenerg-3309	83	33	input	input	NOUN
fuelectenerg-3309	83	34	states	state	NOUN
fuelectenerg-3309	83	35	into	into	ADP
fuelectenerg-3309	83	36	2	2	NUM
fuelectenerg-3309	83	37	=	=	SYM
fuelectenerg-3309	83	38	21	21	NUM
fuelectenerg-3309	83	39	output	output	NOUN
fuelectenerg-3309	83	40	states	state	NOUN
fuelectenerg-3309	83	41	,	,	PUNCT
fuelectenerg-3309	83	42	so	so	CCONJ
fuelectenerg-3309	83	43	information	information	NOUN
fuelectenerg-3309	83	44	is	be	AUX
fuelectenerg-3309	83	45	lost	lose	VERB
fuelectenerg-3309	83	46	in	in	ADP
fuelectenerg-3309	83	47	the	the	DET
fuelectenerg-3309	83	48	merging	merging	NOUN
fuelectenerg-3309	83	49	of	of	ADP
fuelectenerg-3309	83	50	paths	path	NOUN
fuelectenerg-3309	83	51	.	.	PUNCT
fuelectenerg-3309	84	1	a	a	DET
fuelectenerg-3309	84	2	second	second	ADJ
fuelectenerg-3309	84	3	target	target	NOUN
fuelectenerg-3309	84	4	of	of	ADP
fuelectenerg-3309	84	5	this	this	DET
fuelectenerg-3309	84	6	work	work	NOUN
fuelectenerg-3309	84	7	is	be	AUX
fuelectenerg-3309	84	8	to	to	PART
fuelectenerg-3309	84	9	enumerate	enumerate	VERB
fuelectenerg-3309	84	10	and	and	CCONJ
fuelectenerg-3309	84	11	code	code	NOUN
fuelectenerg-3309	84	12	permutations	permutation	NOUN
fuelectenerg-3309	84	13	in	in	ADP
fuelectenerg-3309	84	14	p	p	PROPN
fuelectenerg-3309	84	15	(	(	PUNCT
fuelectenerg-3309	84	16	m	m	NOUN
fuelectenerg-3309	84	17	)	)	PUNCT
fuelectenerg-3309	84	18	of	of	ADP
fuelectenerg-3309	84	19	large	large	ADJ
fuelectenerg-3309	84	20	length	length	NOUN
fuelectenerg-3309	84	21	(	(	PUNCT
fuelectenerg-3309	84	22	note	note	VERB
fuelectenerg-3309	84	23	that	that	SCONJ
fuelectenerg-3309	84	24	the	the	DET
fuelectenerg-3309	84	25	cardinality	cardinality	NOUN
fuelectenerg-3309	84	26	of	of	ADP
fuelectenerg-3309	84	27	the	the	DET
fuelectenerg-3309	84	28	set	set	NOUN
fuelectenerg-3309	84	29	p	p	PROPN
fuelectenerg-3309	84	30	(	(	PUNCT
fuelectenerg-3309	84	31	m	m	NOUN
fuelectenerg-3309	84	32	)	)	PUNCT
fuelectenerg-3309	84	33	is	be	AUX
fuelectenerg-3309	84	34	m	m	PRON
fuelectenerg-3309	84	35	!	!	PUNCT
fuelectenerg-3309	84	36	)	)	PUNCT
fuelectenerg-3309	84	37	.	.	PUNCT
fuelectenerg-3309	85	1	therefore	therefore	ADV
fuelectenerg-3309	85	2	,	,	PUNCT
fuelectenerg-3309	85	3	a	a	DET
fuelectenerg-3309	85	4	reversible	reversible	ADJ
fuelectenerg-3309	85	5	map	map	NOUN
fuelectenerg-3309	85	6	tρ	tρ	NOUN
fuelectenerg-3309	85	7	,	,	PUNCT
fuelectenerg-3309	85	8	s	s	AUX
fuelectenerg-3309	85	9	associated	associate	VERB
fuelectenerg-3309	85	10	with	with	ADP
fuelectenerg-3309	85	11	the	the	DET
fuelectenerg-3309	85	12	pair	pair	NOUN
fuelectenerg-3309	85	13	(	(	PUNCT
fuelectenerg-3309	85	14	ρ	ρ	PROPN
fuelectenerg-3309	85	15	,	,	PUNCT
fuelectenerg-3309	85	16	s	s	PART
fuelectenerg-3309	85	17	)	)	PUNCT
fuelectenerg-3309	85	18	can	can	AUX
fuelectenerg-3309	85	19	be	be	AUX
fuelectenerg-3309	85	20	coded	code	VERB
fuelectenerg-3309	85	21	either	either	ADV
fuelectenerg-3309	85	22	by	by	ADP
fuelectenerg-3309	85	23	the	the	DET
fuelectenerg-3309	85	24	pair	pair	NOUN
fuelectenerg-3309	85	25	(	(	PUNCT
fuelectenerg-3309	85	26	ρ	ρ	PROPN
fuelectenerg-3309	85	27	,	,	PUNCT
fuelectenerg-3309	85	28	s	s	PART
fuelectenerg-3309	85	29	)	)	PUNCT
fuelectenerg-3309	85	30	or	or	CCONJ
fuelectenerg-3309	85	31	by	by	ADP
fuelectenerg-3309	85	32	an	an	DET
fuelectenerg-3309	85	33	enumeration	enumeration	NOUN
fuelectenerg-3309	85	34	of	of	ADP
fuelectenerg-3309	85	35	p	p	PROPN
fuelectenerg-3309	85	36	(	(	PUNCT
fuelectenerg-3309	85	37	m)×p	m)×p	NOUN
fuelectenerg-3309	85	38	(	(	PUNCT
fuelectenerg-3309	85	39	m	m	NOUN
fuelectenerg-3309	85	40	)	)	PUNCT
fuelectenerg-3309	85	41	as	as	ADP
fuelectenerg-3309	85	42	in	in	ADP
fuelectenerg-3309	85	43	section	section	NOUN
fuelectenerg-3309	85	44	2	2	NUM
fuelectenerg-3309	85	45	.	.	PUNCT
fuelectenerg-3309	86	1	this	this	DET
fuelectenerg-3309	86	2	coding	code	VERB
fuelectenerg-3309	86	3	method	method	NOUN
fuelectenerg-3309	86	4	is	be	AUX
fuelectenerg-3309	86	5	associated	associate	VERB
fuelectenerg-3309	86	6	with	with	ADP
fuelectenerg-3309	86	7	a	a	DET
fuelectenerg-3309	86	8	particular	particular	ADJ
fuelectenerg-3309	86	9	class	class	NOUN
fuelectenerg-3309	86	10	of	of	ADP
fuelectenerg-3309	86	11	sparse	sparse	ADJ
fuelectenerg-3309	86	12	boolean	boolean	ADJ
fuelectenerg-3309	86	13	invertible	invertible	ADJ
fuelectenerg-3309	86	14	matrices	matrix	NOUN
fuelectenerg-3309	86	15	introduced	introduce	VERB
fuelectenerg-3309	86	16	in	in	ADP
fuelectenerg-3309	86	17	[	[	X
fuelectenerg-3309	86	18	2	2	NUM
fuelectenerg-3309	86	19	]	]	PUNCT
fuelectenerg-3309	86	20	(	(	PUNCT
fuelectenerg-3309	86	21	see	see	VERB
fuelectenerg-3309	86	22	also	also	ADV
fuelectenerg-3309	86	23	[	[	X
fuelectenerg-3309	86	24	3–6	3–6	NUM
fuelectenerg-3309	86	25	]	]	X
fuelectenerg-3309	86	26	)	)	PUNCT
fuelectenerg-3309	86	27	.	.	PUNCT
fuelectenerg-3309	87	1	notice	notice	VERB
fuelectenerg-3309	87	2	that	that	SCONJ
fuelectenerg-3309	87	3	sparse	sparse	ADJ
fuelectenerg-3309	87	4	matrices	matrix	NOUN
fuelectenerg-3309	87	5	are	be	AUX
fuelectenerg-3309	87	6	very	very	ADV
fuelectenerg-3309	87	7	useful	useful	ADJ
fuelectenerg-3309	87	8	for	for	ADP
fuelectenerg-3309	87	9	fast	fast	ADJ
fuelectenerg-3309	87	10	processing	processing	NOUN
fuelectenerg-3309	87	11	/	/	SYM
fuelectenerg-3309	87	12	transmission	transmission	NOUN
fuelectenerg-3309	87	13	of	of	ADP
fuelectenerg-3309	87	14	data	datum	NOUN
fuelectenerg-3309	87	15	and	and	CCONJ
fuelectenerg-3309	87	16	they	they	PRON
fuelectenerg-3309	87	17	have	have	AUX
fuelectenerg-3309	87	18	been	be	AUX
fuelectenerg-3309	87	19	effectively	effectively	ADV
fuelectenerg-3309	87	20	used	use	VERB
fuelectenerg-3309	87	21	in	in	ADP
fuelectenerg-3309	87	22	[	[	X
fuelectenerg-3309	87	23	6	6	NUM
fuelectenerg-3309	87	24	]	]	PUNCT
fuelectenerg-3309	87	25	for	for	ADP
fuelectenerg-3309	87	26	detecting	detect	VERB
fuelectenerg-3309	87	27	specific	specific	ADJ
fuelectenerg-3309	87	28	characteristics	characteristic	NOUN
fuelectenerg-3309	87	29	on	on	ADP
fuelectenerg-3309	87	30	finite	finite	ADJ
fuelectenerg-3309	87	31	data	datum	NOUN
fuelectenerg-3309	87	32	.	.	PUNCT
fuelectenerg-3309	88	1	the	the	DET
fuelectenerg-3309	88	2	paper	paper	NOUN
fuelectenerg-3309	88	3	is	be	AUX
fuelectenerg-3309	88	4	organized	organize	VERB
fuelectenerg-3309	88	5	in	in	ADP
fuelectenerg-3309	88	6	the	the	DET
fuelectenerg-3309	88	7	following	follow	VERB
fuelectenerg-3309	88	8	sections	section	NOUN
fuelectenerg-3309	88	9	:	:	PUNCT
fuelectenerg-3309	88	10	in	in	ADP
fuelectenerg-3309	88	11	section	section	NOUN
fuelectenerg-3309	88	12	2	2	NUM
fuelectenerg-3309	88	13	we	we	PRON
fuelectenerg-3309	88	14	introduce	introduce	VERB
fuelectenerg-3309	88	15	our	our	PRON
fuelectenerg-3309	88	16	main	main	ADJ
fuelectenerg-3309	88	17	tool	tool	NOUN
fuelectenerg-3309	88	18	,	,	PUNCT
fuelectenerg-3309	88	19	the	the	DET
fuelectenerg-3309	88	20	invertible	invertible	ADJ
fuelectenerg-3309	88	21	map	map	NOUN
fuelectenerg-3309	88	22	p	p	X
fuelectenerg-3309	88	23	(	(	PUNCT
fuelectenerg-3309	88	24	m	m	NOUN
fuelectenerg-3309	88	25	)	)	PUNCT
fuelectenerg-3309	88	26	→	→	SYM
fuelectenerg-3309	88	27	s(m	s(m	PROPN
fuelectenerg-3309	88	28	)	)	PUNCT
fuelectenerg-3309	88	29	(	(	PUNCT
fuelectenerg-3309	88	30	see	see	VERB
fuelectenerg-3309	88	31	(	(	PUNCT
fuelectenerg-3309	88	32	2	2	NUM
fuelectenerg-3309	88	33	)	)	PUNCT
fuelectenerg-3309	88	34	and	and	CCONJ
fuelectenerg-3309	88	35	(	(	PUNCT
fuelectenerg-3309	88	36	3	3	NUM
fuelectenerg-3309	88	37	)	)	PUNCT
fuelectenerg-3309	88	38	)	)	PUNCT
fuelectenerg-3309	88	39	and	and	CCONJ
fuelectenerg-3309	88	40	in	in	ADP
fuelectenerg-3309	88	41	proposition	proposition	NOUN
fuelectenerg-3309	88	42	1	1	NUM
fuelectenerg-3309	88	43	,	,	PUNCT
fuelectenerg-3309	88	44	we	we	PRON
fuelectenerg-3309	88	45	see	see	VERB
fuelectenerg-3309	88	46	that	that	SCONJ
fuelectenerg-3309	88	47	this	this	DET
fuelectenerg-3309	88	48	map	map	NOUN
fuelectenerg-3309	88	49	induces	induce	VERB
fuelectenerg-3309	88	50	the	the	DET
fuelectenerg-3309	88	51	lexicographic	lexicographic	ADJ
fuelectenerg-3309	88	52	order	order	NOUN
fuelectenerg-3309	88	53	of	of	ADP
fuelectenerg-3309	88	54	the	the	DET
fuelectenerg-3309	88	55	enumeration	enumeration	NOUN
fuelectenerg-3309	88	56	of	of	ADP
fuelectenerg-3309	88	57	p	p	PROPN
fuelectenerg-3309	88	58	(	(	PUNCT
fuelectenerg-3309	88	59	m	m	NOUN
fuelectenerg-3309	88	60	)	)	PUNCT
fuelectenerg-3309	88	61	.	.	PUNCT
fuelectenerg-3309	89	1	moreover	moreover	ADV
fuelectenerg-3309	89	2	we	we	PRON
fuelectenerg-3309	89	3	consider	consider	VERB
fuelectenerg-3309	89	4	the	the	DET
fuelectenerg-3309	89	5	cartesian	cartesian	ADJ
fuelectenerg-3309	89	6	product	product	NOUN
fuelectenerg-3309	89	7	r(m	r(m	NOUN
fuelectenerg-3309	89	8	)	)	PUNCT
fuelectenerg-3309	89	9	=	=	SYM
fuelectenerg-3309	89	10	p	p	X
fuelectenerg-3309	89	11	(	(	PUNCT
fuelectenerg-3309	89	12	1)×p	1)×p	NUM
fuelectenerg-3309	89	13	(	(	PUNCT
fuelectenerg-3309	89	14	2)×	2)×	NUM
fuelectenerg-3309	89	15	...	...	PUNCT
fuelectenerg-3309	89	16	×p	×p	PRON
fuelectenerg-3309	89	17	(	(	PUNCT
fuelectenerg-3309	89	18	m	m	NOUN
fuelectenerg-3309	89	19	)	)	PUNCT
fuelectenerg-3309	89	20	of	of	ADP
fuelectenerg-3309	89	21	permutations	permutation	NOUN
fuelectenerg-3309	89	22	to	to	PART
fuelectenerg-3309	89	23	show	show	VERB
fuelectenerg-3309	89	24	in	in	ADP
fuelectenerg-3309	89	25	theorem	theorem	NOUN
fuelectenerg-3309	89	26	1	1	NUM
fuelectenerg-3309	89	27	that	that	SCONJ
fuelectenerg-3309	89	28	each	each	DET
fuelectenerg-3309	89	29	fixed	fix	VERB
fuelectenerg-3309	89	30	element	element	NOUN
fuelectenerg-3309	89	31	of	of	ADP
fuelectenerg-3309	89	32	r(m	r(m	PROPN
fuelectenerg-3309	89	33	)	)	PUNCT
fuelectenerg-3309	89	34	provides	provide	VERB
fuelectenerg-3309	89	35	an	an	DET
fuelectenerg-3309	89	36	enumeration	enumeration	NOUN
fuelectenerg-3309	89	37	of	of	ADP
fuelectenerg-3309	89	38	p	p	PROPN
fuelectenerg-3309	89	39	(	(	PUNCT
fuelectenerg-3309	89	40	m	m	NOUN
fuelectenerg-3309	89	41	)	)	PUNCT
fuelectenerg-3309	89	42	.	.	PUNCT
fuelectenerg-3309	90	1	in	in	ADP
fuelectenerg-3309	90	2	section	section	NOUN
fuelectenerg-3309	90	3	3	3	NUM
fuelectenerg-3309	90	4	we	we	PRON
fuelectenerg-3309	90	5	define	define	VERB
fuelectenerg-3309	90	6	a	a	DET
fuelectenerg-3309	90	7	class	class	NOUN
fuelectenerg-3309	90	8	of	of	ADP
fuelectenerg-3309	90	9	sparse	sparse	ADJ
fuelectenerg-3309	90	10	m×m	m×m	ADJ
fuelectenerg-3309	90	11	boolean	boolean	ADJ
fuelectenerg-3309	90	12	invertible	invertible	ADJ
fuelectenerg-3309	90	13	matrices	matrix	NOUN
fuelectenerg-3309	90	14	zm	zm	PROPN
fuelectenerg-3309	90	15	identified	identify	VERB
fuelectenerg-3309	90	16	by	by	ADP
fuelectenerg-3309	90	17	a	a	DET
fuelectenerg-3309	90	18	pair	pair	NOUN
fuelectenerg-3309	90	19	(	(	PUNCT
fuelectenerg-3309	90	20	ρ	ρ	PROPN
fuelectenerg-3309	90	21	,	,	PUNCT
fuelectenerg-3309	90	22	s	s	PART
fuelectenerg-3309	90	23	)	)	PUNCT
fuelectenerg-3309	90	24	∈	∈	PROPN
fuelectenerg-3309	90	25	p	p	NOUN
fuelectenerg-3309	90	26	(	(	PUNCT
fuelectenerg-3309	90	27	m)×s(m	m)×s(m	NOUN
fuelectenerg-3309	90	28	)	)	PUNCT
fuelectenerg-3309	90	29	and	and	CCONJ
fuelectenerg-3309	90	30	we	we	PRON
fuelectenerg-3309	90	31	use	use	VERB
fuelectenerg-3309	90	32	this	this	DET
fuelectenerg-3309	90	33	class	class	NOUN
fuelectenerg-3309	90	34	of	of	ADP
fuelectenerg-3309	90	35	matrices	matrix	NOUN
fuelectenerg-3309	90	36	enumeration	enumeration	NOUN
fuelectenerg-3309	90	37	and	and	CCONJ
fuelectenerg-3309	90	38	coding	code	VERB
fuelectenerg-3309	90	39	permutations	permutation	NOUN
fuelectenerg-3309	90	40	and	and	CCONJ
fuelectenerg-3309	90	41	reversible	reversible	ADJ
fuelectenerg-3309	90	42	logical	logical	ADJ
fuelectenerg-3309	90	43	circuits	circuit	NOUN
fuelectenerg-3309	90	44	3	3	NUM
fuelectenerg-3309	90	45	to	to	PART
fuelectenerg-3309	90	46	produce	produce	VERB
fuelectenerg-3309	90	47	a	a	DET
fuelectenerg-3309	90	48	class	class	NOUN
fuelectenerg-3309	90	49	of	of	ADP
fuelectenerg-3309	90	50	non	non	ADJ
fuelectenerg-3309	90	51	-	-	ADJ
fuelectenerg-3309	90	52	linear	linear	ADJ
fuelectenerg-3309	90	53	bijection	bijection	NOUN
fuelectenerg-3309	90	54	maps	map	NOUN
fuelectenerg-3309	90	55	tq	tq	ADP
fuelectenerg-3309	90	56	,	,	PUNCT
fuelectenerg-3309	90	57	ρ	ρ	PROPN
fuelectenerg-3309	90	58	,	,	PUNCT
fuelectenerg-3309	90	59	s	s	PART
fuelectenerg-3309	90	60	:	:	PUNCT
fuelectenerg-3309	90	61	{	{	PUNCT
fuelectenerg-3309	90	62	0	0	NUM
fuelectenerg-3309	90	63	,	,	PUNCT
fuelectenerg-3309	90	64	...	...	PUNCT
fuelectenerg-3309	90	65	,	,	PUNCT
fuelectenerg-3309	90	66	qm	qm	PROPN
fuelectenerg-3309	90	67	−	−	PROPN
fuelectenerg-3309	90	68	1	1	NUM
fuelectenerg-3309	90	69	}	}	PUNCT
fuelectenerg-3309	90	70	→	→	SYM
fuelectenerg-3309	90	71	{	{	PUNCT
fuelectenerg-3309	90	72	0	0	NUM
fuelectenerg-3309	90	73	,	,	PUNCT
fuelectenerg-3309	90	74	...	...	PUNCT
fuelectenerg-3309	90	75	,	,	PUNCT
fuelectenerg-3309	90	76	qm	qm	PROPN
fuelectenerg-3309	90	77	−	−	PROPN
fuelectenerg-3309	90	78	1	1	NUM
fuelectenerg-3309	90	79	}	}	PUNCT
fuelectenerg-3309	90	80	,	,	PUNCT
fuelectenerg-3309	90	81	see	see	VERB
fuelectenerg-3309	90	82	our	our	PRON
fuelectenerg-3309	90	83	main	main	ADJ
fuelectenerg-3309	90	84	theorem	theorem	NOUN
fuelectenerg-3309	90	85	2	2	NUM
fuelectenerg-3309	90	86	.	.	PUNCT
fuelectenerg-3309	91	1	in	in	ADP
fuelectenerg-3309	91	2	section	section	NOUN
fuelectenerg-3309	91	3	4	4	NUM
fuelectenerg-3309	91	4	we	we	PRON
fuelectenerg-3309	91	5	show	show	VERB
fuelectenerg-3309	91	6	that	that	SCONJ
fuelectenerg-3309	91	7	any	any	PRON
fuelectenerg-3309	91	8	triple	triple	ADJ
fuelectenerg-3309	91	9	(	(	PUNCT
fuelectenerg-3309	91	10	ρ	ρ	PROPN
fuelectenerg-3309	91	11	,	,	PUNCT
fuelectenerg-3309	91	12	s	s	PROPN
fuelectenerg-3309	91	13	,	,	PUNCT
fuelectenerg-3309	91	14	τ	τ	X
fuelectenerg-3309	91	15	)	)	PUNCT
fuelectenerg-3309	91	16	of	of	ADP
fuelectenerg-3309	91	17	permutations	permutation	NOUN
fuelectenerg-3309	91	18	in	in	ADP
fuelectenerg-3309	91	19	p	p	PROPN
fuelectenerg-3309	91	20	(	(	PUNCT
fuelectenerg-3309	91	21	m	m	NOUN
fuelectenerg-3309	91	22	)	)	PUNCT
fuelectenerg-3309	91	23	provides	provide	VERB
fuelectenerg-3309	91	24	a	a	DET
fuelectenerg-3309	91	25	variety	variety	NOUN
fuelectenerg-3309	91	26	of	of	ADP
fuelectenerg-3309	91	27	maps	map	NOUN
fuelectenerg-3309	91	28	from	from	ADP
fuelectenerg-3309	91	29	{	{	PUNCT
fuelectenerg-3309	91	30	0	0	NUM
fuelectenerg-3309	91	31	,	,	PUNCT
fuelectenerg-3309	91	32	...	...	PUNCT
fuelectenerg-3309	91	33	,	,	PUNCT
fuelectenerg-3309	91	34	2	2	NUM
fuelectenerg-3309	91	35	m	m	NOUN
fuelectenerg-3309	91	36	−	−	NOUN
fuelectenerg-3309	91	37	1	1	NUM
fuelectenerg-3309	91	38	}	}	PUNCT
fuelectenerg-3309	91	39	onto	onto	ADP
fuelectenerg-3309	91	40	{	{	PUNCT
fuelectenerg-3309	91	41	0	0	NUM
fuelectenerg-3309	91	42	,	,	PUNCT
fuelectenerg-3309	91	43	...	...	PUNCT
fuelectenerg-3309	91	44	,	,	PUNCT
fuelectenerg-3309	91	45	2	2	NUM
fuelectenerg-3309	91	46	m	m	NOUN
fuelectenerg-3309	91	47	−	−	NOUN
fuelectenerg-3309	91	48	1	1	NUM
fuelectenerg-3309	91	49	}	}	PUNCT
fuelectenerg-3309	91	50	and	and	CCONJ
fuelectenerg-3309	91	51	we	we	PRON
fuelectenerg-3309	91	52	see	see	VERB
fuelectenerg-3309	91	53	that	that	SCONJ
fuelectenerg-3309	91	54	several	several	ADJ
fuelectenerg-3309	91	55	reversible	reversible	ADJ
fuelectenerg-3309	91	56	logic	logic	NOUN
fuelectenerg-3309	91	57	gates	gate	NOUN
fuelectenerg-3309	91	58	can	can	AUX
fuelectenerg-3309	91	59	be	be	AUX
fuelectenerg-3309	91	60	determined	determine	VERB
fuelectenerg-3309	91	61	by	by	ADP
fuelectenerg-3309	91	62	this	this	DET
fuelectenerg-3309	91	63	triple	triple	NOUN
fuelectenerg-3309	91	64	.	.	PUNCT
fuelectenerg-3309	92	1	finally	finally	ADV
fuelectenerg-3309	92	2	,	,	PUNCT
fuelectenerg-3309	92	3	in	in	ADP
fuelectenerg-3309	92	4	section	section	NOUN
fuelectenerg-3309	92	5	5	5	NUM
fuelectenerg-3309	92	6	we	we	PRON
fuelectenerg-3309	92	7	apply	apply	VERB
fuelectenerg-3309	92	8	theorems	theorem	NOUN
fuelectenerg-3309	92	9	1	1	NUM
fuelectenerg-3309	92	10	and	and	CCONJ
fuelectenerg-3309	92	11	2	2	NUM
fuelectenerg-3309	92	12	,	,	PUNCT
fuelectenerg-3309	92	13	to	to	PART
fuelectenerg-3309	92	14	see	see	VERB
fuelectenerg-3309	92	15	with	with	ADP
fuelectenerg-3309	92	16	an	an	DET
fuelectenerg-3309	92	17	example	example	NOUN
fuelectenerg-3309	92	18	that	that	SCONJ
fuelectenerg-3309	92	19	for	for	ADP
fuelectenerg-3309	92	20	any	any	DET
fuelectenerg-3309	92	21	pair	pair	NOUN
fuelectenerg-3309	92	22	(	(	PUNCT
fuelectenerg-3309	92	23	ρ	ρ	PROPN
fuelectenerg-3309	92	24	,	,	PUNCT
fuelectenerg-3309	92	25	s	s	PART
fuelectenerg-3309	92	26	)	)	PUNCT
fuelectenerg-3309	92	27	∈	∈	PROPN
fuelectenerg-3309	92	28	p	p	X
fuelectenerg-3309	92	29	(	(	PUNCT
fuelectenerg-3309	92	30	m	m	NOUN
fuelectenerg-3309	92	31	)	)	PUNCT
fuelectenerg-3309	92	32	×	×	PROPN
fuelectenerg-3309	92	33	s(m	s(m	PROPN
fuelectenerg-3309	92	34	)	)	PUNCT
fuelectenerg-3309	92	35	and	and	CCONJ
fuelectenerg-3309	92	36	any	any	DET
fuelectenerg-3309	92	37	fixed	fix	VERB
fuelectenerg-3309	92	38	r	r	NOUN
fuelectenerg-3309	92	39	∈	∈	PROPN
fuelectenerg-3309	92	40	r(2	r(2	PROPN
fuelectenerg-3309	92	41	m	m	NOUN
fuelectenerg-3309	92	42	)	)	PUNCT
fuelectenerg-3309	92	43	we	we	PRON
fuelectenerg-3309	92	44	shuffle	shuffle	VERB
fuelectenerg-3309	92	45	the	the	DET
fuelectenerg-3309	92	46	elements	element	NOUN
fuelectenerg-3309	92	47	of	of	ADP
fuelectenerg-3309	92	48	the	the	DET
fuelectenerg-3309	92	49	set	set	NOUN
fuelectenerg-3309	92	50	{	{	PUNCT
fuelectenerg-3309	92	51	0	0	NUM
fuelectenerg-3309	92	52	,	,	PUNCT
fuelectenerg-3309	92	53	...	...	PUNCT
fuelectenerg-3309	92	54	,	,	PUNCT
fuelectenerg-3309	92	55	2m−1	2m−1	NUM
fuelectenerg-3309	92	56	}	}	PUNCT
fuelectenerg-3309	92	57	and	and	CCONJ
fuelectenerg-3309	92	58	we	we	PRON
fuelectenerg-3309	92	59	discus	discus	VERB
fuelectenerg-3309	92	60	the	the	DET
fuelectenerg-3309	92	61	random	random	ADJ
fuelectenerg-3309	92	62	permutation	permutation	NOUN
fuelectenerg-3309	92	63	generation	generation	NOUN
fuelectenerg-3309	92	64	problem	problem	NOUN
fuelectenerg-3309	92	65	.	.	PUNCT
fuelectenerg-3309	93	1	2	2	NUM
fuelectenerg-3309	93	2	enumeration	enumeration	NOUN
fuelectenerg-3309	93	3	methods	method	NOUN
fuelectenerg-3309	93	4	for	for	ADP
fuelectenerg-3309	93	5	p	p	PROPN
fuelectenerg-3309	93	6	(	(	PUNCT
fuelectenerg-3309	93	7	m	m	NOUN
fuelectenerg-3309	93	8	)	)	PUNCT
fuelectenerg-3309	93	9	let	let	VERB
fuelectenerg-3309	93	10	m	m	PRON
fuelectenerg-3309	93	11	≥	≥	NOUN
fuelectenerg-3309	93	12	2	2	NUM
fuelectenerg-3309	93	13	be	be	AUX
fuelectenerg-3309	93	14	a	a	DET
fuelectenerg-3309	93	15	natural	natural	ADJ
fuelectenerg-3309	93	16	number	number	NOUN
fuelectenerg-3309	93	17	.	.	PUNCT
fuelectenerg-3309	94	1	first	first	ADV
fuelectenerg-3309	94	2	we	we	PRON
fuelectenerg-3309	94	3	review	review	VERB
fuelectenerg-3309	94	4	the	the	DET
fuelectenerg-3309	94	5	lexicographical	lexicographical	ADJ
fuelectenerg-3309	94	6	order	order	NOUN
fuelectenerg-3309	94	7	of	of	ADP
fuelectenerg-3309	94	8	the	the	DET
fuelectenerg-3309	94	9	set	set	NOUN
fuelectenerg-3309	94	10	s(m	s(m	PROPN
fuelectenerg-3309	94	11	)	)	PUNCT
fuelectenerg-3309	95	1	=	=	PRON
fuelectenerg-3309	95	2	{	{	PUNCT
fuelectenerg-3309	95	3	s	s	NOUN
fuelectenerg-3309	95	4	=	=	PUNCT
fuelectenerg-3309	95	5	(	(	PUNCT
fuelectenerg-3309	95	6	s1	s1	PROPN
fuelectenerg-3309	95	7	,	,	PUNCT
fuelectenerg-3309	95	8	...	...	PUNCT
fuelectenerg-3309	95	9	,	,	PUNCT
fuelectenerg-3309	95	10	sm	sm	PROPN
fuelectenerg-3309	95	11	)	)	PUNCT
fuelectenerg-3309	95	12	:	:	PUNCT
fuelectenerg-3309	95	13	si	si	PROPN
fuelectenerg-3309	95	14	∈	∈	PROPN
fuelectenerg-3309	95	15	{	{	PUNCT
fuelectenerg-3309	95	16	1	1	NUM
fuelectenerg-3309	95	17	,	,	PUNCT
fuelectenerg-3309	95	18	2	2	NUM
fuelectenerg-3309	95	19	,	,	PUNCT
fuelectenerg-3309	95	20	...	...	PUNCT
fuelectenerg-3309	95	21	,	,	PUNCT
fuelectenerg-3309	95	22	i	i	PRON
fuelectenerg-3309	95	23	}	}	PUNCT
fuelectenerg-3309	95	24	}	}	PUNCT
fuelectenerg-3309	95	25	.	.	PUNCT
fuelectenerg-3309	96	1	(	(	PUNCT
fuelectenerg-3309	96	2	1	1	X
fuelectenerg-3309	96	3	)	)	PUNCT
fuelectenerg-3309	96	4	obviously	obviously	ADV
fuelectenerg-3309	96	5	,	,	PUNCT
fuelectenerg-3309	96	6	the	the	DET
fuelectenerg-3309	96	7	map	map	NOUN
fuelectenerg-3309	96	8	u	u	NOUN
fuelectenerg-3309	96	9	:	:	PUNCT
fuelectenerg-3309	96	10	s(m	s(m	PROPN
fuelectenerg-3309	96	11	)	)	PUNCT
fuelectenerg-3309	96	12	→	→	SYM
fuelectenerg-3309	96	13	{	{	PUNCT
fuelectenerg-3309	96	14	0	0	NUM
fuelectenerg-3309	96	15	,	,	PUNCT
fuelectenerg-3309	96	16	...	...	PUNCT
fuelectenerg-3309	96	17	,	,	PUNCT
fuelectenerg-3309	96	18	m!−	m!−	VERB
fuelectenerg-3309	96	19	1	1	NUM
fuelectenerg-3309	96	20	}	}	PUNCT
fuelectenerg-3309	96	21	:	:	PUNCT
fuelectenerg-3309	96	22	u(s	u(s	X
fuelectenerg-3309	96	23	)	)	PUNCT
fuelectenerg-3309	96	24	=	=	PUNCT
fuelectenerg-3309	97	1	m	m	PROPN
fuelectenerg-3309	97	2	!	!	PUNCT
fuelectenerg-3309	97	3	m∑	m∑	X
fuelectenerg-3309	98	1	i=1	i=1	PROPN
fuelectenerg-3309	98	2	si	si	PROPN
fuelectenerg-3309	99	1	−	−	PROPN
fuelectenerg-3309	99	2	1	1	NUM
fuelectenerg-3309	99	3	i	i	PRON
fuelectenerg-3309	99	4	!	!	PUNCT
fuelectenerg-3309	100	1	(	(	PUNCT
fuelectenerg-3309	100	2	2	2	X
fuelectenerg-3309	100	3	)	)	PUNCT
fuelectenerg-3309	100	4	is	be	AUX
fuelectenerg-3309	100	5	a	a	DET
fuelectenerg-3309	100	6	bijection	bijection	NOUN
fuelectenerg-3309	100	7	and	and	CCONJ
fuelectenerg-3309	100	8	the	the	DET
fuelectenerg-3309	100	9	elements	element	NOUN
fuelectenerg-3309	100	10	si	si	X
fuelectenerg-3309	100	11	∈	∈	PROPN
fuelectenerg-3309	100	12	{	{	PUNCT
fuelectenerg-3309	100	13	1	1	NUM
fuelectenerg-3309	100	14	,	,	PUNCT
fuelectenerg-3309	100	15	...	...	PUNCT
fuelectenerg-3309	100	16	,	,	PUNCT
fuelectenerg-3309	100	17	i	i	PRON
fuelectenerg-3309	100	18	}	}	PUNCT
fuelectenerg-3309	100	19	can	can	AUX
fuelectenerg-3309	100	20	be	be	AUX
fuelectenerg-3309	100	21	thought	think	VERB
fuelectenerg-3309	100	22	of	of	ADP
fuelectenerg-3309	100	23	digits	digit	NOUN
fuelectenerg-3309	100	24	of	of	ADP
fuelectenerg-3309	100	25	the	the	DET
fuelectenerg-3309	100	26	number	number	NOUN
fuelectenerg-3309	100	27	u(s	u(s	PUNCT
fuelectenerg-3309	100	28	)	)	PUNCT
fuelectenerg-3309	100	29	with	with	ADP
fuelectenerg-3309	100	30	respect	respect	NOUN
fuelectenerg-3309	100	31	to	to	ADP
fuelectenerg-3309	100	32	the	the	DET
fuelectenerg-3309	100	33	factorial	factorial	ADJ
fuelectenerg-3309	100	34	number	number	NOUN
fuelectenerg-3309	100	35	system	system	NOUN
fuelectenerg-3309	100	36	.	.	PUNCT
fuelectenerg-3309	101	1	inversely	inversely	ADV
fuelectenerg-3309	101	2	,	,	PUNCT
fuelectenerg-3309	101	3	for	for	ADP
fuelectenerg-3309	101	4	any	any	DET
fuelectenerg-3309	101	5	n	n	ADV
fuelectenerg-3309	101	6	∈	∈	PROPN
fuelectenerg-3309	101	7	{	{	PUNCT
fuelectenerg-3309	101	8	0	0	NUM
fuelectenerg-3309	101	9	,	,	PUNCT
fuelectenerg-3309	101	10	...	...	PUNCT
fuelectenerg-3309	101	11	,	,	PUNCT
fuelectenerg-3309	101	12	m!−	m!−	VERB
fuelectenerg-3309	101	13	1	1	NUM
fuelectenerg-3309	101	14	}	}	PUNCT
fuelectenerg-3309	101	15	,	,	PUNCT
fuelectenerg-3309	101	16	its	its	PRON
fuelectenerg-3309	101	17	digits	digit	NOUN
fuelectenerg-3309	101	18	si(n	si(n	NOUN
fuelectenerg-3309	101	19	)	)	PUNCT
fuelectenerg-3309	101	20	,	,	PUNCT
fuelectenerg-3309	101	21	i	i	PRON
fuelectenerg-3309	101	22	=	=	NOUN
fuelectenerg-3309	101	23	1	1	NUM
fuelectenerg-3309	101	24	,	,	PUNCT
fuelectenerg-3309	101	25	...	...	PUNCT
fuelectenerg-3309	101	26	,	,	PUNCT
fuelectenerg-3309	101	27	m	m	VERB
fuelectenerg-3309	101	28	are	be	AUX
fuelectenerg-3309	101	29	computed	compute	VERB
fuelectenerg-3309	101	30	by	by	ADP
fuelectenerg-3309	101	31	the	the	DET
fuelectenerg-3309	101	32	formula	formula	NOUN
fuelectenerg-3309	101	33	si(n	si(n	NOUN
fuelectenerg-3309	101	34	)	)	PUNCT
fuelectenerg-3309	102	1	=	=	SYM
fuelectenerg-3309	102	2	mod	mod	NOUN
fuelectenerg-3309	102	3	(	(	PUNCT
fuelectenerg-3309	102	4	[	[	X
fuelectenerg-3309	102	5	n	n	X
fuelectenerg-3309	102	6	i	i	PRON
fuelectenerg-3309	102	7	!	!	PUNCT
fuelectenerg-3309	103	1	m	m	VERB
fuelectenerg-3309	103	2	!	!	PUNCT
fuelectenerg-3309	103	3	]	]	PUNCT
fuelectenerg-3309	104	1	,	,	PUNCT
fuelectenerg-3309	104	2	i	i	PRON
fuelectenerg-3309	104	3	)	)	PUNCT
fuelectenerg-3309	105	1	+	+	CCONJ
fuelectenerg-3309	105	2	1	1	NUM
fuelectenerg-3309	105	3	describing	describe	VERB
fuelectenerg-3309	105	4	the	the	DET
fuelectenerg-3309	105	5	inverse	inverse	NOUN
fuelectenerg-3309	105	6	map	map	NOUN
fuelectenerg-3309	105	7	u−1	u−1	PROPN
fuelectenerg-3309	105	8	.	.	PUNCT
fuelectenerg-3309	106	1	here	here	ADV
fuelectenerg-3309	106	2	,	,	PUNCT
fuelectenerg-3309	106	3	[	[	X
fuelectenerg-3309	106	4	x	x	X
fuelectenerg-3309	106	5	]	]	X
fuelectenerg-3309	106	6	is	be	AUX
fuelectenerg-3309	106	7	the	the	DET
fuelectenerg-3309	106	8	floor	floor	NOUN
fuelectenerg-3309	106	9	of	of	ADP
fuelectenerg-3309	106	10	x.	x.	NOUN
fuelectenerg-3309	106	11	from	from	ADP
fuelectenerg-3309	106	12	now	now	ADV
fuelectenerg-3309	106	13	on	on	ADV
fuelectenerg-3309	106	14	we	we	PRON
fuelectenerg-3309	106	15	say	say	VERB
fuelectenerg-3309	106	16	that	that	SCONJ
fuelectenerg-3309	106	17	u	u	PRON
fuelectenerg-3309	106	18	provides	provide	VERB
fuelectenerg-3309	106	19	the	the	DET
fuelectenerg-3309	106	20	lexicographical	lexicographical	ADJ
fuelectenerg-3309	106	21	order	order	NOUN
fuelectenerg-3309	106	22	of	of	ADP
fuelectenerg-3309	106	23	s(m	s(m	PROPN
fuelectenerg-3309	106	24	)	)	PUNCT
fuelectenerg-3309	106	25	.	.	PUNCT
fuelectenerg-3309	107	1	using	use	VERB
fuelectenerg-3309	107	2	the	the	DET
fuelectenerg-3309	107	3	lexicographical	lexicographical	ADJ
fuelectenerg-3309	107	4	order	order	NOUN
fuelectenerg-3309	107	5	of	of	ADP
fuelectenerg-3309	107	6	s(m	s(m	PROPN
fuelectenerg-3309	107	7	)	)	PUNCT
fuelectenerg-3309	107	8	we	we	PRON
fuelectenerg-3309	107	9	may	may	AUX
fuelectenerg-3309	107	10	obtain	obtain	VERB
fuelectenerg-3309	107	11	an	an	DET
fuelectenerg-3309	107	12	enumeration	enumeration	NOUN
fuelectenerg-3309	107	13	of	of	ADP
fuelectenerg-3309	107	14	the	the	DET
fuelectenerg-3309	107	15	group	group	NOUN
fuelectenerg-3309	107	16	of	of	ADP
fuelectenerg-3309	107	17	permutations	permutation	NOUN
fuelectenerg-3309	107	18	p	p	X
fuelectenerg-3309	107	19	(	(	PUNCT
fuelectenerg-3309	107	20	m	m	NOUN
fuelectenerg-3309	107	21	)	)	PUNCT
fuelectenerg-3309	107	22	of	of	ADP
fuelectenerg-3309	107	23	the	the	DET
fuelectenerg-3309	107	24	set	set	NOUN
fuelectenerg-3309	107	25	{	{	PUNCT
fuelectenerg-3309	107	26	1	1	NUM
fuelectenerg-3309	107	27	,	,	PUNCT
fuelectenerg-3309	107	28	...	...	PUNCT
fuelectenerg-3309	107	29	,	,	PUNCT
fuelectenerg-3309	107	30	m	m	VERB
fuelectenerg-3309	107	31	}	}	PUNCT
fuelectenerg-3309	107	32	as	as	ADV
fuelectenerg-3309	107	33	well	well	ADV
fuelectenerg-3309	107	34	.	.	PUNCT
fuelectenerg-3309	108	1	in	in	ADP
fuelectenerg-3309	108	2	fact	fact	NOUN
fuelectenerg-3309	108	3	,	,	PUNCT
fuelectenerg-3309	108	4	let	let	VERB
fuelectenerg-3309	108	5	us	we	PRON
fuelectenerg-3309	108	6	define	define	VERB
fuelectenerg-3309	108	7	the	the	DET
fuelectenerg-3309	108	8	map	map	NOUN
fuelectenerg-3309	108	9	q	q	NOUN
fuelectenerg-3309	108	10	:	:	PUNCT
fuelectenerg-3309	108	11	p	p	X
fuelectenerg-3309	108	12	(	(	PUNCT
fuelectenerg-3309	108	13	m	m	NOUN
fuelectenerg-3309	108	14	)	)	PUNCT
fuelectenerg-3309	108	15	→	→	SYM
fuelectenerg-3309	108	16	s(m	s(m	PROPN
fuelectenerg-3309	108	17	)	)	PUNCT
fuelectenerg-3309	108	18	:	:	PUNCT
fuelectenerg-3309	109	1	q(ρ	q(ρ	X
fuelectenerg-3309	109	2	)	)	PUNCT
fuelectenerg-3309	109	3	=	=	SYM
fuelectenerg-3309	109	4	s	s	NOUN
fuelectenerg-3309	109	5	=	=	PUNCT
fuelectenerg-3309	109	6	(	(	PUNCT
fuelectenerg-3309	109	7	s1	s1	PROPN
fuelectenerg-3309	109	8	,	,	PUNCT
fuelectenerg-3309	109	9	...	...	PUNCT
fuelectenerg-3309	109	10	,	,	PUNCT
fuelectenerg-3309	109	11	sm	sm	PROPN
fuelectenerg-3309	109	12	)	)	PUNCT
fuelectenerg-3309	109	13	,	,	PUNCT
fuelectenerg-3309	109	14	(	(	PUNCT
fuelectenerg-3309	109	15	3	3	X
fuelectenerg-3309	109	16	)	)	PUNCT
fuelectenerg-3309	109	17	where	where	SCONJ
fuelectenerg-3309	109	18	each	each	DET
fuelectenerg-3309	109	19	element	element	NOUN
fuelectenerg-3309	109	20	si	si	PROPN
fuelectenerg-3309	109	21	∈	∈	PROPN
fuelectenerg-3309	109	22	s(m	s(m	PROPN
fuelectenerg-3309	109	23	)	)	PUNCT
fuelectenerg-3309	109	24	is	be	AUX
fuelectenerg-3309	109	25	defined	define	VERB
fuelectenerg-3309	109	26	by	by	ADP
fuelectenerg-3309	109	27	using	use	VERB
fuelectenerg-3309	109	28	the	the	DET
fuelectenerg-3309	109	29	following	follow	VERB
fuelectenerg-3309	109	30	iteration	iteration	NOUN
fuelectenerg-3309	109	31	scheme	scheme	NOUN
fuelectenerg-3309	109	32	:	:	PUNCT
fuelectenerg-3309	109	33	enumeration	enumeration	NOUN
fuelectenerg-3309	109	34	and	and	CCONJ
fuelectenerg-3309	109	35	coding	code	VERB
fuelectenerg-3309	109	36	permutations	permutation	NOUN
fuelectenerg-3309	109	37	and	and	CCONJ
fuelectenerg-3309	109	38	reversible	reversible	ADJ
fuelectenerg-3309	109	39	logical	logical	ADJ
fuelectenerg-3309	109	40	circuits	circuit	NOUN
fuelectenerg-3309	109	41	3	3	NUM
fuelectenerg-3309	109	42	to	to	PART
fuelectenerg-3309	109	43	produce	produce	VERB
fuelectenerg-3309	109	44	a	a	DET
fuelectenerg-3309	109	45	class	class	NOUN
fuelectenerg-3309	109	46	of	of	ADP
fuelectenerg-3309	109	47	non	non	ADJ
fuelectenerg-3309	109	48	-	-	ADJ
fuelectenerg-3309	109	49	linear	linear	ADJ
fuelectenerg-3309	109	50	bijection	bijection	NOUN
fuelectenerg-3309	109	51	maps	map	NOUN
fuelectenerg-3309	109	52	tq	tq	ADP
fuelectenerg-3309	109	53	,	,	PUNCT
fuelectenerg-3309	109	54	ρ	ρ	PROPN
fuelectenerg-3309	109	55	,	,	PUNCT
fuelectenerg-3309	109	56	s	s	PART
fuelectenerg-3309	109	57	:	:	PUNCT
fuelectenerg-3309	109	58	{	{	PUNCT
fuelectenerg-3309	109	59	0	0	NUM
fuelectenerg-3309	109	60	,	,	PUNCT
fuelectenerg-3309	109	61	...	...	PUNCT
fuelectenerg-3309	109	62	,	,	PUNCT
fuelectenerg-3309	109	63	qm	qm	PROPN
fuelectenerg-3309	109	64	−	−	PROPN
fuelectenerg-3309	109	65	1	1	NUM
fuelectenerg-3309	109	66	}	}	PUNCT
fuelectenerg-3309	109	67	→	→	SYM
fuelectenerg-3309	109	68	{	{	PUNCT
fuelectenerg-3309	109	69	0	0	NUM
fuelectenerg-3309	109	70	,	,	PUNCT
fuelectenerg-3309	109	71	...	...	PUNCT
fuelectenerg-3309	109	72	,	,	PUNCT
fuelectenerg-3309	109	73	qm	qm	PROPN
fuelectenerg-3309	109	74	−	−	PROPN
fuelectenerg-3309	109	75	1	1	NUM
fuelectenerg-3309	109	76	}	}	PUNCT
fuelectenerg-3309	109	77	,	,	PUNCT
fuelectenerg-3309	109	78	see	see	VERB
fuelectenerg-3309	109	79	our	our	PRON
fuelectenerg-3309	109	80	main	main	ADJ
fuelectenerg-3309	109	81	theorem	theorem	NOUN
fuelectenerg-3309	109	82	2	2	NUM
fuelectenerg-3309	109	83	.	.	PUNCT
fuelectenerg-3309	109	84	in	in	ADP
fuelectenerg-3309	109	85	section	section	NOUN
fuelectenerg-3309	109	86	4	4	NUM
fuelectenerg-3309	109	87	we	we	PRON
fuelectenerg-3309	109	88	show	show	VERB
fuelectenerg-3309	109	89	that	that	SCONJ
fuelectenerg-3309	109	90	any	any	PRON
fuelectenerg-3309	109	91	triple	triple	ADJ
fuelectenerg-3309	109	92	(	(	PUNCT
fuelectenerg-3309	109	93	ρ	ρ	PROPN
fuelectenerg-3309	109	94	,	,	PUNCT
fuelectenerg-3309	109	95	s	s	PROPN
fuelectenerg-3309	109	96	,	,	PUNCT
fuelectenerg-3309	109	97	τ	τ	X
fuelectenerg-3309	109	98	)	)	PUNCT
fuelectenerg-3309	109	99	of	of	ADP
fuelectenerg-3309	109	100	permutations	permutation	NOUN
fuelectenerg-3309	109	101	in	in	ADP
fuelectenerg-3309	109	102	p	p	PROPN
fuelectenerg-3309	109	103	(	(	PUNCT
fuelectenerg-3309	109	104	m	m	NOUN
fuelectenerg-3309	109	105	)	)	PUNCT
fuelectenerg-3309	109	106	provides	provide	VERB
fuelectenerg-3309	109	107	a	a	DET
fuelectenerg-3309	109	108	variety	variety	NOUN
fuelectenerg-3309	109	109	of	of	ADP
fuelectenerg-3309	109	110	maps	map	NOUN
fuelectenerg-3309	109	111	from	from	ADP
fuelectenerg-3309	109	112	{	{	PUNCT
fuelectenerg-3309	109	113	0	0	NUM
fuelectenerg-3309	109	114	,	,	PUNCT
fuelectenerg-3309	109	115	...	...	PUNCT
fuelectenerg-3309	109	116	,	,	PUNCT
fuelectenerg-3309	109	117	2	2	NUM
fuelectenerg-3309	109	118	m	m	NOUN
fuelectenerg-3309	109	119	−	−	NOUN
fuelectenerg-3309	109	120	1	1	NUM
fuelectenerg-3309	109	121	}	}	PUNCT
fuelectenerg-3309	109	122	onto	onto	ADP
fuelectenerg-3309	109	123	{	{	PUNCT
fuelectenerg-3309	109	124	0	0	NUM
fuelectenerg-3309	109	125	,	,	PUNCT
fuelectenerg-3309	109	126	...	...	PUNCT
fuelectenerg-3309	109	127	,	,	PUNCT
fuelectenerg-3309	109	128	2	2	NUM
fuelectenerg-3309	109	129	m	m	NOUN
fuelectenerg-3309	109	130	−	−	NOUN
fuelectenerg-3309	109	131	1	1	NUM
fuelectenerg-3309	109	132	}	}	PUNCT
fuelectenerg-3309	109	133	and	and	CCONJ
fuelectenerg-3309	109	134	we	we	PRON
fuelectenerg-3309	109	135	see	see	VERB
fuelectenerg-3309	109	136	that	that	SCONJ
fuelectenerg-3309	109	137	several	several	ADJ
fuelectenerg-3309	109	138	reversible	reversible	ADJ
fuelectenerg-3309	109	139	logic	logic	NOUN
fuelectenerg-3309	109	140	gates	gate	NOUN
fuelectenerg-3309	109	141	can	can	AUX
fuelectenerg-3309	109	142	be	be	AUX
fuelectenerg-3309	109	143	determined	determine	VERB
fuelectenerg-3309	109	144	by	by	ADP
fuelectenerg-3309	109	145	this	this	DET
fuelectenerg-3309	109	146	triple	triple	NOUN
fuelectenerg-3309	109	147	.	.	PUNCT
fuelectenerg-3309	110	1	finally	finally	ADV
fuelectenerg-3309	110	2	,	,	PUNCT
fuelectenerg-3309	110	3	in	in	ADP
fuelectenerg-3309	110	4	section	section	NOUN
fuelectenerg-3309	110	5	5	5	NUM
fuelectenerg-3309	110	6	we	we	PRON
fuelectenerg-3309	110	7	apply	apply	VERB
fuelectenerg-3309	110	8	theorems	theorem	NOUN
fuelectenerg-3309	110	9	1	1	NUM
fuelectenerg-3309	110	10	and	and	CCONJ
fuelectenerg-3309	110	11	2	2	NUM
fuelectenerg-3309	110	12	,	,	PUNCT
fuelectenerg-3309	110	13	to	to	PART
fuelectenerg-3309	110	14	see	see	VERB
fuelectenerg-3309	110	15	with	with	ADP
fuelectenerg-3309	110	16	an	an	DET
fuelectenerg-3309	110	17	example	example	NOUN
fuelectenerg-3309	110	18	that	that	SCONJ
fuelectenerg-3309	110	19	for	for	ADP
fuelectenerg-3309	110	20	any	any	DET
fuelectenerg-3309	110	21	pair	pair	NOUN
fuelectenerg-3309	110	22	(	(	PUNCT
fuelectenerg-3309	110	23	ρ	ρ	PROPN
fuelectenerg-3309	110	24	,	,	PUNCT
fuelectenerg-3309	110	25	s	s	PART
fuelectenerg-3309	110	26	)	)	PUNCT
fuelectenerg-3309	110	27	∈	∈	PROPN
fuelectenerg-3309	110	28	p	p	X
fuelectenerg-3309	110	29	(	(	PUNCT
fuelectenerg-3309	110	30	m	m	NOUN
fuelectenerg-3309	110	31	)	)	PUNCT
fuelectenerg-3309	110	32	×	×	PROPN
fuelectenerg-3309	110	33	s(m	s(m	PROPN
fuelectenerg-3309	110	34	)	)	PUNCT
fuelectenerg-3309	110	35	and	and	CCONJ
fuelectenerg-3309	110	36	any	any	DET
fuelectenerg-3309	110	37	fixed	fix	VERB
fuelectenerg-3309	110	38	r	r	NOUN
fuelectenerg-3309	110	39	∈	∈	PROPN
fuelectenerg-3309	110	40	r(2	r(2	PROPN
fuelectenerg-3309	110	41	m	m	NOUN
fuelectenerg-3309	110	42	)	)	PUNCT
fuelectenerg-3309	110	43	we	we	PRON
fuelectenerg-3309	110	44	shuffle	shuffle	VERB
fuelectenerg-3309	110	45	the	the	DET
fuelectenerg-3309	110	46	elements	element	NOUN
fuelectenerg-3309	110	47	of	of	ADP
fuelectenerg-3309	110	48	the	the	DET
fuelectenerg-3309	110	49	set	set	NOUN
fuelectenerg-3309	110	50	{	{	PUNCT
fuelectenerg-3309	110	51	0	0	NUM
fuelectenerg-3309	110	52	,	,	PUNCT
fuelectenerg-3309	110	53	...	...	PUNCT
fuelectenerg-3309	110	54	,	,	PUNCT
fuelectenerg-3309	110	55	2m−1	2m−1	NUM
fuelectenerg-3309	110	56	}	}	PUNCT
fuelectenerg-3309	110	57	and	and	CCONJ
fuelectenerg-3309	110	58	we	we	PRON
fuelectenerg-3309	110	59	discus	discus	VERB
fuelectenerg-3309	110	60	the	the	DET
fuelectenerg-3309	110	61	random	random	ADJ
fuelectenerg-3309	110	62	permutation	permutation	NOUN
fuelectenerg-3309	110	63	generation	generation	NOUN
fuelectenerg-3309	110	64	problem	problem	NOUN
fuelectenerg-3309	110	65	.	.	PUNCT
fuelectenerg-3309	111	1	2	2	NUM
fuelectenerg-3309	111	2	enumeration	enumeration	NOUN
fuelectenerg-3309	111	3	methods	method	NOUN
fuelectenerg-3309	111	4	for	for	ADP
fuelectenerg-3309	111	5	p	p	PROPN
fuelectenerg-3309	111	6	(	(	PUNCT
fuelectenerg-3309	111	7	m	m	NOUN
fuelectenerg-3309	111	8	)	)	PUNCT
fuelectenerg-3309	111	9	let	let	VERB
fuelectenerg-3309	111	10	m	m	PRON
fuelectenerg-3309	111	11	≥	≥	NOUN
fuelectenerg-3309	111	12	2	2	NUM
fuelectenerg-3309	111	13	be	be	AUX
fuelectenerg-3309	111	14	a	a	DET
fuelectenerg-3309	111	15	natural	natural	ADJ
fuelectenerg-3309	111	16	number	number	NOUN
fuelectenerg-3309	111	17	.	.	PUNCT
fuelectenerg-3309	112	1	first	first	ADV
fuelectenerg-3309	112	2	we	we	PRON
fuelectenerg-3309	112	3	review	review	VERB
fuelectenerg-3309	112	4	the	the	DET
fuelectenerg-3309	112	5	lexicographical	lexicographical	ADJ
fuelectenerg-3309	112	6	order	order	NOUN
fuelectenerg-3309	112	7	of	of	ADP
fuelectenerg-3309	112	8	the	the	DET
fuelectenerg-3309	112	9	set	set	NOUN
fuelectenerg-3309	112	10	s(m	s(m	PROPN
fuelectenerg-3309	112	11	)	)	PUNCT
fuelectenerg-3309	113	1	=	=	PRON
fuelectenerg-3309	113	2	{	{	PUNCT
fuelectenerg-3309	113	3	s	s	NOUN
fuelectenerg-3309	113	4	=	=	PUNCT
fuelectenerg-3309	113	5	(	(	PUNCT
fuelectenerg-3309	113	6	s1	s1	PROPN
fuelectenerg-3309	113	7	,	,	PUNCT
fuelectenerg-3309	113	8	...	...	PUNCT
fuelectenerg-3309	113	9	,	,	PUNCT
fuelectenerg-3309	113	10	sm	sm	PROPN
fuelectenerg-3309	113	11	)	)	PUNCT
fuelectenerg-3309	113	12	:	:	PUNCT
fuelectenerg-3309	113	13	si	si	PROPN
fuelectenerg-3309	113	14	∈	∈	PROPN
fuelectenerg-3309	113	15	{	{	PUNCT
fuelectenerg-3309	113	16	1	1	NUM
fuelectenerg-3309	113	17	,	,	PUNCT
fuelectenerg-3309	113	18	2	2	NUM
fuelectenerg-3309	113	19	,	,	PUNCT
fuelectenerg-3309	113	20	...	...	PUNCT
fuelectenerg-3309	113	21	,	,	PUNCT
fuelectenerg-3309	113	22	i	i	PRON
fuelectenerg-3309	113	23	}	}	PUNCT
fuelectenerg-3309	113	24	}	}	PUNCT
fuelectenerg-3309	113	25	.	.	PUNCT
fuelectenerg-3309	114	1	(	(	PUNCT
fuelectenerg-3309	114	2	1	1	X
fuelectenerg-3309	114	3	)	)	PUNCT
fuelectenerg-3309	114	4	obviously	obviously	ADV
fuelectenerg-3309	114	5	,	,	PUNCT
fuelectenerg-3309	114	6	the	the	DET
fuelectenerg-3309	114	7	map	map	NOUN
fuelectenerg-3309	114	8	u	u	NOUN
fuelectenerg-3309	114	9	:	:	PUNCT
fuelectenerg-3309	114	10	s(m	s(m	PROPN
fuelectenerg-3309	114	11	)	)	PUNCT
fuelectenerg-3309	114	12	→	→	SYM
fuelectenerg-3309	114	13	{	{	PUNCT
fuelectenerg-3309	114	14	0	0	NUM
fuelectenerg-3309	114	15	,	,	PUNCT
fuelectenerg-3309	114	16	...	...	PUNCT
fuelectenerg-3309	114	17	,	,	PUNCT
fuelectenerg-3309	114	18	m!−	m!−	VERB
fuelectenerg-3309	114	19	1	1	NUM
fuelectenerg-3309	114	20	}	}	PUNCT
fuelectenerg-3309	114	21	:	:	PUNCT
fuelectenerg-3309	114	22	u(s	u(s	X
fuelectenerg-3309	114	23	)	)	PUNCT
fuelectenerg-3309	114	24	=	=	PUNCT
fuelectenerg-3309	115	1	m	m	PROPN
fuelectenerg-3309	115	2	!	!	PUNCT
fuelectenerg-3309	115	3	m∑	m∑	X
fuelectenerg-3309	116	1	i=1	i=1	PROPN
fuelectenerg-3309	116	2	si	si	PROPN
fuelectenerg-3309	117	1	−	−	PROPN
fuelectenerg-3309	117	2	1	1	NUM
fuelectenerg-3309	117	3	i	i	PRON
fuelectenerg-3309	117	4	!	!	PUNCT
fuelectenerg-3309	118	1	(	(	PUNCT
fuelectenerg-3309	118	2	2	2	X
fuelectenerg-3309	118	3	)	)	PUNCT
fuelectenerg-3309	118	4	is	be	AUX
fuelectenerg-3309	118	5	a	a	DET
fuelectenerg-3309	118	6	bijection	bijection	NOUN
fuelectenerg-3309	118	7	and	and	CCONJ
fuelectenerg-3309	118	8	the	the	DET
fuelectenerg-3309	118	9	elements	element	NOUN
fuelectenerg-3309	118	10	si	si	X
fuelectenerg-3309	118	11	∈	∈	PROPN
fuelectenerg-3309	118	12	{	{	PUNCT
fuelectenerg-3309	118	13	1	1	NUM
fuelectenerg-3309	118	14	,	,	PUNCT
fuelectenerg-3309	118	15	...	...	PUNCT
fuelectenerg-3309	118	16	,	,	PUNCT
fuelectenerg-3309	118	17	i	i	PRON
fuelectenerg-3309	118	18	}	}	PUNCT
fuelectenerg-3309	118	19	can	can	AUX
fuelectenerg-3309	118	20	be	be	AUX
fuelectenerg-3309	118	21	thought	think	VERB
fuelectenerg-3309	118	22	of	of	ADP
fuelectenerg-3309	118	23	digits	digit	NOUN
fuelectenerg-3309	118	24	of	of	ADP
fuelectenerg-3309	118	25	the	the	DET
fuelectenerg-3309	118	26	number	number	NOUN
fuelectenerg-3309	118	27	u(s	u(s	PUNCT
fuelectenerg-3309	118	28	)	)	PUNCT
fuelectenerg-3309	118	29	with	with	ADP
fuelectenerg-3309	118	30	respect	respect	NOUN
fuelectenerg-3309	118	31	to	to	ADP
fuelectenerg-3309	118	32	the	the	DET
fuelectenerg-3309	118	33	factorial	factorial	ADJ
fuelectenerg-3309	118	34	number	number	NOUN
fuelectenerg-3309	118	35	system	system	NOUN
fuelectenerg-3309	118	36	.	.	PUNCT
fuelectenerg-3309	119	1	inversely	inversely	ADV
fuelectenerg-3309	119	2	,	,	PUNCT
fuelectenerg-3309	119	3	for	for	ADP
fuelectenerg-3309	119	4	any	any	DET
fuelectenerg-3309	119	5	n	n	ADV
fuelectenerg-3309	119	6	∈	∈	PROPN
fuelectenerg-3309	119	7	{	{	PUNCT
fuelectenerg-3309	119	8	0	0	NUM
fuelectenerg-3309	119	9	,	,	PUNCT
fuelectenerg-3309	119	10	...	...	PUNCT
fuelectenerg-3309	119	11	,	,	PUNCT
fuelectenerg-3309	119	12	m!−	m!−	VERB
fuelectenerg-3309	119	13	1	1	NUM
fuelectenerg-3309	119	14	}	}	PUNCT
fuelectenerg-3309	119	15	,	,	PUNCT
fuelectenerg-3309	119	16	its	its	PRON
fuelectenerg-3309	119	17	digits	digit	NOUN
fuelectenerg-3309	119	18	si(n	si(n	NOUN
fuelectenerg-3309	119	19	)	)	PUNCT
fuelectenerg-3309	119	20	,	,	PUNCT
fuelectenerg-3309	119	21	i	i	PRON
fuelectenerg-3309	119	22	=	=	NOUN
fuelectenerg-3309	119	23	1	1	NUM
fuelectenerg-3309	119	24	,	,	PUNCT
fuelectenerg-3309	119	25	...	...	PUNCT
fuelectenerg-3309	119	26	,	,	PUNCT
fuelectenerg-3309	119	27	m	m	VERB
fuelectenerg-3309	119	28	are	be	AUX
fuelectenerg-3309	119	29	computed	compute	VERB
fuelectenerg-3309	119	30	by	by	ADP
fuelectenerg-3309	119	31	the	the	DET
fuelectenerg-3309	119	32	formula	formula	NOUN
fuelectenerg-3309	119	33	si(n	si(n	NOUN
fuelectenerg-3309	119	34	)	)	PUNCT
fuelectenerg-3309	120	1	=	=	SYM
fuelectenerg-3309	120	2	mod	mod	NOUN
fuelectenerg-3309	120	3	(	(	PUNCT
fuelectenerg-3309	120	4	[	[	X
fuelectenerg-3309	120	5	n	n	X
fuelectenerg-3309	120	6	i	i	PRON
fuelectenerg-3309	120	7	!	!	PUNCT
fuelectenerg-3309	121	1	m	m	VERB
fuelectenerg-3309	121	2	!	!	PUNCT
fuelectenerg-3309	121	3	]	]	PUNCT
fuelectenerg-3309	122	1	,	,	PUNCT
fuelectenerg-3309	122	2	i	i	PRON
fuelectenerg-3309	122	3	)	)	PUNCT
fuelectenerg-3309	123	1	+	+	CCONJ
fuelectenerg-3309	123	2	1	1	NUM
fuelectenerg-3309	123	3	describing	describe	VERB
fuelectenerg-3309	123	4	the	the	DET
fuelectenerg-3309	123	5	inverse	inverse	NOUN
fuelectenerg-3309	123	6	map	map	NOUN
fuelectenerg-3309	123	7	u−1	u−1	PROPN
fuelectenerg-3309	123	8	.	.	PUNCT
fuelectenerg-3309	124	1	here	here	ADV
fuelectenerg-3309	124	2	,	,	PUNCT
fuelectenerg-3309	124	3	[	[	X
fuelectenerg-3309	124	4	x	x	X
fuelectenerg-3309	124	5	]	]	X
fuelectenerg-3309	124	6	is	be	AUX
fuelectenerg-3309	124	7	the	the	DET
fuelectenerg-3309	124	8	floor	floor	NOUN
fuelectenerg-3309	124	9	of	of	ADP
fuelectenerg-3309	124	10	x.	x.	NOUN
fuelectenerg-3309	124	11	from	from	ADP
fuelectenerg-3309	124	12	now	now	ADV
fuelectenerg-3309	124	13	on	on	ADV
fuelectenerg-3309	124	14	we	we	PRON
fuelectenerg-3309	124	15	say	say	VERB
fuelectenerg-3309	124	16	that	that	SCONJ
fuelectenerg-3309	124	17	u	u	PRON
fuelectenerg-3309	124	18	provides	provide	VERB
fuelectenerg-3309	124	19	the	the	DET
fuelectenerg-3309	124	20	lexicographical	lexicographical	ADJ
fuelectenerg-3309	124	21	order	order	NOUN
fuelectenerg-3309	124	22	of	of	ADP
fuelectenerg-3309	124	23	s(m	s(m	PROPN
fuelectenerg-3309	124	24	)	)	PUNCT
fuelectenerg-3309	124	25	.	.	PUNCT
fuelectenerg-3309	125	1	using	use	VERB
fuelectenerg-3309	125	2	the	the	DET
fuelectenerg-3309	125	3	lexicographical	lexicographical	ADJ
fuelectenerg-3309	125	4	order	order	NOUN
fuelectenerg-3309	125	5	of	of	ADP
fuelectenerg-3309	125	6	s(m	s(m	PROPN
fuelectenerg-3309	125	7	)	)	PUNCT
fuelectenerg-3309	125	8	we	we	PRON
fuelectenerg-3309	125	9	may	may	AUX
fuelectenerg-3309	125	10	obtain	obtain	VERB
fuelectenerg-3309	125	11	an	an	DET
fuelectenerg-3309	125	12	enumeration	enumeration	NOUN
fuelectenerg-3309	125	13	of	of	ADP
fuelectenerg-3309	125	14	the	the	DET
fuelectenerg-3309	125	15	group	group	NOUN
fuelectenerg-3309	125	16	of	of	ADP
fuelectenerg-3309	125	17	permutations	permutation	NOUN
fuelectenerg-3309	125	18	p	p	X
fuelectenerg-3309	125	19	(	(	PUNCT
fuelectenerg-3309	125	20	m	m	NOUN
fuelectenerg-3309	125	21	)	)	PUNCT
fuelectenerg-3309	125	22	of	of	ADP
fuelectenerg-3309	125	23	the	the	DET
fuelectenerg-3309	125	24	set	set	NOUN
fuelectenerg-3309	125	25	{	{	PUNCT
fuelectenerg-3309	125	26	1	1	NUM
fuelectenerg-3309	125	27	,	,	PUNCT
fuelectenerg-3309	125	28	...	...	PUNCT
fuelectenerg-3309	125	29	,	,	PUNCT
fuelectenerg-3309	125	30	m	m	VERB
fuelectenerg-3309	125	31	}	}	PUNCT
fuelectenerg-3309	125	32	as	as	ADV
fuelectenerg-3309	125	33	well	well	ADV
fuelectenerg-3309	125	34	.	.	PUNCT
fuelectenerg-3309	126	1	in	in	ADP
fuelectenerg-3309	126	2	fact	fact	NOUN
fuelectenerg-3309	126	3	,	,	PUNCT
fuelectenerg-3309	126	4	let	let	VERB
fuelectenerg-3309	126	5	us	we	PRON
fuelectenerg-3309	126	6	define	define	VERB
fuelectenerg-3309	126	7	the	the	DET
fuelectenerg-3309	126	8	map	map	NOUN
fuelectenerg-3309	126	9	q	q	NOUN
fuelectenerg-3309	126	10	:	:	PUNCT
fuelectenerg-3309	126	11	p	p	X
fuelectenerg-3309	126	12	(	(	PUNCT
fuelectenerg-3309	126	13	m	m	NOUN
fuelectenerg-3309	126	14	)	)	PUNCT
fuelectenerg-3309	126	15	→	→	SYM
fuelectenerg-3309	126	16	s(m	s(m	PROPN
fuelectenerg-3309	126	17	)	)	PUNCT
fuelectenerg-3309	126	18	:	:	PUNCT
fuelectenerg-3309	127	1	q(ρ	q(ρ	X
fuelectenerg-3309	127	2	)	)	PUNCT
fuelectenerg-3309	127	3	=	=	SYM
fuelectenerg-3309	127	4	s	s	NOUN
fuelectenerg-3309	127	5	=	=	PUNCT
fuelectenerg-3309	127	6	(	(	PUNCT
fuelectenerg-3309	127	7	s1	s1	PROPN
fuelectenerg-3309	127	8	,	,	PUNCT
fuelectenerg-3309	127	9	...	...	PUNCT
fuelectenerg-3309	127	10	,	,	PUNCT
fuelectenerg-3309	127	11	sm	sm	PROPN
fuelectenerg-3309	127	12	)	)	PUNCT
fuelectenerg-3309	127	13	,	,	PUNCT
fuelectenerg-3309	127	14	(	(	PUNCT
fuelectenerg-3309	127	15	3	3	X
fuelectenerg-3309	127	16	)	)	PUNCT
fuelectenerg-3309	127	17	where	where	SCONJ
fuelectenerg-3309	127	18	each	each	DET
fuelectenerg-3309	127	19	element	element	NOUN
fuelectenerg-3309	127	20	si	si	PROPN
fuelectenerg-3309	127	21	∈	∈	PROPN
fuelectenerg-3309	127	22	s(m	s(m	PROPN
fuelectenerg-3309	127	23	)	)	PUNCT
fuelectenerg-3309	127	24	is	be	AUX
fuelectenerg-3309	127	25	defined	define	VERB
fuelectenerg-3309	127	26	by	by	ADP
fuelectenerg-3309	127	27	using	use	VERB
fuelectenerg-3309	127	28	the	the	DET
fuelectenerg-3309	127	29	following	follow	VERB
fuelectenerg-3309	127	30	iteration	iteration	NOUN
fuelectenerg-3309	127	31	scheme	scheme	NOUN
fuelectenerg-3309	127	32	:	:	PUNCT
fuelectenerg-3309	127	33	4	4	NUM
fuelectenerg-3309	127	34	n.	n.	NOUN
fuelectenerg-3309	127	35	atreas	atreas	PROPN
fuelectenerg-3309	127	36	and	and	CCONJ
fuelectenerg-3309	127	37	c.	c.	PROPN
fuelectenerg-3309	127	38	karanikas	karanikas	PROPN
fuelectenerg-3309	127	39	for	for	ADP
fuelectenerg-3309	127	40	the	the	DET
fuelectenerg-3309	127	41	above	above	ADJ
fuelectenerg-3309	127	42	selection	selection	NOUN
fuelectenerg-3309	127	43	of	of	ADP
fuelectenerg-3309	127	44	m	m	PROPN
fuelectenerg-3309	127	45	and	and	CCONJ
fuelectenerg-3309	127	46	the	the	DET
fuelectenerg-3309	127	47	initial	initial	ADJ
fuelectenerg-3309	127	48	permutation	permutation	NOUN
fuelectenerg-3309	127	49	ρ	ρ	PROPN
fuelectenerg-3309	127	50	in	in	ADP
fuelectenerg-3309	127	51	(	(	PUNCT
fuelectenerg-3309	127	52	3	3	NUM
fuelectenerg-3309	127	53	)	)	PUNCT
fuelectenerg-3309	127	54	,	,	PUNCT
fuelectenerg-3309	127	55	we	we	PRON
fuelectenerg-3309	127	56	store	store	VERB
fuelectenerg-3309	127	57	the	the	DET
fuelectenerg-3309	127	58	position	position	NOUN
fuelectenerg-3309	127	59	of	of	ADP
fuelectenerg-3309	127	60	the	the	DET
fuelectenerg-3309	127	61	biggest	big	ADJ
fuelectenerg-3309	127	62	element	element	NOUN
fuelectenerg-3309	127	63	in	in	ADP
fuelectenerg-3309	127	64	ρ	ρ	PROPN
fuelectenerg-3309	127	65	,	,	PUNCT
fuelectenerg-3309	127	66	i.e.	i.e.	X
fuelectenerg-3309	127	67	we	we	PRON
fuelectenerg-3309	127	68	define	define	VERB
fuelectenerg-3309	127	69	sm	sm	NOUN
fuelectenerg-3309	127	70	=	=	SYM
fuelectenerg-3309	127	71	ρ−1(m	ρ−1(m	NOUN
fuelectenerg-3309	127	72	)	)	PUNCT
fuelectenerg-3309	127	73	and	and	CCONJ
fuelectenerg-3309	127	74	at	at	ADP
fuelectenerg-3309	127	75	the	the	DET
fuelectenerg-3309	127	76	same	same	ADJ
fuelectenerg-3309	127	77	time	time	NOUN
fuelectenerg-3309	127	78	we	we	PRON
fuelectenerg-3309	127	79	delete	delete	VERB
fuelectenerg-3309	127	80	this	this	DET
fuelectenerg-3309	127	81	element	element	NOUN
fuelectenerg-3309	127	82	ρ(sm	ρ(sm	NOUN
fuelectenerg-3309	127	83	)	)	PUNCT
fuelectenerg-3309	127	84	=	=	PRON
fuelectenerg-3309	127	85	m	m	VERB
fuelectenerg-3309	127	86	from	from	ADP
fuelectenerg-3309	127	87	ρ	ρ	PROPN
fuelectenerg-3309	127	88	and	and	CCONJ
fuelectenerg-3309	127	89	so	so	ADV
fuelectenerg-3309	127	90	we	we	PRON
fuelectenerg-3309	127	91	form	form	VERB
fuelectenerg-3309	127	92	a	a	DET
fuelectenerg-3309	127	93	new	new	ADJ
fuelectenerg-3309	127	94	permutation	permutation	NOUN
fuelectenerg-3309	127	95	ρ(m−1	ρ(m−1	X
fuelectenerg-3309	127	96	)	)	PUNCT
fuelectenerg-3309	127	97	∈	∈	PROPN
fuelectenerg-3309	128	1	p	p	NOUN
fuelectenerg-3309	128	2	(	(	PUNCT
fuelectenerg-3309	128	3	m−	m−	PROPN
fuelectenerg-3309	128	4	1	1	NUM
fuelectenerg-3309	128	5	)	)	PUNCT
fuelectenerg-3309	128	6	by	by	ADP
fuelectenerg-3309	128	7	ρ(m−1)(j	ρ(m−1)(j	ADJ
fuelectenerg-3309	128	8	)	)	PUNCT
fuelectenerg-3309	128	9	=	=	SYM
fuelectenerg-3309	128	10	{	{	PUNCT
fuelectenerg-3309	128	11	ρ(j	ρ(j	PROPN
fuelectenerg-3309	128	12	)	)	PUNCT
fuelectenerg-3309	128	13	if	if	SCONJ
fuelectenerg-3309	128	14	j	j	PROPN
fuelectenerg-3309	128	15	<	<	X
fuelectenerg-3309	128	16	sm	sm	PROPN
fuelectenerg-3309	128	17	ρ(j	ρ(j	PROPN
fuelectenerg-3309	128	18	+	+	PROPN
fuelectenerg-3309	128	19	1	1	X
fuelectenerg-3309	128	20	)	)	PUNCT
fuelectenerg-3309	128	21	if	if	SCONJ
fuelectenerg-3309	128	22	j	j	PROPN
fuelectenerg-3309	128	23	≥	≥	AUX
fuelectenerg-3309	128	24	sm	sm	INTJ
fuelectenerg-3309	128	25	,	,	PUNCT
fuelectenerg-3309	128	26	j	j	PROPN
fuelectenerg-3309	128	27	=	=	SYM
fuelectenerg-3309	128	28	1	1	NUM
fuelectenerg-3309	128	29	,	,	PUNCT
fuelectenerg-3309	128	30	...	...	PUNCT
fuelectenerg-3309	128	31	,	,	PUNCT
fuelectenerg-3309	128	32	m−	m−	PROPN
fuelectenerg-3309	128	33	1	1	NUM
fuelectenerg-3309	128	34	.	.	PUNCT
fuelectenerg-3309	129	1	then	then	ADV
fuelectenerg-3309	129	2	we	we	PRON
fuelectenerg-3309	129	3	follow	follow	VERB
fuelectenerg-3309	129	4	the	the	DET
fuelectenerg-3309	129	5	previous	previous	ADJ
fuelectenerg-3309	129	6	step	step	NOUN
fuelectenerg-3309	129	7	for	for	ADP
fuelectenerg-3309	129	8	the	the	DET
fuelectenerg-3309	129	9	permutation	permutation	NOUN
fuelectenerg-3309	129	10	ρ(m−1	ρ(m−1	PROPN
fuelectenerg-3309	129	11	)	)	PUNCT
fuelectenerg-3309	129	12	,	,	PUNCT
fuelectenerg-3309	129	13	i.e.	i.e.	X
fuelectenerg-3309	129	14	we	we	PRON
fuelectenerg-3309	129	15	store	store	VERB
fuelectenerg-3309	129	16	the	the	DET
fuelectenerg-3309	129	17	position	position	NOUN
fuelectenerg-3309	129	18	of	of	ADP
fuelectenerg-3309	129	19	its	its	PRON
fuelectenerg-3309	129	20	biggest	big	ADJ
fuelectenerg-3309	129	21	element	element	NOUN
fuelectenerg-3309	129	22	by	by	ADP
fuelectenerg-3309	129	23	defining	define	VERB
fuelectenerg-3309	129	24	sm−1	sm−1	NOUN
fuelectenerg-3309	129	25	=	=	SYM
fuelectenerg-3309	130	1	ρ−1	ρ−1	PROPN
fuelectenerg-3309	130	2	(	(	PUNCT
fuelectenerg-3309	130	3	m−1)(m−	m−1)(m−	NOUN
fuelectenerg-3309	130	4	1	1	NUM
fuelectenerg-3309	130	5	)	)	PUNCT
fuelectenerg-3309	130	6	and	and	CCONJ
fuelectenerg-3309	130	7	at	at	ADP
fuelectenerg-3309	130	8	the	the	DET
fuelectenerg-3309	130	9	same	same	ADJ
fuelectenerg-3309	130	10	time	time	NOUN
fuelectenerg-3309	130	11	we	we	PRON
fuelectenerg-3309	130	12	delete	delete	VERB
fuelectenerg-3309	130	13	the	the	DET
fuelectenerg-3309	130	14	element	element	NOUN
fuelectenerg-3309	130	15	m−	m−	PROPN
fuelectenerg-3309	130	16	1	1	NUM
fuelectenerg-3309	130	17	from	from	ADP
fuelectenerg-3309	130	18	ρ(m−1	ρ(m−1	PROPN
fuelectenerg-3309	130	19	)	)	PUNCT
fuelectenerg-3309	130	20	and	and	CCONJ
fuelectenerg-3309	130	21	we	we	PRON
fuelectenerg-3309	130	22	form	form	VERB
fuelectenerg-3309	130	23	a	a	DET
fuelectenerg-3309	130	24	new	new	ADJ
fuelectenerg-3309	130	25	permutation	permutation	NOUN
fuelectenerg-3309	130	26	ρ(m−2	ρ(m−2	X
fuelectenerg-3309	130	27	)	)	PUNCT
fuelectenerg-3309	130	28	∈	∈	PROPN
fuelectenerg-3309	130	29	p	p	X
fuelectenerg-3309	130	30	(	(	PUNCT
fuelectenerg-3309	130	31	m−	m−	PROPN
fuelectenerg-3309	130	32	2	2	NUM
fuelectenerg-3309	130	33	)	)	PUNCT
fuelectenerg-3309	130	34	by	by	ADP
fuelectenerg-3309	130	35	ρ(m−2)(j	ρ(m−2)(j	NOUN
fuelectenerg-3309	130	36	)	)	PUNCT
fuelectenerg-3309	130	37	=	=	PRON
fuelectenerg-3309	130	38	{	{	PUNCT
fuelectenerg-3309	130	39	ρ(m−1)(j	ρ(m−1)(j	ADJ
fuelectenerg-3309	130	40	)	)	PUNCT
fuelectenerg-3309	130	41	if	if	SCONJ
fuelectenerg-3309	130	42	j	j	PROPN
fuelectenerg-3309	130	43	<	<	X
fuelectenerg-3309	130	44	sm−1	sm−1	PROPN
fuelectenerg-3309	130	45	ρ(m−1)(j	ρ(m−1)(j	NOUN
fuelectenerg-3309	131	1	+	+	CCONJ
fuelectenerg-3309	132	1	1	1	X
fuelectenerg-3309	132	2	)	)	PUNCT
fuelectenerg-3309	132	3	if	if	SCONJ
fuelectenerg-3309	132	4	j	j	PROPN
fuelectenerg-3309	132	5	≥	≥	AUX
fuelectenerg-3309	132	6	sm−1	sm−1	PROPN
fuelectenerg-3309	132	7	,	,	PUNCT
fuelectenerg-3309	132	8	j	j	PROPN
fuelectenerg-3309	132	9	=	=	SYM
fuelectenerg-3309	132	10	1	1	NUM
fuelectenerg-3309	132	11	,	,	PUNCT
fuelectenerg-3309	132	12	...	...	PUNCT
fuelectenerg-3309	132	13	,	,	PUNCT
fuelectenerg-3309	132	14	m−	m−	PROPN
fuelectenerg-3309	132	15	2	2	NUM
fuelectenerg-3309	132	16	.	.	PUNCT
fuelectenerg-3309	132	17	we	we	PRON
fuelectenerg-3309	132	18	continue	continue	VERB
fuelectenerg-3309	132	19	in	in	ADP
fuelectenerg-3309	132	20	the	the	DET
fuelectenerg-3309	132	21	same	same	ADJ
fuelectenerg-3309	132	22	spirit	spirit	NOUN
fuelectenerg-3309	132	23	until	until	SCONJ
fuelectenerg-3309	132	24	s	s	NOUN
fuelectenerg-3309	132	25	is	be	AUX
fuelectenerg-3309	132	26	completely	completely	ADV
fuelectenerg-3309	132	27	determined	determine	VERB
fuelectenerg-3309	132	28	.	.	PUNCT
fuelectenerg-3309	133	1	example	example	NOUN
fuelectenerg-3309	134	1	1	1	NUM
fuelectenerg-3309	134	2	let	let	VERB
fuelectenerg-3309	134	3	ρ	ρ	PROPN
fuelectenerg-3309	134	4	=	=	SYM
fuelectenerg-3309	134	5	(	(	PUNCT
fuelectenerg-3309	134	6	2	2	NUM
fuelectenerg-3309	134	7	,	,	PUNCT
fuelectenerg-3309	134	8	3	3	NUM
fuelectenerg-3309	134	9	,	,	PUNCT
fuelectenerg-3309	134	10	4	4	NUM
fuelectenerg-3309	134	11	,	,	PUNCT
fuelectenerg-3309	134	12	1	1	NUM
fuelectenerg-3309	134	13	)	)	PUNCT
fuelectenerg-3309	134	14	.	.	PUNCT
fuelectenerg-3309	135	1	in	in	ADP
fuelectenerg-3309	135	2	order	order	NOUN
fuelectenerg-3309	135	3	to	to	PART
fuelectenerg-3309	135	4	determine	determine	VERB
fuelectenerg-3309	135	5	the	the	DET
fuelectenerg-3309	135	6	set	set	NOUN
fuelectenerg-3309	135	7	s	s	PART
fuelectenerg-3309	135	8	=	=	NOUN
fuelectenerg-3309	135	9	{	{	PUNCT
fuelectenerg-3309	135	10	s1	s1	NOUN
fuelectenerg-3309	135	11	,	,	PUNCT
fuelectenerg-3309	135	12	s2	s2	PROPN
fuelectenerg-3309	135	13	,	,	PUNCT
fuelectenerg-3309	135	14	s3	s3	PROPN
fuelectenerg-3309	135	15	,	,	PUNCT
fuelectenerg-3309	135	16	s4	s4	PROPN
fuelectenerg-3309	135	17	}	}	PUNCT
fuelectenerg-3309	135	18	in	in	ADP
fuelectenerg-3309	135	19	(	(	PUNCT
fuelectenerg-3309	135	20	3	3	X
fuelectenerg-3309	135	21	)	)	PUNCT
fuelectenerg-3309	135	22	we	we	PRON
fuelectenerg-3309	135	23	are	be	AUX
fuelectenerg-3309	135	24	based	base	VERB
fuelectenerg-3309	135	25	on	on	ADP
fuelectenerg-3309	135	26	the	the	DET
fuelectenerg-3309	135	27	above	above	ADJ
fuelectenerg-3309	135	28	iteration	iteration	NOUN
fuelectenerg-3309	135	29	scheme	scheme	NOUN
fuelectenerg-3309	135	30	and	and	CCONJ
fuelectenerg-3309	135	31	so	so	ADV
fuelectenerg-3309	135	32	we	we	PRON
fuelectenerg-3309	135	33	proceed	proceed	VERB
fuelectenerg-3309	135	34	in	in	ADP
fuelectenerg-3309	135	35	the	the	DET
fuelectenerg-3309	135	36	following	following	ADJ
fuelectenerg-3309	135	37	way	way	NOUN
fuelectenerg-3309	135	38	:	:	PUNCT
fuelectenerg-3309	135	39	(	(	PUNCT
fuelectenerg-3309	135	40	i	i	NOUN
fuelectenerg-3309	135	41	)	)	PUNCT
fuelectenerg-3309	135	42	define	define	VERB
fuelectenerg-3309	135	43	s4	s4	NOUN
fuelectenerg-3309	135	44	=	=	SYM
fuelectenerg-3309	135	45	ρ−1(4	ρ−1(4	X
fuelectenerg-3309	135	46	)	)	PUNCT
fuelectenerg-3309	135	47	=	=	SYM
fuelectenerg-3309	135	48	3	3	NUM
fuelectenerg-3309	135	49	and	and	CCONJ
fuelectenerg-3309	135	50	ρ(3	ρ(3	NUM
fuelectenerg-3309	135	51	)	)	PUNCT
fuelectenerg-3309	135	52	=	=	PUNCT
fuelectenerg-3309	135	53	(	(	PUNCT
fuelectenerg-3309	135	54	2	2	NUM
fuelectenerg-3309	135	55	,	,	PUNCT
fuelectenerg-3309	135	56	3	3	NUM
fuelectenerg-3309	135	57	,	,	PUNCT
fuelectenerg-3309	135	58	1	1	NUM
fuelectenerg-3309	135	59	)	)	PUNCT
fuelectenerg-3309	135	60	.	.	PUNCT
fuelectenerg-3309	136	1	(	(	PUNCT
fuelectenerg-3309	136	2	ii	ii	NOUN
fuelectenerg-3309	136	3	)	)	PUNCT
fuelectenerg-3309	136	4	define	define	VERB
fuelectenerg-3309	136	5	s3	s3	PROPN
fuelectenerg-3309	136	6	=	=	PROPN
fuelectenerg-3309	136	7	ρ−1	ρ−1	PROPN
fuelectenerg-3309	136	8	(	(	PUNCT
fuelectenerg-3309	136	9	3)(3	3)(3	NUM
fuelectenerg-3309	136	10	)	)	PUNCT
fuelectenerg-3309	136	11	=	=	SYM
fuelectenerg-3309	136	12	2	2	NUM
fuelectenerg-3309	136	13	and	and	CCONJ
fuelectenerg-3309	136	14	ρ(2	ρ(2	PROPN
fuelectenerg-3309	136	15	)	)	PUNCT
fuelectenerg-3309	137	1	=	=	PUNCT
fuelectenerg-3309	137	2	(	(	PUNCT
fuelectenerg-3309	137	3	2	2	NUM
fuelectenerg-3309	137	4	,	,	PUNCT
fuelectenerg-3309	137	5	1	1	NUM
fuelectenerg-3309	137	6	)	)	PUNCT
fuelectenerg-3309	137	7	.	.	PUNCT
fuelectenerg-3309	138	1	(	(	PUNCT
fuelectenerg-3309	138	2	iii	iii	X
fuelectenerg-3309	138	3	)	)	PUNCT
fuelectenerg-3309	138	4	define	define	VERB
fuelectenerg-3309	138	5	s2	s2	NOUN
fuelectenerg-3309	138	6	=	=	SYM
fuelectenerg-3309	138	7	ρ−1	ρ−1	PROPN
fuelectenerg-3309	138	8	(	(	PUNCT
fuelectenerg-3309	138	9	2)(2	2)(2	NUM
fuelectenerg-3309	138	10	)	)	PUNCT
fuelectenerg-3309	138	11	=	=	SYM
fuelectenerg-3309	138	12	1	1	NUM
fuelectenerg-3309	138	13	and	and	CCONJ
fuelectenerg-3309	138	14	ρ(1	ρ(1	PROPN
fuelectenerg-3309	138	15	)	)	PUNCT
fuelectenerg-3309	138	16	=	=	PUNCT
fuelectenerg-3309	138	17	(	(	PUNCT
fuelectenerg-3309	138	18	1	1	NUM
fuelectenerg-3309	138	19	)	)	PUNCT
fuelectenerg-3309	138	20	.	.	PUNCT
fuelectenerg-3309	139	1	(	(	PUNCT
fuelectenerg-3309	139	2	iv	iv	X
fuelectenerg-3309	139	3	)	)	PUNCT
fuelectenerg-3309	139	4	define	define	VERB
fuelectenerg-3309	139	5	s1	s1	NOUN
fuelectenerg-3309	139	6	=	=	SYM
fuelectenerg-3309	139	7	ρ−1	ρ−1	PROPN
fuelectenerg-3309	139	8	(	(	PUNCT
fuelectenerg-3309	139	9	1)(1	1)(1	NUM
fuelectenerg-3309	139	10	)	)	PUNCT
fuelectenerg-3309	139	11	=	=	SYM
fuelectenerg-3309	139	12	1	1	NUM
fuelectenerg-3309	139	13	and	and	CCONJ
fuelectenerg-3309	139	14	ρ(4	ρ(4	NOUN
fuelectenerg-3309	139	15	)	)	PUNCT
fuelectenerg-3309	140	1	=	=	PUNCT
fuelectenerg-3309	140	2	∅.	∅.	ADP
fuelectenerg-3309	140	3	now	now	ADV
fuelectenerg-3309	140	4	we	we	PRON
fuelectenerg-3309	140	5	have	have	VERB
fuelectenerg-3309	140	6	the	the	DET
fuelectenerg-3309	140	7	following	following	NOUN
fuelectenerg-3309	140	8	:	:	PUNCT
fuelectenerg-3309	140	9	proposition	proposition	NOUN
fuelectenerg-3309	140	10	1	1	NUM
fuelectenerg-3309	140	11	[	[	X
fuelectenerg-3309	140	12	2	2	X
fuelectenerg-3309	140	13	]	]	PUNCT
fuelectenerg-3309	140	14	let	let	VERB
fuelectenerg-3309	140	15	u	u	PRON
fuelectenerg-3309	140	16	and	and	CCONJ
fuelectenerg-3309	140	17	q	q	NOUN
fuelectenerg-3309	140	18	be	be	AUX
fuelectenerg-3309	140	19	two	two	NUM
fuelectenerg-3309	140	20	maps	map	NOUN
fuelectenerg-3309	140	21	as	as	ADP
fuelectenerg-3309	140	22	in	in	ADP
fuelectenerg-3309	140	23	(	(	PUNCT
fuelectenerg-3309	140	24	2	2	NUM
fuelectenerg-3309	140	25	)	)	PUNCT
fuelectenerg-3309	140	26	and	and	CCONJ
fuelectenerg-3309	140	27	(	(	PUNCT
fuelectenerg-3309	140	28	3	3	X
fuelectenerg-3309	140	29	)	)	PUNCT
fuelectenerg-3309	140	30	respectively	respectively	ADV
fuelectenerg-3309	140	31	.	.	PUNCT
fuelectenerg-3309	141	1	then	then	ADV
fuelectenerg-3309	141	2	q	q	X
fuelectenerg-3309	141	3	is	be	AUX
fuelectenerg-3309	141	4	a	a	DET
fuelectenerg-3309	141	5	bijection	bijection	NOUN
fuelectenerg-3309	141	6	and	and	CCONJ
fuelectenerg-3309	141	7	so	so	ADV
fuelectenerg-3309	141	8	the	the	DET
fuelectenerg-3309	141	9	composition	composition	NOUN
fuelectenerg-3309	141	10	map	map	NOUN
fuelectenerg-3309	141	11	uq	uq	NOUN
fuelectenerg-3309	141	12	:	:	PUNCT
fuelectenerg-3309	141	13	p	p	X
fuelectenerg-3309	141	14	(	(	PUNCT
fuelectenerg-3309	141	15	m	m	NOUN
fuelectenerg-3309	141	16	)	)	PUNCT
fuelectenerg-3309	141	17	→	→	SYM
fuelectenerg-3309	141	18	{	{	PUNCT
fuelectenerg-3309	141	19	0	0	NUM
fuelectenerg-3309	141	20	,	,	PUNCT
fuelectenerg-3309	141	21	...	...	PUNCT
fuelectenerg-3309	141	22	,	,	PUNCT
fuelectenerg-3309	141	23	m!−	m!−	VERB
fuelectenerg-3309	141	24	1	1	NUM
fuelectenerg-3309	141	25	}	}	PUNCT
fuelectenerg-3309	141	26	provides	provide	VERB
fuelectenerg-3309	141	27	an	an	DET
fuelectenerg-3309	141	28	enumeration	enumeration	NOUN
fuelectenerg-3309	141	29	of	of	ADP
fuelectenerg-3309	141	30	p	p	PROPN
fuelectenerg-3309	141	31	(	(	PUNCT
fuelectenerg-3309	141	32	m	m	NOUN
fuelectenerg-3309	141	33	)	)	PUNCT
fuelectenerg-3309	141	34	.	.	PUNCT
fuelectenerg-3309	142	1	242	242	NUM
fuelectenerg-3309	142	2	c.	c.	PROPN
fuelectenerg-3309	142	3	karanikas	karanikas	PROPN
fuelectenerg-3309	142	4	,	,	PUNCT
fuelectenerg-3309	142	5	n.	n.	PROPN
fuelectenerg-3309	142	6	atreas	atreas	PROPN
fuelectenerg-3309	142	7	enumeration	enumeration	PROPN
fuelectenerg-3309	142	8	and	and	CCONJ
fuelectenerg-3309	142	9	coding	code	VERB
fuelectenerg-3309	142	10	permutations	permutation	NOUN
fuelectenerg-3309	142	11	and	and	CCONJ
fuelectenerg-3309	142	12	reversible	reversible	ADJ
fuelectenerg-3309	142	13	logical	logical	ADJ
fuelectenerg-3309	142	14	circuits	circuit	NOUN
fuelectenerg-3309	142	15	243	243	NUM
fuelectenerg-3309	142	16	4	4	NUM
fuelectenerg-3309	142	17	n.	n.	NOUN
fuelectenerg-3309	142	18	atreas	atreas	PROPN
fuelectenerg-3309	142	19	and	and	CCONJ
fuelectenerg-3309	142	20	c.	c.	PROPN
fuelectenerg-3309	142	21	karanikas	karanikas	PROPN
fuelectenerg-3309	142	22	for	for	ADP
fuelectenerg-3309	142	23	the	the	DET
fuelectenerg-3309	142	24	above	above	ADJ
fuelectenerg-3309	142	25	selection	selection	NOUN
fuelectenerg-3309	142	26	of	of	ADP
fuelectenerg-3309	142	27	m	m	PROPN
fuelectenerg-3309	142	28	and	and	CCONJ
fuelectenerg-3309	142	29	the	the	DET
fuelectenerg-3309	142	30	initial	initial	ADJ
fuelectenerg-3309	142	31	permutation	permutation	NOUN
fuelectenerg-3309	142	32	ρ	ρ	PROPN
fuelectenerg-3309	142	33	in	in	ADP
fuelectenerg-3309	142	34	(	(	PUNCT
fuelectenerg-3309	142	35	3	3	NUM
fuelectenerg-3309	142	36	)	)	PUNCT
fuelectenerg-3309	142	37	,	,	PUNCT
fuelectenerg-3309	142	38	we	we	PRON
fuelectenerg-3309	142	39	store	store	VERB
fuelectenerg-3309	142	40	the	the	DET
fuelectenerg-3309	142	41	position	position	NOUN
fuelectenerg-3309	142	42	of	of	ADP
fuelectenerg-3309	142	43	the	the	DET
fuelectenerg-3309	142	44	biggest	big	ADJ
fuelectenerg-3309	142	45	element	element	NOUN
fuelectenerg-3309	142	46	in	in	ADP
fuelectenerg-3309	142	47	ρ	ρ	PROPN
fuelectenerg-3309	142	48	,	,	PUNCT
fuelectenerg-3309	142	49	i.e.	i.e.	X
fuelectenerg-3309	142	50	we	we	PRON
fuelectenerg-3309	142	51	define	define	VERB
fuelectenerg-3309	142	52	sm	sm	NOUN
fuelectenerg-3309	142	53	=	=	SYM
fuelectenerg-3309	142	54	ρ−1(m	ρ−1(m	NOUN
fuelectenerg-3309	142	55	)	)	PUNCT
fuelectenerg-3309	142	56	and	and	CCONJ
fuelectenerg-3309	142	57	at	at	ADP
fuelectenerg-3309	142	58	the	the	DET
fuelectenerg-3309	142	59	same	same	ADJ
fuelectenerg-3309	142	60	time	time	NOUN
fuelectenerg-3309	142	61	we	we	PRON
fuelectenerg-3309	142	62	delete	delete	VERB
fuelectenerg-3309	142	63	this	this	DET
fuelectenerg-3309	142	64	element	element	NOUN
fuelectenerg-3309	142	65	ρ(sm	ρ(sm	NOUN
fuelectenerg-3309	142	66	)	)	PUNCT
fuelectenerg-3309	142	67	=	=	PRON
fuelectenerg-3309	142	68	m	m	VERB
fuelectenerg-3309	142	69	from	from	ADP
fuelectenerg-3309	142	70	ρ	ρ	PROPN
fuelectenerg-3309	142	71	and	and	CCONJ
fuelectenerg-3309	142	72	so	so	ADV
fuelectenerg-3309	142	73	we	we	PRON
fuelectenerg-3309	142	74	form	form	VERB
fuelectenerg-3309	142	75	a	a	DET
fuelectenerg-3309	142	76	new	new	ADJ
fuelectenerg-3309	142	77	permutation	permutation	NOUN
fuelectenerg-3309	142	78	ρ(m−1	ρ(m−1	X
fuelectenerg-3309	143	1	)	)	PUNCT
fuelectenerg-3309	143	2	∈	∈	PROPN
fuelectenerg-3309	144	1	p	p	NOUN
fuelectenerg-3309	144	2	(	(	PUNCT
fuelectenerg-3309	144	3	m−	m−	PROPN
fuelectenerg-3309	144	4	1	1	NUM
fuelectenerg-3309	144	5	)	)	PUNCT
fuelectenerg-3309	144	6	by	by	ADP
fuelectenerg-3309	144	7	ρ(m−1)(j	ρ(m−1)(j	ADJ
fuelectenerg-3309	144	8	)	)	PUNCT
fuelectenerg-3309	144	9	=	=	SYM
fuelectenerg-3309	144	10	{	{	PUNCT
fuelectenerg-3309	144	11	ρ(j	ρ(j	PROPN
fuelectenerg-3309	144	12	)	)	PUNCT
fuelectenerg-3309	144	13	if	if	SCONJ
fuelectenerg-3309	144	14	j	j	PROPN
fuelectenerg-3309	144	15	<	<	X
fuelectenerg-3309	144	16	sm	sm	PROPN
fuelectenerg-3309	144	17	ρ(j	ρ(j	PROPN
fuelectenerg-3309	144	18	+	+	PROPN
fuelectenerg-3309	144	19	1	1	X
fuelectenerg-3309	144	20	)	)	PUNCT
fuelectenerg-3309	144	21	if	if	SCONJ
fuelectenerg-3309	144	22	j	j	PROPN
fuelectenerg-3309	144	23	≥	≥	AUX
fuelectenerg-3309	144	24	sm	sm	INTJ
fuelectenerg-3309	144	25	,	,	PUNCT
fuelectenerg-3309	144	26	j	j	PROPN
fuelectenerg-3309	144	27	=	=	SYM
fuelectenerg-3309	144	28	1	1	NUM
fuelectenerg-3309	144	29	,	,	PUNCT
fuelectenerg-3309	144	30	...	...	PUNCT
fuelectenerg-3309	144	31	,	,	PUNCT
fuelectenerg-3309	144	32	m−	m−	PROPN
fuelectenerg-3309	144	33	1	1	NUM
fuelectenerg-3309	144	34	.	.	PUNCT
fuelectenerg-3309	145	1	then	then	ADV
fuelectenerg-3309	145	2	we	we	PRON
fuelectenerg-3309	145	3	follow	follow	VERB
fuelectenerg-3309	145	4	the	the	DET
fuelectenerg-3309	145	5	previous	previous	ADJ
fuelectenerg-3309	145	6	step	step	NOUN
fuelectenerg-3309	145	7	for	for	ADP
fuelectenerg-3309	145	8	the	the	DET
fuelectenerg-3309	145	9	permutation	permutation	NOUN
fuelectenerg-3309	145	10	ρ(m−1	ρ(m−1	PROPN
fuelectenerg-3309	145	11	)	)	PUNCT
fuelectenerg-3309	145	12	,	,	PUNCT
fuelectenerg-3309	145	13	i.e.	i.e.	X
fuelectenerg-3309	145	14	we	we	PRON
fuelectenerg-3309	145	15	store	store	VERB
fuelectenerg-3309	145	16	the	the	DET
fuelectenerg-3309	145	17	position	position	NOUN
fuelectenerg-3309	145	18	of	of	ADP
fuelectenerg-3309	145	19	its	its	PRON
fuelectenerg-3309	145	20	biggest	big	ADJ
fuelectenerg-3309	145	21	element	element	NOUN
fuelectenerg-3309	145	22	by	by	ADP
fuelectenerg-3309	145	23	defining	define	VERB
fuelectenerg-3309	145	24	sm−1	sm−1	NOUN
fuelectenerg-3309	145	25	=	=	SYM
fuelectenerg-3309	146	1	ρ−1	ρ−1	PROPN
fuelectenerg-3309	146	2	(	(	PUNCT
fuelectenerg-3309	146	3	m−1)(m−	m−1)(m−	NOUN
fuelectenerg-3309	146	4	1	1	NUM
fuelectenerg-3309	146	5	)	)	PUNCT
fuelectenerg-3309	146	6	and	and	CCONJ
fuelectenerg-3309	146	7	at	at	ADP
fuelectenerg-3309	146	8	the	the	DET
fuelectenerg-3309	146	9	same	same	ADJ
fuelectenerg-3309	146	10	time	time	NOUN
fuelectenerg-3309	146	11	we	we	PRON
fuelectenerg-3309	146	12	delete	delete	VERB
fuelectenerg-3309	146	13	the	the	DET
fuelectenerg-3309	146	14	element	element	NOUN
fuelectenerg-3309	146	15	m−	m−	PROPN
fuelectenerg-3309	146	16	1	1	NUM
fuelectenerg-3309	146	17	from	from	ADP
fuelectenerg-3309	146	18	ρ(m−1	ρ(m−1	PROPN
fuelectenerg-3309	146	19	)	)	PUNCT
fuelectenerg-3309	146	20	and	and	CCONJ
fuelectenerg-3309	146	21	we	we	PRON
fuelectenerg-3309	146	22	form	form	VERB
fuelectenerg-3309	146	23	a	a	DET
fuelectenerg-3309	146	24	new	new	ADJ
fuelectenerg-3309	146	25	permutation	permutation	NOUN
fuelectenerg-3309	146	26	ρ(m−2	ρ(m−2	X
fuelectenerg-3309	146	27	)	)	PUNCT
fuelectenerg-3309	146	28	∈	∈	PROPN
fuelectenerg-3309	146	29	p	p	X
fuelectenerg-3309	146	30	(	(	PUNCT
fuelectenerg-3309	146	31	m−	m−	PROPN
fuelectenerg-3309	146	32	2	2	NUM
fuelectenerg-3309	146	33	)	)	PUNCT
fuelectenerg-3309	146	34	by	by	ADP
fuelectenerg-3309	146	35	ρ(m−2)(j	ρ(m−2)(j	NOUN
fuelectenerg-3309	146	36	)	)	PUNCT
fuelectenerg-3309	146	37	=	=	PRON
fuelectenerg-3309	146	38	{	{	PUNCT
fuelectenerg-3309	146	39	ρ(m−1)(j	ρ(m−1)(j	ADJ
fuelectenerg-3309	146	40	)	)	PUNCT
fuelectenerg-3309	146	41	if	if	SCONJ
fuelectenerg-3309	146	42	j	j	PROPN
fuelectenerg-3309	146	43	<	<	X
fuelectenerg-3309	146	44	sm−1	sm−1	PROPN
fuelectenerg-3309	146	45	ρ(m−1)(j	ρ(m−1)(j	NOUN
fuelectenerg-3309	147	1	+	+	CCONJ
fuelectenerg-3309	148	1	1	1	X
fuelectenerg-3309	148	2	)	)	PUNCT
fuelectenerg-3309	148	3	if	if	SCONJ
fuelectenerg-3309	148	4	j	j	PROPN
fuelectenerg-3309	148	5	≥	≥	AUX
fuelectenerg-3309	148	6	sm−1	sm−1	PROPN
fuelectenerg-3309	148	7	,	,	PUNCT
fuelectenerg-3309	148	8	j	j	PROPN
fuelectenerg-3309	148	9	=	=	SYM
fuelectenerg-3309	148	10	1	1	NUM
fuelectenerg-3309	148	11	,	,	PUNCT
fuelectenerg-3309	148	12	...	...	PUNCT
fuelectenerg-3309	148	13	,	,	PUNCT
fuelectenerg-3309	148	14	m−	m−	PROPN
fuelectenerg-3309	148	15	2	2	NUM
fuelectenerg-3309	148	16	.	.	PUNCT
fuelectenerg-3309	148	17	we	we	PRON
fuelectenerg-3309	148	18	continue	continue	VERB
fuelectenerg-3309	148	19	in	in	ADP
fuelectenerg-3309	148	20	the	the	DET
fuelectenerg-3309	148	21	same	same	ADJ
fuelectenerg-3309	148	22	spirit	spirit	NOUN
fuelectenerg-3309	148	23	until	until	SCONJ
fuelectenerg-3309	148	24	s	s	NOUN
fuelectenerg-3309	148	25	is	be	AUX
fuelectenerg-3309	148	26	completely	completely	ADV
fuelectenerg-3309	148	27	determined	determine	VERB
fuelectenerg-3309	148	28	.	.	PUNCT
fuelectenerg-3309	149	1	example	example	NOUN
fuelectenerg-3309	150	1	1	1	NUM
fuelectenerg-3309	150	2	let	let	VERB
fuelectenerg-3309	150	3	ρ	ρ	PROPN
fuelectenerg-3309	150	4	=	=	SYM
fuelectenerg-3309	150	5	(	(	PUNCT
fuelectenerg-3309	150	6	2	2	NUM
fuelectenerg-3309	150	7	,	,	PUNCT
fuelectenerg-3309	150	8	3	3	NUM
fuelectenerg-3309	150	9	,	,	PUNCT
fuelectenerg-3309	150	10	4	4	NUM
fuelectenerg-3309	150	11	,	,	PUNCT
fuelectenerg-3309	150	12	1	1	NUM
fuelectenerg-3309	150	13	)	)	PUNCT
fuelectenerg-3309	150	14	.	.	PUNCT
fuelectenerg-3309	151	1	in	in	ADP
fuelectenerg-3309	151	2	order	order	NOUN
fuelectenerg-3309	151	3	to	to	PART
fuelectenerg-3309	151	4	determine	determine	VERB
fuelectenerg-3309	151	5	the	the	DET
fuelectenerg-3309	151	6	set	set	NOUN
fuelectenerg-3309	151	7	s	s	PART
fuelectenerg-3309	151	8	=	=	NOUN
fuelectenerg-3309	151	9	{	{	PUNCT
fuelectenerg-3309	151	10	s1	s1	NOUN
fuelectenerg-3309	151	11	,	,	PUNCT
fuelectenerg-3309	151	12	s2	s2	PROPN
fuelectenerg-3309	151	13	,	,	PUNCT
fuelectenerg-3309	151	14	s3	s3	PROPN
fuelectenerg-3309	151	15	,	,	PUNCT
fuelectenerg-3309	151	16	s4	s4	PROPN
fuelectenerg-3309	151	17	}	}	PUNCT
fuelectenerg-3309	151	18	in	in	ADP
fuelectenerg-3309	151	19	(	(	PUNCT
fuelectenerg-3309	151	20	3	3	X
fuelectenerg-3309	151	21	)	)	PUNCT
fuelectenerg-3309	151	22	we	we	PRON
fuelectenerg-3309	151	23	are	be	AUX
fuelectenerg-3309	151	24	based	base	VERB
fuelectenerg-3309	151	25	on	on	ADP
fuelectenerg-3309	151	26	the	the	DET
fuelectenerg-3309	151	27	above	above	ADJ
fuelectenerg-3309	151	28	iteration	iteration	NOUN
fuelectenerg-3309	151	29	scheme	scheme	NOUN
fuelectenerg-3309	151	30	and	and	CCONJ
fuelectenerg-3309	151	31	so	so	ADV
fuelectenerg-3309	151	32	we	we	PRON
fuelectenerg-3309	151	33	proceed	proceed	VERB
fuelectenerg-3309	151	34	in	in	ADP
fuelectenerg-3309	151	35	the	the	DET
fuelectenerg-3309	151	36	following	following	ADJ
fuelectenerg-3309	151	37	way	way	NOUN
fuelectenerg-3309	151	38	:	:	PUNCT
fuelectenerg-3309	151	39	(	(	PUNCT
fuelectenerg-3309	151	40	i	i	NOUN
fuelectenerg-3309	151	41	)	)	PUNCT
fuelectenerg-3309	151	42	define	define	VERB
fuelectenerg-3309	151	43	s4	s4	NOUN
fuelectenerg-3309	151	44	=	=	SYM
fuelectenerg-3309	151	45	ρ−1(4	ρ−1(4	X
fuelectenerg-3309	151	46	)	)	PUNCT
fuelectenerg-3309	151	47	=	=	SYM
fuelectenerg-3309	151	48	3	3	NUM
fuelectenerg-3309	151	49	and	and	CCONJ
fuelectenerg-3309	151	50	ρ(3	ρ(3	NUM
fuelectenerg-3309	151	51	)	)	PUNCT
fuelectenerg-3309	151	52	=	=	PUNCT
fuelectenerg-3309	151	53	(	(	PUNCT
fuelectenerg-3309	151	54	2	2	NUM
fuelectenerg-3309	151	55	,	,	PUNCT
fuelectenerg-3309	151	56	3	3	NUM
fuelectenerg-3309	151	57	,	,	PUNCT
fuelectenerg-3309	151	58	1	1	NUM
fuelectenerg-3309	151	59	)	)	PUNCT
fuelectenerg-3309	151	60	.	.	PUNCT
fuelectenerg-3309	152	1	(	(	PUNCT
fuelectenerg-3309	152	2	ii	ii	NOUN
fuelectenerg-3309	152	3	)	)	PUNCT
fuelectenerg-3309	152	4	define	define	VERB
fuelectenerg-3309	152	5	s3	s3	PROPN
fuelectenerg-3309	152	6	=	=	PROPN
fuelectenerg-3309	152	7	ρ−1	ρ−1	PROPN
fuelectenerg-3309	152	8	(	(	PUNCT
fuelectenerg-3309	152	9	3)(3	3)(3	NUM
fuelectenerg-3309	152	10	)	)	PUNCT
fuelectenerg-3309	152	11	=	=	SYM
fuelectenerg-3309	152	12	2	2	NUM
fuelectenerg-3309	152	13	and	and	CCONJ
fuelectenerg-3309	152	14	ρ(2	ρ(2	PROPN
fuelectenerg-3309	152	15	)	)	PUNCT
fuelectenerg-3309	153	1	=	=	PUNCT
fuelectenerg-3309	153	2	(	(	PUNCT
fuelectenerg-3309	153	3	2	2	NUM
fuelectenerg-3309	153	4	,	,	PUNCT
fuelectenerg-3309	153	5	1	1	NUM
fuelectenerg-3309	153	6	)	)	PUNCT
fuelectenerg-3309	153	7	.	.	PUNCT
fuelectenerg-3309	154	1	(	(	PUNCT
fuelectenerg-3309	154	2	iii	iii	X
fuelectenerg-3309	154	3	)	)	PUNCT
fuelectenerg-3309	154	4	define	define	VERB
fuelectenerg-3309	154	5	s2	s2	NOUN
fuelectenerg-3309	154	6	=	=	SYM
fuelectenerg-3309	154	7	ρ−1	ρ−1	PROPN
fuelectenerg-3309	154	8	(	(	PUNCT
fuelectenerg-3309	154	9	2)(2	2)(2	NUM
fuelectenerg-3309	154	10	)	)	PUNCT
fuelectenerg-3309	154	11	=	=	SYM
fuelectenerg-3309	154	12	1	1	NUM
fuelectenerg-3309	154	13	and	and	CCONJ
fuelectenerg-3309	154	14	ρ(1	ρ(1	PROPN
fuelectenerg-3309	154	15	)	)	PUNCT
fuelectenerg-3309	154	16	=	=	PUNCT
fuelectenerg-3309	154	17	(	(	PUNCT
fuelectenerg-3309	154	18	1	1	NUM
fuelectenerg-3309	154	19	)	)	PUNCT
fuelectenerg-3309	154	20	.	.	PUNCT
fuelectenerg-3309	155	1	(	(	PUNCT
fuelectenerg-3309	155	2	iv	iv	X
fuelectenerg-3309	155	3	)	)	PUNCT
fuelectenerg-3309	155	4	define	define	VERB
fuelectenerg-3309	155	5	s1	s1	NOUN
fuelectenerg-3309	155	6	=	=	SYM
fuelectenerg-3309	155	7	ρ−1	ρ−1	PROPN
fuelectenerg-3309	155	8	(	(	PUNCT
fuelectenerg-3309	155	9	1)(1	1)(1	NUM
fuelectenerg-3309	155	10	)	)	PUNCT
fuelectenerg-3309	155	11	=	=	SYM
fuelectenerg-3309	155	12	1	1	NUM
fuelectenerg-3309	155	13	and	and	CCONJ
fuelectenerg-3309	155	14	ρ(4	ρ(4	NOUN
fuelectenerg-3309	155	15	)	)	PUNCT
fuelectenerg-3309	156	1	=	=	PUNCT
fuelectenerg-3309	156	2	∅.	∅.	ADP
fuelectenerg-3309	156	3	now	now	ADV
fuelectenerg-3309	156	4	we	we	PRON
fuelectenerg-3309	156	5	have	have	VERB
fuelectenerg-3309	156	6	the	the	DET
fuelectenerg-3309	156	7	following	following	NOUN
fuelectenerg-3309	156	8	:	:	PUNCT
fuelectenerg-3309	156	9	proposition	proposition	NOUN
fuelectenerg-3309	156	10	1	1	NUM
fuelectenerg-3309	156	11	[	[	X
fuelectenerg-3309	156	12	2	2	X
fuelectenerg-3309	156	13	]	]	PUNCT
fuelectenerg-3309	156	14	let	let	VERB
fuelectenerg-3309	156	15	u	u	PRON
fuelectenerg-3309	156	16	and	and	CCONJ
fuelectenerg-3309	156	17	q	q	NOUN
fuelectenerg-3309	156	18	be	be	AUX
fuelectenerg-3309	156	19	two	two	NUM
fuelectenerg-3309	156	20	maps	map	NOUN
fuelectenerg-3309	156	21	as	as	ADP
fuelectenerg-3309	156	22	in	in	ADP
fuelectenerg-3309	156	23	(	(	PUNCT
fuelectenerg-3309	156	24	2	2	NUM
fuelectenerg-3309	156	25	)	)	PUNCT
fuelectenerg-3309	156	26	and	and	CCONJ
fuelectenerg-3309	156	27	(	(	PUNCT
fuelectenerg-3309	156	28	3	3	X
fuelectenerg-3309	156	29	)	)	PUNCT
fuelectenerg-3309	156	30	respectively	respectively	ADV
fuelectenerg-3309	156	31	.	.	PUNCT
fuelectenerg-3309	157	1	then	then	ADV
fuelectenerg-3309	157	2	q	q	X
fuelectenerg-3309	157	3	is	be	AUX
fuelectenerg-3309	157	4	a	a	DET
fuelectenerg-3309	157	5	bijection	bijection	NOUN
fuelectenerg-3309	157	6	and	and	CCONJ
fuelectenerg-3309	157	7	so	so	ADV
fuelectenerg-3309	157	8	the	the	DET
fuelectenerg-3309	157	9	composition	composition	NOUN
fuelectenerg-3309	157	10	map	map	NOUN
fuelectenerg-3309	157	11	uq	uq	NOUN
fuelectenerg-3309	157	12	:	:	PUNCT
fuelectenerg-3309	157	13	p	p	X
fuelectenerg-3309	157	14	(	(	PUNCT
fuelectenerg-3309	157	15	m	m	NOUN
fuelectenerg-3309	157	16	)	)	PUNCT
fuelectenerg-3309	157	17	→	→	SYM
fuelectenerg-3309	157	18	{	{	PUNCT
fuelectenerg-3309	157	19	0	0	NUM
fuelectenerg-3309	157	20	,	,	PUNCT
fuelectenerg-3309	157	21	...	...	PUNCT
fuelectenerg-3309	157	22	,	,	PUNCT
fuelectenerg-3309	157	23	m!−	m!−	VERB
fuelectenerg-3309	157	24	1	1	NUM
fuelectenerg-3309	157	25	}	}	PUNCT
fuelectenerg-3309	157	26	provides	provide	VERB
fuelectenerg-3309	157	27	an	an	DET
fuelectenerg-3309	157	28	enumeration	enumeration	NOUN
fuelectenerg-3309	157	29	of	of	ADP
fuelectenerg-3309	157	30	p	p	PROPN
fuelectenerg-3309	157	31	(	(	PUNCT
fuelectenerg-3309	157	32	m	m	NOUN
fuelectenerg-3309	157	33	)	)	PUNCT
fuelectenerg-3309	157	34	.	.	PUNCT
fuelectenerg-3309	158	1	244	244	NUM
fuelectenerg-3309	158	2	c.	c.	PROPN
fuelectenerg-3309	158	3	karanikas	karanikas	PROPN
fuelectenerg-3309	158	4	,	,	PUNCT
fuelectenerg-3309	158	5	n.	n.	PROPN
fuelectenerg-3309	158	6	atreas	atreas	PROPN
fuelectenerg-3309	158	7	enumeration	enumeration	PROPN
fuelectenerg-3309	158	8	and	and	CCONJ
fuelectenerg-3309	158	9	coding	code	VERB
fuelectenerg-3309	158	10	permutations	permutation	NOUN
fuelectenerg-3309	158	11	and	and	CCONJ
fuelectenerg-3309	158	12	reversible	reversible	ADJ
fuelectenerg-3309	158	13	logical	logical	ADJ
fuelectenerg-3309	158	14	circuits	circuit	NOUN
fuelectenerg-3309	158	15	245	245	NUM
fuelectenerg-3309	158	16	4	4	NUM
fuelectenerg-3309	158	17	n.	n.	NOUN
fuelectenerg-3309	158	18	atreas	atreas	PROPN
fuelectenerg-3309	158	19	and	and	CCONJ
fuelectenerg-3309	158	20	c.	c.	PROPN
fuelectenerg-3309	158	21	karanikas	karanikas	PROPN
fuelectenerg-3309	158	22	for	for	ADP
fuelectenerg-3309	158	23	the	the	DET
fuelectenerg-3309	158	24	above	above	ADJ
fuelectenerg-3309	158	25	selection	selection	NOUN
fuelectenerg-3309	158	26	of	of	ADP
fuelectenerg-3309	158	27	m	m	PROPN
fuelectenerg-3309	158	28	and	and	CCONJ
fuelectenerg-3309	158	29	the	the	DET
fuelectenerg-3309	158	30	initial	initial	ADJ
fuelectenerg-3309	158	31	permutation	permutation	NOUN
fuelectenerg-3309	158	32	ρ	ρ	PROPN
fuelectenerg-3309	158	33	in	in	ADP
fuelectenerg-3309	158	34	(	(	PUNCT
fuelectenerg-3309	158	35	3	3	NUM
fuelectenerg-3309	158	36	)	)	PUNCT
fuelectenerg-3309	158	37	,	,	PUNCT
fuelectenerg-3309	158	38	we	we	PRON
fuelectenerg-3309	158	39	store	store	VERB
fuelectenerg-3309	158	40	the	the	DET
fuelectenerg-3309	158	41	position	position	NOUN
fuelectenerg-3309	158	42	of	of	ADP
fuelectenerg-3309	158	43	the	the	DET
fuelectenerg-3309	158	44	biggest	big	ADJ
fuelectenerg-3309	158	45	element	element	NOUN
fuelectenerg-3309	158	46	in	in	ADP
fuelectenerg-3309	158	47	ρ	ρ	PROPN
fuelectenerg-3309	158	48	,	,	PUNCT
fuelectenerg-3309	158	49	i.e.	i.e.	X
fuelectenerg-3309	158	50	we	we	PRON
fuelectenerg-3309	158	51	define	define	VERB
fuelectenerg-3309	158	52	sm	sm	NOUN
fuelectenerg-3309	158	53	=	=	SYM
fuelectenerg-3309	158	54	ρ−1(m	ρ−1(m	NOUN
fuelectenerg-3309	158	55	)	)	PUNCT
fuelectenerg-3309	158	56	and	and	CCONJ
fuelectenerg-3309	158	57	at	at	ADP
fuelectenerg-3309	158	58	the	the	DET
fuelectenerg-3309	158	59	same	same	ADJ
fuelectenerg-3309	158	60	time	time	NOUN
fuelectenerg-3309	158	61	we	we	PRON
fuelectenerg-3309	158	62	delete	delete	VERB
fuelectenerg-3309	158	63	this	this	DET
fuelectenerg-3309	158	64	element	element	NOUN
fuelectenerg-3309	158	65	ρ(sm	ρ(sm	NOUN
fuelectenerg-3309	158	66	)	)	PUNCT
fuelectenerg-3309	158	67	=	=	PRON
fuelectenerg-3309	158	68	m	m	VERB
fuelectenerg-3309	158	69	from	from	ADP
fuelectenerg-3309	158	70	ρ	ρ	PROPN
fuelectenerg-3309	158	71	and	and	CCONJ
fuelectenerg-3309	158	72	so	so	ADV
fuelectenerg-3309	158	73	we	we	PRON
fuelectenerg-3309	158	74	form	form	VERB
fuelectenerg-3309	158	75	a	a	DET
fuelectenerg-3309	158	76	new	new	ADJ
fuelectenerg-3309	158	77	permutation	permutation	NOUN
fuelectenerg-3309	158	78	ρ(m−1	ρ(m−1	X
fuelectenerg-3309	159	1	)	)	PUNCT
fuelectenerg-3309	159	2	∈	∈	PROPN
fuelectenerg-3309	160	1	p	p	NOUN
fuelectenerg-3309	160	2	(	(	PUNCT
fuelectenerg-3309	160	3	m−	m−	PROPN
fuelectenerg-3309	160	4	1	1	NUM
fuelectenerg-3309	160	5	)	)	PUNCT
fuelectenerg-3309	160	6	by	by	ADP
fuelectenerg-3309	160	7	ρ(m−1)(j	ρ(m−1)(j	ADJ
fuelectenerg-3309	160	8	)	)	PUNCT
fuelectenerg-3309	160	9	=	=	SYM
fuelectenerg-3309	160	10	{	{	PUNCT
fuelectenerg-3309	160	11	ρ(j	ρ(j	PROPN
fuelectenerg-3309	160	12	)	)	PUNCT
fuelectenerg-3309	160	13	if	if	SCONJ
fuelectenerg-3309	160	14	j	j	PROPN
fuelectenerg-3309	160	15	<	<	X
fuelectenerg-3309	160	16	sm	sm	PROPN
fuelectenerg-3309	160	17	ρ(j	ρ(j	PROPN
fuelectenerg-3309	160	18	+	+	PROPN
fuelectenerg-3309	160	19	1	1	X
fuelectenerg-3309	160	20	)	)	PUNCT
fuelectenerg-3309	160	21	if	if	SCONJ
fuelectenerg-3309	160	22	j	j	PROPN
fuelectenerg-3309	160	23	≥	≥	AUX
fuelectenerg-3309	160	24	sm	sm	INTJ
fuelectenerg-3309	160	25	,	,	PUNCT
fuelectenerg-3309	160	26	j	j	PROPN
fuelectenerg-3309	160	27	=	=	SYM
fuelectenerg-3309	160	28	1	1	NUM
fuelectenerg-3309	160	29	,	,	PUNCT
fuelectenerg-3309	160	30	...	...	PUNCT
fuelectenerg-3309	160	31	,	,	PUNCT
fuelectenerg-3309	160	32	m−	m−	PROPN
fuelectenerg-3309	160	33	1	1	NUM
fuelectenerg-3309	160	34	.	.	PUNCT
fuelectenerg-3309	161	1	then	then	ADV
fuelectenerg-3309	161	2	we	we	PRON
fuelectenerg-3309	161	3	follow	follow	VERB
fuelectenerg-3309	161	4	the	the	DET
fuelectenerg-3309	161	5	previous	previous	ADJ
fuelectenerg-3309	161	6	step	step	NOUN
fuelectenerg-3309	161	7	for	for	ADP
fuelectenerg-3309	161	8	the	the	DET
fuelectenerg-3309	161	9	permutation	permutation	NOUN
fuelectenerg-3309	161	10	ρ(m−1	ρ(m−1	PROPN
fuelectenerg-3309	161	11	)	)	PUNCT
fuelectenerg-3309	161	12	,	,	PUNCT
fuelectenerg-3309	161	13	i.e.	i.e.	X
fuelectenerg-3309	161	14	we	we	PRON
fuelectenerg-3309	161	15	store	store	VERB
fuelectenerg-3309	161	16	the	the	DET
fuelectenerg-3309	161	17	position	position	NOUN
fuelectenerg-3309	161	18	of	of	ADP
fuelectenerg-3309	161	19	its	its	PRON
fuelectenerg-3309	161	20	biggest	big	ADJ
fuelectenerg-3309	161	21	element	element	NOUN
fuelectenerg-3309	161	22	by	by	ADP
fuelectenerg-3309	161	23	defining	define	VERB
fuelectenerg-3309	161	24	sm−1	sm−1	NOUN
fuelectenerg-3309	161	25	=	=	SYM
fuelectenerg-3309	162	1	ρ−1	ρ−1	PROPN
fuelectenerg-3309	162	2	(	(	PUNCT
fuelectenerg-3309	162	3	m−1)(m−	m−1)(m−	NOUN
fuelectenerg-3309	162	4	1	1	NUM
fuelectenerg-3309	162	5	)	)	PUNCT
fuelectenerg-3309	162	6	and	and	CCONJ
fuelectenerg-3309	162	7	at	at	ADP
fuelectenerg-3309	162	8	the	the	DET
fuelectenerg-3309	162	9	same	same	ADJ
fuelectenerg-3309	162	10	time	time	NOUN
fuelectenerg-3309	162	11	we	we	PRON
fuelectenerg-3309	162	12	delete	delete	VERB
fuelectenerg-3309	162	13	the	the	DET
fuelectenerg-3309	162	14	element	element	NOUN
fuelectenerg-3309	162	15	m−	m−	PROPN
fuelectenerg-3309	162	16	1	1	NUM
fuelectenerg-3309	162	17	from	from	ADP
fuelectenerg-3309	162	18	ρ(m−1	ρ(m−1	PROPN
fuelectenerg-3309	162	19	)	)	PUNCT
fuelectenerg-3309	162	20	and	and	CCONJ
fuelectenerg-3309	162	21	we	we	PRON
fuelectenerg-3309	162	22	form	form	VERB
fuelectenerg-3309	162	23	a	a	DET
fuelectenerg-3309	162	24	new	new	ADJ
fuelectenerg-3309	162	25	permutation	permutation	NOUN
fuelectenerg-3309	162	26	ρ(m−2	ρ(m−2	X
fuelectenerg-3309	162	27	)	)	PUNCT
fuelectenerg-3309	162	28	∈	∈	PROPN
fuelectenerg-3309	162	29	p	p	X
fuelectenerg-3309	162	30	(	(	PUNCT
fuelectenerg-3309	162	31	m−	m−	PROPN
fuelectenerg-3309	162	32	2	2	NUM
fuelectenerg-3309	162	33	)	)	PUNCT
fuelectenerg-3309	162	34	by	by	ADP
fuelectenerg-3309	162	35	ρ(m−2)(j	ρ(m−2)(j	NOUN
fuelectenerg-3309	162	36	)	)	PUNCT
fuelectenerg-3309	162	37	=	=	PRON
fuelectenerg-3309	162	38	{	{	PUNCT
fuelectenerg-3309	162	39	ρ(m−1)(j	ρ(m−1)(j	ADJ
fuelectenerg-3309	162	40	)	)	PUNCT
fuelectenerg-3309	162	41	if	if	SCONJ
fuelectenerg-3309	162	42	j	j	PROPN
fuelectenerg-3309	162	43	<	<	X
fuelectenerg-3309	162	44	sm−1	sm−1	PROPN
fuelectenerg-3309	162	45	ρ(m−1)(j	ρ(m−1)(j	NOUN
fuelectenerg-3309	163	1	+	+	CCONJ
fuelectenerg-3309	164	1	1	1	X
fuelectenerg-3309	164	2	)	)	PUNCT
fuelectenerg-3309	164	3	if	if	SCONJ
fuelectenerg-3309	164	4	j	j	PROPN
fuelectenerg-3309	164	5	≥	≥	AUX
fuelectenerg-3309	164	6	sm−1	sm−1	PROPN
fuelectenerg-3309	164	7	,	,	PUNCT
fuelectenerg-3309	164	8	j	j	PROPN
fuelectenerg-3309	164	9	=	=	SYM
fuelectenerg-3309	164	10	1	1	NUM
fuelectenerg-3309	164	11	,	,	PUNCT
fuelectenerg-3309	164	12	...	...	PUNCT
fuelectenerg-3309	164	13	,	,	PUNCT
fuelectenerg-3309	164	14	m−	m−	PROPN
fuelectenerg-3309	164	15	2	2	NUM
fuelectenerg-3309	164	16	.	.	PUNCT
fuelectenerg-3309	164	17	we	we	PRON
fuelectenerg-3309	164	18	continue	continue	VERB
fuelectenerg-3309	164	19	in	in	ADP
fuelectenerg-3309	164	20	the	the	DET
fuelectenerg-3309	164	21	same	same	ADJ
fuelectenerg-3309	164	22	spirit	spirit	NOUN
fuelectenerg-3309	164	23	until	until	SCONJ
fuelectenerg-3309	164	24	s	s	NOUN
fuelectenerg-3309	164	25	is	be	AUX
fuelectenerg-3309	164	26	completely	completely	ADV
fuelectenerg-3309	164	27	determined	determine	VERB
fuelectenerg-3309	164	28	.	.	PUNCT
fuelectenerg-3309	165	1	example	example	NOUN
fuelectenerg-3309	166	1	1	1	NUM
fuelectenerg-3309	166	2	let	let	VERB
fuelectenerg-3309	166	3	ρ	ρ	PROPN
fuelectenerg-3309	166	4	=	=	SYM
fuelectenerg-3309	166	5	(	(	PUNCT
fuelectenerg-3309	166	6	2	2	NUM
fuelectenerg-3309	166	7	,	,	PUNCT
fuelectenerg-3309	166	8	3	3	NUM
fuelectenerg-3309	166	9	,	,	PUNCT
fuelectenerg-3309	166	10	4	4	NUM
fuelectenerg-3309	166	11	,	,	PUNCT
fuelectenerg-3309	166	12	1	1	NUM
fuelectenerg-3309	166	13	)	)	PUNCT
fuelectenerg-3309	166	14	.	.	PUNCT
fuelectenerg-3309	167	1	in	in	ADP
fuelectenerg-3309	167	2	order	order	NOUN
fuelectenerg-3309	167	3	to	to	PART
fuelectenerg-3309	167	4	determine	determine	VERB
fuelectenerg-3309	167	5	the	the	DET
fuelectenerg-3309	167	6	set	set	NOUN
fuelectenerg-3309	167	7	s	s	PART
fuelectenerg-3309	167	8	=	=	NOUN
fuelectenerg-3309	167	9	{	{	PUNCT
fuelectenerg-3309	167	10	s1	s1	NOUN
fuelectenerg-3309	167	11	,	,	PUNCT
fuelectenerg-3309	167	12	s2	s2	PROPN
fuelectenerg-3309	167	13	,	,	PUNCT
fuelectenerg-3309	167	14	s3	s3	PROPN
fuelectenerg-3309	167	15	,	,	PUNCT
fuelectenerg-3309	167	16	s4	s4	PROPN
fuelectenerg-3309	167	17	}	}	PUNCT
fuelectenerg-3309	167	18	in	in	ADP
fuelectenerg-3309	167	19	(	(	PUNCT
fuelectenerg-3309	167	20	3	3	X
fuelectenerg-3309	167	21	)	)	PUNCT
fuelectenerg-3309	167	22	we	we	PRON
fuelectenerg-3309	167	23	are	be	AUX
fuelectenerg-3309	167	24	based	base	VERB
fuelectenerg-3309	167	25	on	on	ADP
fuelectenerg-3309	167	26	the	the	DET
fuelectenerg-3309	167	27	above	above	ADJ
fuelectenerg-3309	167	28	iteration	iteration	NOUN
fuelectenerg-3309	167	29	scheme	scheme	NOUN
fuelectenerg-3309	167	30	and	and	CCONJ
fuelectenerg-3309	167	31	so	so	ADV
fuelectenerg-3309	167	32	we	we	PRON
fuelectenerg-3309	167	33	proceed	proceed	VERB
fuelectenerg-3309	167	34	in	in	ADP
fuelectenerg-3309	167	35	the	the	DET
fuelectenerg-3309	167	36	following	following	ADJ
fuelectenerg-3309	167	37	way	way	NOUN
fuelectenerg-3309	167	38	:	:	PUNCT
fuelectenerg-3309	167	39	(	(	PUNCT
fuelectenerg-3309	167	40	i	i	NOUN
fuelectenerg-3309	167	41	)	)	PUNCT
fuelectenerg-3309	167	42	define	define	VERB
fuelectenerg-3309	167	43	s4	s4	NOUN
fuelectenerg-3309	167	44	=	=	SYM
fuelectenerg-3309	167	45	ρ−1(4	ρ−1(4	X
fuelectenerg-3309	167	46	)	)	PUNCT
fuelectenerg-3309	167	47	=	=	SYM
fuelectenerg-3309	167	48	3	3	NUM
fuelectenerg-3309	167	49	and	and	CCONJ
fuelectenerg-3309	167	50	ρ(3	ρ(3	NUM
fuelectenerg-3309	167	51	)	)	PUNCT
fuelectenerg-3309	167	52	=	=	PUNCT
fuelectenerg-3309	167	53	(	(	PUNCT
fuelectenerg-3309	167	54	2	2	NUM
fuelectenerg-3309	167	55	,	,	PUNCT
fuelectenerg-3309	167	56	3	3	NUM
fuelectenerg-3309	167	57	,	,	PUNCT
fuelectenerg-3309	167	58	1	1	NUM
fuelectenerg-3309	167	59	)	)	PUNCT
fuelectenerg-3309	167	60	.	.	PUNCT
fuelectenerg-3309	168	1	(	(	PUNCT
fuelectenerg-3309	168	2	ii	ii	NOUN
fuelectenerg-3309	168	3	)	)	PUNCT
fuelectenerg-3309	168	4	define	define	VERB
fuelectenerg-3309	168	5	s3	s3	PROPN
fuelectenerg-3309	168	6	=	=	PROPN
fuelectenerg-3309	168	7	ρ−1	ρ−1	PROPN
fuelectenerg-3309	168	8	(	(	PUNCT
fuelectenerg-3309	168	9	3)(3	3)(3	NUM
fuelectenerg-3309	168	10	)	)	PUNCT
fuelectenerg-3309	168	11	=	=	SYM
fuelectenerg-3309	168	12	2	2	NUM
fuelectenerg-3309	168	13	and	and	CCONJ
fuelectenerg-3309	168	14	ρ(2	ρ(2	PROPN
fuelectenerg-3309	168	15	)	)	PUNCT
fuelectenerg-3309	169	1	=	=	PUNCT
fuelectenerg-3309	169	2	(	(	PUNCT
fuelectenerg-3309	169	3	2	2	NUM
fuelectenerg-3309	169	4	,	,	PUNCT
fuelectenerg-3309	169	5	1	1	NUM
fuelectenerg-3309	169	6	)	)	PUNCT
fuelectenerg-3309	169	7	.	.	PUNCT
fuelectenerg-3309	170	1	(	(	PUNCT
fuelectenerg-3309	170	2	iii	iii	X
fuelectenerg-3309	170	3	)	)	PUNCT
fuelectenerg-3309	170	4	define	define	VERB
fuelectenerg-3309	170	5	s2	s2	NOUN
fuelectenerg-3309	170	6	=	=	SYM
fuelectenerg-3309	170	7	ρ−1	ρ−1	PROPN
fuelectenerg-3309	170	8	(	(	PUNCT
fuelectenerg-3309	170	9	2)(2	2)(2	NUM
fuelectenerg-3309	170	10	)	)	PUNCT
fuelectenerg-3309	170	11	=	=	SYM
fuelectenerg-3309	170	12	1	1	NUM
fuelectenerg-3309	170	13	and	and	CCONJ
fuelectenerg-3309	170	14	ρ(1	ρ(1	PROPN
fuelectenerg-3309	170	15	)	)	PUNCT
fuelectenerg-3309	170	16	=	=	PUNCT
fuelectenerg-3309	170	17	(	(	PUNCT
fuelectenerg-3309	170	18	1	1	NUM
fuelectenerg-3309	170	19	)	)	PUNCT
fuelectenerg-3309	170	20	.	.	PUNCT
fuelectenerg-3309	171	1	(	(	PUNCT
fuelectenerg-3309	171	2	iv	iv	X
fuelectenerg-3309	171	3	)	)	PUNCT
fuelectenerg-3309	171	4	define	define	VERB
fuelectenerg-3309	171	5	s1	s1	NOUN
fuelectenerg-3309	171	6	=	=	SYM
fuelectenerg-3309	171	7	ρ−1	ρ−1	PROPN
fuelectenerg-3309	171	8	(	(	PUNCT
fuelectenerg-3309	171	9	1)(1	1)(1	NUM
fuelectenerg-3309	171	10	)	)	PUNCT
fuelectenerg-3309	171	11	=	=	SYM
fuelectenerg-3309	171	12	1	1	NUM
fuelectenerg-3309	171	13	and	and	CCONJ
fuelectenerg-3309	171	14	ρ(4	ρ(4	NOUN
fuelectenerg-3309	171	15	)	)	PUNCT
fuelectenerg-3309	172	1	=	=	PUNCT
fuelectenerg-3309	172	2	∅.	∅.	ADP
fuelectenerg-3309	172	3	now	now	ADV
fuelectenerg-3309	172	4	we	we	PRON
fuelectenerg-3309	172	5	have	have	VERB
fuelectenerg-3309	172	6	the	the	DET
fuelectenerg-3309	172	7	following	following	NOUN
fuelectenerg-3309	172	8	:	:	PUNCT
fuelectenerg-3309	172	9	proposition	proposition	NOUN
fuelectenerg-3309	172	10	1	1	NUM
fuelectenerg-3309	172	11	[	[	X
fuelectenerg-3309	172	12	2	2	X
fuelectenerg-3309	172	13	]	]	PUNCT
fuelectenerg-3309	172	14	let	let	VERB
fuelectenerg-3309	172	15	u	u	PRON
fuelectenerg-3309	172	16	and	and	CCONJ
fuelectenerg-3309	172	17	q	q	NOUN
fuelectenerg-3309	172	18	be	be	AUX
fuelectenerg-3309	172	19	two	two	NUM
fuelectenerg-3309	172	20	maps	map	NOUN
fuelectenerg-3309	172	21	as	as	ADP
fuelectenerg-3309	172	22	in	in	ADP
fuelectenerg-3309	172	23	(	(	PUNCT
fuelectenerg-3309	172	24	2	2	NUM
fuelectenerg-3309	172	25	)	)	PUNCT
fuelectenerg-3309	172	26	and	and	CCONJ
fuelectenerg-3309	172	27	(	(	PUNCT
fuelectenerg-3309	172	28	3	3	X
fuelectenerg-3309	172	29	)	)	PUNCT
fuelectenerg-3309	172	30	respectively	respectively	ADV
fuelectenerg-3309	172	31	.	.	PUNCT
fuelectenerg-3309	173	1	then	then	ADV
fuelectenerg-3309	173	2	q	q	X
fuelectenerg-3309	173	3	is	be	AUX
fuelectenerg-3309	173	4	a	a	DET
fuelectenerg-3309	173	5	bijection	bijection	NOUN
fuelectenerg-3309	173	6	and	and	CCONJ
fuelectenerg-3309	173	7	so	so	ADV
fuelectenerg-3309	173	8	the	the	DET
fuelectenerg-3309	173	9	composition	composition	NOUN
fuelectenerg-3309	173	10	map	map	NOUN
fuelectenerg-3309	173	11	uq	uq	NOUN
fuelectenerg-3309	173	12	:	:	PUNCT
fuelectenerg-3309	173	13	p	p	X
fuelectenerg-3309	173	14	(	(	PUNCT
fuelectenerg-3309	173	15	m	m	NOUN
fuelectenerg-3309	173	16	)	)	PUNCT
fuelectenerg-3309	173	17	→	→	SYM
fuelectenerg-3309	173	18	{	{	PUNCT
fuelectenerg-3309	173	19	0	0	NUM
fuelectenerg-3309	173	20	,	,	PUNCT
fuelectenerg-3309	173	21	...	...	PUNCT
fuelectenerg-3309	173	22	,	,	PUNCT
fuelectenerg-3309	173	23	m!−	m!−	VERB
fuelectenerg-3309	173	24	1	1	NUM
fuelectenerg-3309	173	25	}	}	PUNCT
fuelectenerg-3309	173	26	provides	provide	VERB
fuelectenerg-3309	173	27	an	an	DET
fuelectenerg-3309	173	28	enumeration	enumeration	NOUN
fuelectenerg-3309	173	29	of	of	ADP
fuelectenerg-3309	173	30	p	p	PROPN
fuelectenerg-3309	173	31	(	(	PUNCT
fuelectenerg-3309	173	32	m	m	NOUN
fuelectenerg-3309	173	33	)	)	PUNCT
fuelectenerg-3309	173	34	.	.	PUNCT
fuelectenerg-3309	174	1	enumeration	enumeration	NOUN
fuelectenerg-3309	174	2	and	and	CCONJ
fuelectenerg-3309	174	3	coding	code	VERB
fuelectenerg-3309	174	4	permutations	permutation	NOUN
fuelectenerg-3309	174	5	and	and	CCONJ
fuelectenerg-3309	174	6	reversible	reversible	ADJ
fuelectenerg-3309	174	7	logical	logical	ADJ
fuelectenerg-3309	174	8	circuits	circuit	NOUN
fuelectenerg-3309	174	9	5	5	NUM
fuelectenerg-3309	174	10	example	example	NOUN
fuelectenerg-3309	174	11	2	2	NUM
fuelectenerg-3309	174	12	for	for	ADP
fuelectenerg-3309	174	13	m	m	NOUN
fuelectenerg-3309	174	14	=	=	NOUN
fuelectenerg-3309	174	15	4	4	NUM
fuelectenerg-3309	174	16	,	,	PUNCT
fuelectenerg-3309	174	17	we	we	PRON
fuelectenerg-3309	174	18	demonstrate	demonstrate	VERB
fuelectenerg-3309	174	19	the	the	DET
fuelectenerg-3309	174	20	enumeration	enumeration	NOUN
fuelectenerg-3309	174	21	of	of	ADP
fuelectenerg-3309	174	22	the	the	DET
fuelectenerg-3309	174	23	elements	element	NOUN
fuelectenerg-3309	174	24	of	of	ADP
fuelectenerg-3309	174	25	p	p	NOUN
fuelectenerg-3309	174	26	(	(	PUNCT
fuelectenerg-3309	174	27	4	4	NUM
fuelectenerg-3309	174	28	)	)	PUNCT
fuelectenerg-3309	174	29	derived	derive	VERB
fuelectenerg-3309	174	30	from	from	ADP
fuelectenerg-3309	174	31	proposition	proposition	NOUN
fuelectenerg-3309	174	32	(	(	PUNCT
fuelectenerg-3309	174	33	1	1	NUM
fuelectenerg-3309	174	34	)	)	PUNCT
fuelectenerg-3309	174	35	and	and	CCONJ
fuelectenerg-3309	174	36	the	the	DET
fuelectenerg-3309	174	37	lexicographical	lexicographical	ADJ
fuelectenerg-3309	174	38	order	order	NOUN
fuelectenerg-3309	174	39	of	of	ADP
fuelectenerg-3309	174	40	the	the	DET
fuelectenerg-3309	174	41	elements	element	NOUN
fuelectenerg-3309	174	42	of	of	ADP
fuelectenerg-3309	174	43	s(4	s(4	NOUN
fuelectenerg-3309	174	44	)	)	PUNCT
fuelectenerg-3309	174	45	derived	derive	VERB
fuelectenerg-3309	174	46	from	from	ADP
fuelectenerg-3309	174	47	(	(	PUNCT
fuelectenerg-3309	174	48	2	2	NUM
fuelectenerg-3309	174	49	)	)	PUNCT
fuelectenerg-3309	174	50	.	.	PUNCT
fuelectenerg-3309	175	1	p	p	X
fuelectenerg-3309	175	2	(	(	PUNCT
fuelectenerg-3309	175	3	4	4	NUM
fuelectenerg-3309	175	4	)	)	PUNCT
fuelectenerg-3309	175	5	=	=	PRON
fuelectenerg-3309	175	6	{	{	PUNCT
fuelectenerg-3309	175	7	(	(	PUNCT
fuelectenerg-3309	175	8	4	4	NUM
fuelectenerg-3309	175	9	,	,	PUNCT
fuelectenerg-3309	175	10	3	3	NUM
fuelectenerg-3309	175	11	,	,	PUNCT
fuelectenerg-3309	175	12	2	2	NUM
fuelectenerg-3309	175	13	,	,	PUNCT
fuelectenerg-3309	175	14	1	1	NUM
fuelectenerg-3309	175	15	)	)	PUNCT
fuelectenerg-3309	175	16	,	,	PUNCT
fuelectenerg-3309	175	17	(	(	PUNCT
fuelectenerg-3309	175	18	3	3	NUM
fuelectenerg-3309	175	19	,	,	PUNCT
fuelectenerg-3309	175	20	4	4	NUM
fuelectenerg-3309	175	21	,	,	PUNCT
fuelectenerg-3309	175	22	2	2	NUM
fuelectenerg-3309	175	23	,	,	PUNCT
fuelectenerg-3309	175	24	1	1	NUM
fuelectenerg-3309	175	25	)	)	PUNCT
fuelectenerg-3309	175	26	,	,	PUNCT
fuelectenerg-3309	175	27	(	(	PUNCT
fuelectenerg-3309	175	28	3	3	NUM
fuelectenerg-3309	175	29	,	,	PUNCT
fuelectenerg-3309	175	30	2	2	NUM
fuelectenerg-3309	175	31	,	,	PUNCT
fuelectenerg-3309	175	32	4	4	NUM
fuelectenerg-3309	175	33	,	,	PUNCT
fuelectenerg-3309	175	34	1	1	NUM
fuelectenerg-3309	175	35	)	)	PUNCT
fuelectenerg-3309	175	36	,	,	PUNCT
fuelectenerg-3309	175	37	(	(	PUNCT
fuelectenerg-3309	175	38	3	3	NUM
fuelectenerg-3309	175	39	,	,	PUNCT
fuelectenerg-3309	175	40	2	2	NUM
fuelectenerg-3309	175	41	,	,	PUNCT
fuelectenerg-3309	175	42	1	1	NUM
fuelectenerg-3309	175	43	,	,	PUNCT
fuelectenerg-3309	175	44	4	4	NUM
fuelectenerg-3309	175	45	)	)	PUNCT
fuelectenerg-3309	175	46	,	,	PUNCT
fuelectenerg-3309	175	47	(	(	PUNCT
fuelectenerg-3309	175	48	4	4	NUM
fuelectenerg-3309	175	49	,	,	PUNCT
fuelectenerg-3309	175	50	2	2	NUM
fuelectenerg-3309	175	51	,	,	PUNCT
fuelectenerg-3309	175	52	3	3	NUM
fuelectenerg-3309	175	53	,	,	PUNCT
fuelectenerg-3309	175	54	1	1	NUM
fuelectenerg-3309	175	55	)	)	PUNCT
fuelectenerg-3309	175	56	,	,	PUNCT
fuelectenerg-3309	175	57	(	(	PUNCT
fuelectenerg-3309	175	58	2	2	NUM
fuelectenerg-3309	175	59	,	,	PUNCT
fuelectenerg-3309	175	60	4	4	NUM
fuelectenerg-3309	175	61	,	,	PUNCT
fuelectenerg-3309	175	62	3	3	NUM
fuelectenerg-3309	175	63	,	,	PUNCT
fuelectenerg-3309	175	64	1	1	NUM
fuelectenerg-3309	175	65	)	)	PUNCT
fuelectenerg-3309	175	66	,	,	PUNCT
fuelectenerg-3309	175	67	(	(	PUNCT
fuelectenerg-3309	175	68	2	2	NUM
fuelectenerg-3309	175	69	,	,	PUNCT
fuelectenerg-3309	175	70	3	3	NUM
fuelectenerg-3309	175	71	,	,	PUNCT
fuelectenerg-3309	175	72	4	4	NUM
fuelectenerg-3309	175	73	,	,	PUNCT
fuelectenerg-3309	175	74	1	1	NUM
fuelectenerg-3309	175	75	)	)	PUNCT
fuelectenerg-3309	175	76	,	,	PUNCT
fuelectenerg-3309	175	77	(	(	PUNCT
fuelectenerg-3309	175	78	2	2	NUM
fuelectenerg-3309	175	79	,	,	PUNCT
fuelectenerg-3309	175	80	3	3	NUM
fuelectenerg-3309	175	81	,	,	PUNCT
fuelectenerg-3309	175	82	1	1	NUM
fuelectenerg-3309	175	83	,	,	PUNCT
fuelectenerg-3309	175	84	4	4	NUM
fuelectenerg-3309	175	85	)	)	PUNCT
fuelectenerg-3309	175	86	,	,	PUNCT
fuelectenerg-3309	175	87	(	(	PUNCT
fuelectenerg-3309	175	88	4	4	NUM
fuelectenerg-3309	175	89	,	,	PUNCT
fuelectenerg-3309	175	90	2	2	NUM
fuelectenerg-3309	175	91	,	,	PUNCT
fuelectenerg-3309	175	92	1	1	NUM
fuelectenerg-3309	175	93	,	,	PUNCT
fuelectenerg-3309	175	94	3	3	NUM
fuelectenerg-3309	175	95	)	)	PUNCT
fuelectenerg-3309	175	96	,	,	PUNCT
fuelectenerg-3309	175	97	(	(	PUNCT
fuelectenerg-3309	175	98	2	2	NUM
fuelectenerg-3309	175	99	,	,	PUNCT
fuelectenerg-3309	175	100	4	4	NUM
fuelectenerg-3309	175	101	,	,	PUNCT
fuelectenerg-3309	175	102	1	1	NUM
fuelectenerg-3309	175	103	,	,	PUNCT
fuelectenerg-3309	175	104	3	3	NUM
fuelectenerg-3309	175	105	)	)	PUNCT
fuelectenerg-3309	175	106	,	,	PUNCT
fuelectenerg-3309	175	107	(	(	PUNCT
fuelectenerg-3309	175	108	2	2	NUM
fuelectenerg-3309	175	109	,	,	PUNCT
fuelectenerg-3309	175	110	1	1	NUM
fuelectenerg-3309	175	111	,	,	PUNCT
fuelectenerg-3309	175	112	4	4	NUM
fuelectenerg-3309	175	113	,	,	PUNCT
fuelectenerg-3309	175	114	3	3	NUM
fuelectenerg-3309	175	115	)	)	PUNCT
fuelectenerg-3309	175	116	,	,	PUNCT
fuelectenerg-3309	175	117	(	(	PUNCT
fuelectenerg-3309	175	118	2	2	NUM
fuelectenerg-3309	175	119	,	,	PUNCT
fuelectenerg-3309	175	120	1	1	NUM
fuelectenerg-3309	175	121	,	,	PUNCT
fuelectenerg-3309	175	122	3	3	NUM
fuelectenerg-3309	175	123	,	,	PUNCT
fuelectenerg-3309	175	124	4	4	NUM
fuelectenerg-3309	175	125	)	)	PUNCT
fuelectenerg-3309	175	126	,	,	PUNCT
fuelectenerg-3309	175	127	(	(	PUNCT
fuelectenerg-3309	175	128	4	4	NUM
fuelectenerg-3309	175	129	,	,	PUNCT
fuelectenerg-3309	175	130	3	3	NUM
fuelectenerg-3309	175	131	,	,	PUNCT
fuelectenerg-3309	175	132	1	1	NUM
fuelectenerg-3309	175	133	,	,	PUNCT
fuelectenerg-3309	175	134	2	2	NUM
fuelectenerg-3309	175	135	)	)	PUNCT
fuelectenerg-3309	175	136	,	,	PUNCT
fuelectenerg-3309	175	137	(	(	PUNCT
fuelectenerg-3309	175	138	3	3	NUM
fuelectenerg-3309	175	139	,	,	PUNCT
fuelectenerg-3309	175	140	4	4	NUM
fuelectenerg-3309	175	141	,	,	PUNCT
fuelectenerg-3309	175	142	1	1	NUM
fuelectenerg-3309	175	143	,	,	PUNCT
fuelectenerg-3309	175	144	2	2	NUM
fuelectenerg-3309	175	145	)	)	PUNCT
fuelectenerg-3309	175	146	,	,	PUNCT
fuelectenerg-3309	175	147	(	(	PUNCT
fuelectenerg-3309	175	148	3	3	NUM
fuelectenerg-3309	175	149	,	,	PUNCT
fuelectenerg-3309	175	150	1	1	NUM
fuelectenerg-3309	175	151	,	,	PUNCT
fuelectenerg-3309	175	152	4	4	NUM
fuelectenerg-3309	175	153	,	,	PUNCT
fuelectenerg-3309	175	154	2	2	NUM
fuelectenerg-3309	175	155	)	)	PUNCT
fuelectenerg-3309	175	156	,	,	PUNCT
fuelectenerg-3309	175	157	(	(	PUNCT
fuelectenerg-3309	175	158	3	3	NUM
fuelectenerg-3309	175	159	,	,	PUNCT
fuelectenerg-3309	175	160	1	1	NUM
fuelectenerg-3309	175	161	,	,	PUNCT
fuelectenerg-3309	175	162	2	2	NUM
fuelectenerg-3309	175	163	,	,	PUNCT
fuelectenerg-3309	175	164	4	4	NUM
fuelectenerg-3309	175	165	)	)	PUNCT
fuelectenerg-3309	175	166	,	,	PUNCT
fuelectenerg-3309	175	167	(	(	PUNCT
fuelectenerg-3309	175	168	4	4	NUM
fuelectenerg-3309	175	169	,	,	PUNCT
fuelectenerg-3309	175	170	1	1	NUM
fuelectenerg-3309	175	171	,	,	PUNCT
fuelectenerg-3309	175	172	3	3	NUM
fuelectenerg-3309	175	173	,	,	PUNCT
fuelectenerg-3309	175	174	2	2	NUM
fuelectenerg-3309	175	175	)	)	PUNCT
fuelectenerg-3309	175	176	,	,	PUNCT
fuelectenerg-3309	175	177	(	(	PUNCT
fuelectenerg-3309	175	178	1	1	NUM
fuelectenerg-3309	175	179	,	,	PUNCT
fuelectenerg-3309	175	180	4	4	NUM
fuelectenerg-3309	175	181	,	,	PUNCT
fuelectenerg-3309	175	182	3	3	NUM
fuelectenerg-3309	175	183	,	,	PUNCT
fuelectenerg-3309	175	184	2	2	NUM
fuelectenerg-3309	175	185	)	)	PUNCT
fuelectenerg-3309	175	186	,	,	PUNCT
fuelectenerg-3309	175	187	(	(	PUNCT
fuelectenerg-3309	175	188	1	1	NUM
fuelectenerg-3309	175	189	,	,	PUNCT
fuelectenerg-3309	175	190	3	3	NUM
fuelectenerg-3309	175	191	,	,	PUNCT
fuelectenerg-3309	175	192	4	4	NUM
fuelectenerg-3309	175	193	,	,	PUNCT
fuelectenerg-3309	175	194	2	2	NUM
fuelectenerg-3309	175	195	)	)	PUNCT
fuelectenerg-3309	175	196	,	,	PUNCT
fuelectenerg-3309	175	197	(	(	PUNCT
fuelectenerg-3309	175	198	1	1	NUM
fuelectenerg-3309	175	199	,	,	PUNCT
fuelectenerg-3309	175	200	3	3	NUM
fuelectenerg-3309	175	201	,	,	PUNCT
fuelectenerg-3309	175	202	2	2	NUM
fuelectenerg-3309	175	203	,	,	PUNCT
fuelectenerg-3309	175	204	4	4	NUM
fuelectenerg-3309	175	205	)	)	PUNCT
fuelectenerg-3309	175	206	,	,	PUNCT
fuelectenerg-3309	175	207	(	(	PUNCT
fuelectenerg-3309	175	208	4	4	NUM
fuelectenerg-3309	175	209	,	,	PUNCT
fuelectenerg-3309	175	210	1	1	NUM
fuelectenerg-3309	175	211	,	,	PUNCT
fuelectenerg-3309	175	212	2	2	NUM
fuelectenerg-3309	175	213	,	,	PUNCT
fuelectenerg-3309	175	214	3	3	NUM
fuelectenerg-3309	175	215	)	)	PUNCT
fuelectenerg-3309	175	216	,	,	PUNCT
fuelectenerg-3309	175	217	(	(	PUNCT
fuelectenerg-3309	175	218	1	1	NUM
fuelectenerg-3309	175	219	,	,	PUNCT
fuelectenerg-3309	175	220	4	4	NUM
fuelectenerg-3309	175	221	,	,	PUNCT
fuelectenerg-3309	175	222	2	2	NUM
fuelectenerg-3309	175	223	,	,	PUNCT
fuelectenerg-3309	175	224	3	3	NUM
fuelectenerg-3309	175	225	)	)	PUNCT
fuelectenerg-3309	175	226	,	,	PUNCT
fuelectenerg-3309	175	227	(	(	PUNCT
fuelectenerg-3309	175	228	1	1	NUM
fuelectenerg-3309	175	229	,	,	PUNCT
fuelectenerg-3309	175	230	2	2	NUM
fuelectenerg-3309	175	231	,	,	PUNCT
fuelectenerg-3309	175	232	4	4	NUM
fuelectenerg-3309	175	233	,	,	PUNCT
fuelectenerg-3309	175	234	3	3	NUM
fuelectenerg-3309	175	235	)	)	PUNCT
fuelectenerg-3309	175	236	,	,	PUNCT
fuelectenerg-3309	175	237	(	(	PUNCT
fuelectenerg-3309	175	238	1	1	NUM
fuelectenerg-3309	175	239	,	,	PUNCT
fuelectenerg-3309	175	240	2	2	NUM
fuelectenerg-3309	175	241	,	,	PUNCT
fuelectenerg-3309	175	242	3	3	NUM
fuelectenerg-3309	175	243	,	,	PUNCT
fuelectenerg-3309	175	244	4	4	NUM
fuelectenerg-3309	175	245	)	)	PUNCT
fuelectenerg-3309	175	246	}	}	PUNCT
fuelectenerg-3309	175	247	.	.	PUNCT
fuelectenerg-3309	176	1	s(4	s(4	NOUN
fuelectenerg-3309	176	2	)	)	PUNCT
fuelectenerg-3309	177	1	=	=	PRON
fuelectenerg-3309	177	2	{	{	PUNCT
fuelectenerg-3309	177	3	(	(	PUNCT
fuelectenerg-3309	177	4	1	1	NUM
fuelectenerg-3309	177	5	,	,	PUNCT
fuelectenerg-3309	177	6	1	1	NUM
fuelectenerg-3309	177	7	,	,	PUNCT
fuelectenerg-3309	177	8	1	1	NUM
fuelectenerg-3309	177	9	,	,	PUNCT
fuelectenerg-3309	177	10	1	1	NUM
fuelectenerg-3309	177	11	)	)	PUNCT
fuelectenerg-3309	177	12	,	,	PUNCT
fuelectenerg-3309	177	13	(	(	PUNCT
fuelectenerg-3309	177	14	1	1	NUM
fuelectenerg-3309	177	15	,	,	PUNCT
fuelectenerg-3309	177	16	1	1	NUM
fuelectenerg-3309	177	17	,	,	PUNCT
fuelectenerg-3309	177	18	1	1	NUM
fuelectenerg-3309	177	19	,	,	PUNCT
fuelectenerg-3309	177	20	2	2	NUM
fuelectenerg-3309	177	21	)	)	PUNCT
fuelectenerg-3309	177	22	,	,	PUNCT
fuelectenerg-3309	177	23	(	(	PUNCT
fuelectenerg-3309	177	24	1	1	NUM
fuelectenerg-3309	177	25	,	,	PUNCT
fuelectenerg-3309	177	26	1	1	NUM
fuelectenerg-3309	177	27	,	,	PUNCT
fuelectenerg-3309	177	28	1	1	NUM
fuelectenerg-3309	177	29	,	,	PUNCT
fuelectenerg-3309	177	30	3	3	NUM
fuelectenerg-3309	177	31	)	)	PUNCT
fuelectenerg-3309	177	32	,	,	PUNCT
fuelectenerg-3309	177	33	(	(	PUNCT
fuelectenerg-3309	177	34	1	1	NUM
fuelectenerg-3309	177	35	,	,	PUNCT
fuelectenerg-3309	177	36	1	1	NUM
fuelectenerg-3309	177	37	,	,	PUNCT
fuelectenerg-3309	177	38	1	1	NUM
fuelectenerg-3309	177	39	,	,	PUNCT
fuelectenerg-3309	177	40	4	4	NUM
fuelectenerg-3309	177	41	)	)	PUNCT
fuelectenerg-3309	177	42	,	,	PUNCT
fuelectenerg-3309	177	43	(	(	PUNCT
fuelectenerg-3309	177	44	1	1	NUM
fuelectenerg-3309	177	45	,	,	PUNCT
fuelectenerg-3309	177	46	1	1	NUM
fuelectenerg-3309	177	47	,	,	PUNCT
fuelectenerg-3309	177	48	2	2	NUM
fuelectenerg-3309	177	49	,	,	PUNCT
fuelectenerg-3309	177	50	1	1	NUM
fuelectenerg-3309	177	51	)	)	PUNCT
fuelectenerg-3309	177	52	,	,	PUNCT
fuelectenerg-3309	177	53	(	(	PUNCT
fuelectenerg-3309	177	54	1	1	NUM
fuelectenerg-3309	177	55	,	,	PUNCT
fuelectenerg-3309	177	56	1	1	NUM
fuelectenerg-3309	177	57	,	,	PUNCT
fuelectenerg-3309	177	58	2	2	NUM
fuelectenerg-3309	177	59	,	,	PUNCT
fuelectenerg-3309	177	60	2	2	NUM
fuelectenerg-3309	177	61	)	)	PUNCT
fuelectenerg-3309	177	62	,	,	PUNCT
fuelectenerg-3309	177	63	(	(	PUNCT
fuelectenerg-3309	177	64	1	1	NUM
fuelectenerg-3309	177	65	,	,	PUNCT
fuelectenerg-3309	177	66	1	1	NUM
fuelectenerg-3309	177	67	,	,	PUNCT
fuelectenerg-3309	177	68	2	2	NUM
fuelectenerg-3309	177	69	,	,	PUNCT
fuelectenerg-3309	177	70	3	3	NUM
fuelectenerg-3309	177	71	)	)	PUNCT
fuelectenerg-3309	177	72	,	,	PUNCT
fuelectenerg-3309	177	73	(	(	PUNCT
fuelectenerg-3309	177	74	1	1	NUM
fuelectenerg-3309	177	75	,	,	PUNCT
fuelectenerg-3309	177	76	1	1	NUM
fuelectenerg-3309	177	77	,	,	PUNCT
fuelectenerg-3309	177	78	2	2	NUM
fuelectenerg-3309	177	79	,	,	PUNCT
fuelectenerg-3309	177	80	4	4	NUM
fuelectenerg-3309	177	81	)	)	PUNCT
fuelectenerg-3309	177	82	,	,	PUNCT
fuelectenerg-3309	177	83	(	(	PUNCT
fuelectenerg-3309	177	84	1	1	NUM
fuelectenerg-3309	177	85	,	,	PUNCT
fuelectenerg-3309	177	86	1	1	NUM
fuelectenerg-3309	177	87	,	,	PUNCT
fuelectenerg-3309	177	88	3	3	NUM
fuelectenerg-3309	177	89	,	,	PUNCT
fuelectenerg-3309	177	90	1	1	NUM
fuelectenerg-3309	177	91	)	)	PUNCT
fuelectenerg-3309	177	92	,	,	PUNCT
fuelectenerg-3309	177	93	(	(	PUNCT
fuelectenerg-3309	177	94	1	1	NUM
fuelectenerg-3309	177	95	,	,	PUNCT
fuelectenerg-3309	177	96	1	1	NUM
fuelectenerg-3309	177	97	,	,	PUNCT
fuelectenerg-3309	177	98	3	3	NUM
fuelectenerg-3309	177	99	,	,	PUNCT
fuelectenerg-3309	177	100	2	2	NUM
fuelectenerg-3309	177	101	)	)	PUNCT
fuelectenerg-3309	177	102	,	,	PUNCT
fuelectenerg-3309	177	103	(	(	PUNCT
fuelectenerg-3309	177	104	1	1	NUM
fuelectenerg-3309	177	105	,	,	PUNCT
fuelectenerg-3309	177	106	1	1	NUM
fuelectenerg-3309	177	107	,	,	PUNCT
fuelectenerg-3309	177	108	3	3	NUM
fuelectenerg-3309	177	109	,	,	PUNCT
fuelectenerg-3309	177	110	3	3	NUM
fuelectenerg-3309	177	111	)	)	PUNCT
fuelectenerg-3309	177	112	,	,	PUNCT
fuelectenerg-3309	177	113	(	(	PUNCT
fuelectenerg-3309	177	114	1	1	NUM
fuelectenerg-3309	177	115	,	,	PUNCT
fuelectenerg-3309	177	116	1	1	NUM
fuelectenerg-3309	177	117	,	,	PUNCT
fuelectenerg-3309	177	118	3	3	NUM
fuelectenerg-3309	177	119	,	,	PUNCT
fuelectenerg-3309	177	120	4	4	NUM
fuelectenerg-3309	177	121	)	)	PUNCT
fuelectenerg-3309	177	122	,	,	PUNCT
fuelectenerg-3309	177	123	(	(	PUNCT
fuelectenerg-3309	177	124	1	1	NUM
fuelectenerg-3309	177	125	,	,	PUNCT
fuelectenerg-3309	177	126	2	2	NUM
fuelectenerg-3309	177	127	,	,	PUNCT
fuelectenerg-3309	177	128	1	1	NUM
fuelectenerg-3309	177	129	,	,	PUNCT
fuelectenerg-3309	177	130	1	1	NUM
fuelectenerg-3309	177	131	)	)	PUNCT
fuelectenerg-3309	177	132	,	,	PUNCT
fuelectenerg-3309	177	133	(	(	PUNCT
fuelectenerg-3309	177	134	1	1	NUM
fuelectenerg-3309	177	135	,	,	PUNCT
fuelectenerg-3309	177	136	2	2	NUM
fuelectenerg-3309	177	137	,	,	PUNCT
fuelectenerg-3309	177	138	1	1	NUM
fuelectenerg-3309	177	139	,	,	PUNCT
fuelectenerg-3309	177	140	2	2	NUM
fuelectenerg-3309	177	141	)	)	PUNCT
fuelectenerg-3309	177	142	,	,	PUNCT
fuelectenerg-3309	177	143	(	(	PUNCT
fuelectenerg-3309	177	144	1	1	NUM
fuelectenerg-3309	177	145	,	,	PUNCT
fuelectenerg-3309	177	146	2	2	NUM
fuelectenerg-3309	177	147	,	,	PUNCT
fuelectenerg-3309	177	148	1	1	NUM
fuelectenerg-3309	177	149	,	,	PUNCT
fuelectenerg-3309	177	150	3	3	NUM
fuelectenerg-3309	177	151	)	)	PUNCT
fuelectenerg-3309	177	152	,	,	PUNCT
fuelectenerg-3309	177	153	(	(	PUNCT
fuelectenerg-3309	177	154	1	1	NUM
fuelectenerg-3309	177	155	,	,	PUNCT
fuelectenerg-3309	177	156	2	2	NUM
fuelectenerg-3309	177	157	,	,	PUNCT
fuelectenerg-3309	177	158	1	1	NUM
fuelectenerg-3309	177	159	,	,	PUNCT
fuelectenerg-3309	177	160	4	4	NUM
fuelectenerg-3309	177	161	)	)	PUNCT
fuelectenerg-3309	177	162	,	,	PUNCT
fuelectenerg-3309	177	163	(	(	PUNCT
fuelectenerg-3309	177	164	1	1	NUM
fuelectenerg-3309	177	165	,	,	PUNCT
fuelectenerg-3309	177	166	2	2	NUM
fuelectenerg-3309	177	167	,	,	PUNCT
fuelectenerg-3309	177	168	2	2	NUM
fuelectenerg-3309	177	169	,	,	PUNCT
fuelectenerg-3309	177	170	1	1	NUM
fuelectenerg-3309	177	171	)	)	PUNCT
fuelectenerg-3309	177	172	,	,	PUNCT
fuelectenerg-3309	177	173	(	(	PUNCT
fuelectenerg-3309	177	174	1	1	NUM
fuelectenerg-3309	177	175	,	,	PUNCT
fuelectenerg-3309	177	176	2	2	NUM
fuelectenerg-3309	177	177	,	,	PUNCT
fuelectenerg-3309	177	178	2	2	NUM
fuelectenerg-3309	177	179	,	,	PUNCT
fuelectenerg-3309	177	180	2	2	NUM
fuelectenerg-3309	177	181	)	)	PUNCT
fuelectenerg-3309	177	182	,	,	PUNCT
fuelectenerg-3309	177	183	(	(	PUNCT
fuelectenerg-3309	177	184	1	1	NUM
fuelectenerg-3309	177	185	,	,	PUNCT
fuelectenerg-3309	177	186	2	2	NUM
fuelectenerg-3309	177	187	,	,	PUNCT
fuelectenerg-3309	177	188	2	2	NUM
fuelectenerg-3309	177	189	,	,	PUNCT
fuelectenerg-3309	177	190	3	3	NUM
fuelectenerg-3309	177	191	)	)	PUNCT
fuelectenerg-3309	177	192	,	,	PUNCT
fuelectenerg-3309	177	193	(	(	PUNCT
fuelectenerg-3309	177	194	1	1	NUM
fuelectenerg-3309	177	195	,	,	PUNCT
fuelectenerg-3309	177	196	2	2	NUM
fuelectenerg-3309	177	197	,	,	PUNCT
fuelectenerg-3309	177	198	2	2	NUM
fuelectenerg-3309	177	199	,	,	PUNCT
fuelectenerg-3309	177	200	4	4	NUM
fuelectenerg-3309	177	201	)	)	PUNCT
fuelectenerg-3309	177	202	,	,	PUNCT
fuelectenerg-3309	177	203	(	(	PUNCT
fuelectenerg-3309	177	204	1	1	NUM
fuelectenerg-3309	177	205	,	,	PUNCT
fuelectenerg-3309	177	206	2	2	NUM
fuelectenerg-3309	177	207	,	,	PUNCT
fuelectenerg-3309	177	208	3	3	NUM
fuelectenerg-3309	177	209	,	,	PUNCT
fuelectenerg-3309	177	210	1	1	NUM
fuelectenerg-3309	177	211	)	)	PUNCT
fuelectenerg-3309	177	212	,	,	PUNCT
fuelectenerg-3309	177	213	(	(	PUNCT
fuelectenerg-3309	177	214	1	1	NUM
fuelectenerg-3309	177	215	,	,	PUNCT
fuelectenerg-3309	177	216	2	2	NUM
fuelectenerg-3309	177	217	,	,	PUNCT
fuelectenerg-3309	177	218	3	3	NUM
fuelectenerg-3309	177	219	,	,	PUNCT
fuelectenerg-3309	177	220	2	2	NUM
fuelectenerg-3309	177	221	)	)	PUNCT
fuelectenerg-3309	177	222	,	,	PUNCT
fuelectenerg-3309	177	223	(	(	PUNCT
fuelectenerg-3309	177	224	1	1	NUM
fuelectenerg-3309	177	225	,	,	PUNCT
fuelectenerg-3309	177	226	2	2	NUM
fuelectenerg-3309	177	227	,	,	PUNCT
fuelectenerg-3309	177	228	3	3	NUM
fuelectenerg-3309	177	229	,	,	PUNCT
fuelectenerg-3309	177	230	3	3	NUM
fuelectenerg-3309	177	231	)	)	PUNCT
fuelectenerg-3309	177	232	,	,	PUNCT
fuelectenerg-3309	177	233	(	(	PUNCT
fuelectenerg-3309	177	234	1	1	NUM
fuelectenerg-3309	177	235	,	,	PUNCT
fuelectenerg-3309	177	236	2	2	NUM
fuelectenerg-3309	177	237	,	,	PUNCT
fuelectenerg-3309	177	238	3	3	NUM
fuelectenerg-3309	177	239	,	,	PUNCT
fuelectenerg-3309	177	240	4	4	NUM
fuelectenerg-3309	177	241	)	)	PUNCT
fuelectenerg-3309	177	242	}	}	PUNCT
fuelectenerg-3309	177	243	.	.	PUNCT
fuelectenerg-3309	178	1	for	for	ADP
fuelectenerg-3309	178	2	instance	instance	NOUN
fuelectenerg-3309	178	3	,	,	PUNCT
fuelectenerg-3309	178	4	the	the	DET
fuelectenerg-3309	178	5	permutation	permutation	NOUN
fuelectenerg-3309	178	6	ρ	ρ	X
fuelectenerg-3309	178	7	=	=	SYM
fuelectenerg-3309	178	8	(	(	PUNCT
fuelectenerg-3309	178	9	4	4	NUM
fuelectenerg-3309	178	10	,	,	PUNCT
fuelectenerg-3309	178	11	3	3	NUM
fuelectenerg-3309	178	12	,	,	PUNCT
fuelectenerg-3309	178	13	2	2	NUM
fuelectenerg-3309	178	14	,	,	PUNCT
fuelectenerg-3309	178	15	1	1	NUM
fuelectenerg-3309	178	16	)	)	PUNCT
fuelectenerg-3309	178	17	is	be	AUX
fuelectenerg-3309	178	18	uniquely	uniquely	ADV
fuelectenerg-3309	178	19	associated	associate	VERB
fuelectenerg-3309	178	20	with	with	ADP
fuelectenerg-3309	178	21	the	the	DET
fuelectenerg-3309	178	22	set	set	NOUN
fuelectenerg-3309	178	23	q(ρ	q(ρ	PROPN
fuelectenerg-3309	178	24	)	)	PUNCT
fuelectenerg-3309	178	25	=	=	PUNCT
fuelectenerg-3309	179	1	(	(	PUNCT
fuelectenerg-3309	179	2	1	1	NUM
fuelectenerg-3309	179	3	,	,	PUNCT
fuelectenerg-3309	179	4	1	1	NUM
fuelectenerg-3309	179	5	,	,	PUNCT
fuelectenerg-3309	179	6	1	1	NUM
fuelectenerg-3309	179	7	,	,	PUNCT
fuelectenerg-3309	179	8	1	1	NUM
fuelectenerg-3309	179	9	)	)	PUNCT
fuelectenerg-3309	179	10	(	(	PUNCT
fuelectenerg-3309	179	11	apply	apply	VERB
fuelectenerg-3309	179	12	example	example	NOUN
fuelectenerg-3309	179	13	1	1	NUM
fuelectenerg-3309	179	14	)	)	PUNCT
fuelectenerg-3309	179	15	and	and	CCONJ
fuelectenerg-3309	179	16	then	then	ADV
fuelectenerg-3309	179	17	uq(ρ	uq(ρ	NUM
fuelectenerg-3309	179	18	)	)	PUNCT
fuelectenerg-3309	180	1	=	=	SYM
fuelectenerg-3309	180	2	0	0	NUM
fuelectenerg-3309	180	3	by	by	ADP
fuelectenerg-3309	180	4	(	(	PUNCT
fuelectenerg-3309	180	5	2	2	NUM
fuelectenerg-3309	180	6	)	)	PUNCT
fuelectenerg-3309	180	7	.	.	PUNCT
fuelectenerg-3309	181	1	in	in	ADP
fuelectenerg-3309	181	2	the	the	DET
fuelectenerg-3309	181	3	same	same	ADJ
fuelectenerg-3309	181	4	spirit	spirit	NOUN
fuelectenerg-3309	181	5	,	,	PUNCT
fuelectenerg-3309	181	6	the	the	DET
fuelectenerg-3309	181	7	permutation	permutation	NOUN
fuelectenerg-3309	181	8	ρ	ρ	X
fuelectenerg-3309	181	9	=	=	SYM
fuelectenerg-3309	181	10	(	(	PUNCT
fuelectenerg-3309	181	11	3	3	NUM
fuelectenerg-3309	181	12	,	,	PUNCT
fuelectenerg-3309	181	13	4	4	NUM
fuelectenerg-3309	181	14	,	,	PUNCT
fuelectenerg-3309	181	15	2	2	NUM
fuelectenerg-3309	181	16	,	,	PUNCT
fuelectenerg-3309	181	17	1	1	NUM
fuelectenerg-3309	181	18	)	)	PUNCT
fuelectenerg-3309	181	19	is	be	AUX
fuelectenerg-3309	181	20	uniquely	uniquely	ADV
fuelectenerg-3309	181	21	associated	associate	VERB
fuelectenerg-3309	181	22	with	with	ADP
fuelectenerg-3309	181	23	the	the	DET
fuelectenerg-3309	181	24	set	set	NOUN
fuelectenerg-3309	181	25	q(ρ	q(ρ	PROPN
fuelectenerg-3309	181	26	)	)	PUNCT
fuelectenerg-3309	181	27	=	=	PUNCT
fuelectenerg-3309	182	1	(	(	PUNCT
fuelectenerg-3309	182	2	1	1	NUM
fuelectenerg-3309	182	3	,	,	PUNCT
fuelectenerg-3309	182	4	1	1	NUM
fuelectenerg-3309	182	5	,	,	PUNCT
fuelectenerg-3309	182	6	1	1	NUM
fuelectenerg-3309	182	7	,	,	PUNCT
fuelectenerg-3309	182	8	2	2	NUM
fuelectenerg-3309	182	9	)	)	PUNCT
fuelectenerg-3309	182	10	(	(	PUNCT
fuelectenerg-3309	182	11	apply	apply	VERB
fuelectenerg-3309	182	12	example	example	NOUN
fuelectenerg-3309	182	13	1	1	NUM
fuelectenerg-3309	182	14	)	)	PUNCT
fuelectenerg-3309	182	15	and	and	CCONJ
fuelectenerg-3309	182	16	then	then	ADV
fuelectenerg-3309	182	17	uq(ρ	uq(ρ	NUM
fuelectenerg-3309	182	18	)	)	PUNCT
fuelectenerg-3309	182	19	=	=	SYM
fuelectenerg-3309	183	1	1	1	NUM
fuelectenerg-3309	183	2	by	by	ADP
fuelectenerg-3309	183	3	(	(	PUNCT
fuelectenerg-3309	183	4	2	2	NUM
fuelectenerg-3309	183	5	)	)	PUNCT
fuelectenerg-3309	183	6	.	.	PUNCT
fuelectenerg-3309	184	1	remark	remark	NOUN
fuelectenerg-3309	184	2	1	1	NUM
fuelectenerg-3309	184	3	the	the	DET
fuelectenerg-3309	184	4	set	set	PROPN
fuelectenerg-3309	184	5	s(m	s(m	PROPN
fuelectenerg-3309	184	6	)	)	PUNCT
fuelectenerg-3309	184	7	in	in	ADP
fuelectenerg-3309	184	8	(	(	PUNCT
fuelectenerg-3309	184	9	1	1	X
fuelectenerg-3309	184	10	)	)	PUNCT
fuelectenerg-3309	184	11	seems	seem	VERB
fuelectenerg-3309	184	12	to	to	PART
fuelectenerg-3309	184	13	be	be	AUX
fuelectenerg-3309	184	14	similar	similar	ADJ
fuelectenerg-3309	184	15	with	with	ADP
fuelectenerg-3309	184	16	a	a	DET
fuelectenerg-3309	184	17	lehmer	lehmer	NOUN
fuelectenerg-3309	184	18	code	code	NOUN
fuelectenerg-3309	185	1	[	[	X
fuelectenerg-3309	185	2	7	7	NUM
fuelectenerg-3309	185	3	]	]	PUNCT
fuelectenerg-3309	185	4	,	,	PUNCT
fuelectenerg-3309	185	5	but	but	CCONJ
fuelectenerg-3309	185	6	our	our	PRON
fuelectenerg-3309	185	7	approach	approach	NOUN
fuelectenerg-3309	185	8	seems	seem	VERB
fuelectenerg-3309	185	9	to	to	PART
fuelectenerg-3309	185	10	be	be	AUX
fuelectenerg-3309	185	11	more	more	ADV
fuelectenerg-3309	185	12	efficient	efficient	ADJ
fuelectenerg-3309	185	13	for	for	ADP
fuelectenerg-3309	185	14	the	the	DET
fuelectenerg-3309	185	15	purpose	purpose	NOUN
fuelectenerg-3309	185	16	of	of	ADP
fuelectenerg-3309	185	17	obtaining	obtain	VERB
fuelectenerg-3309	185	18	a	a	DET
fuelectenerg-3309	185	19	great	great	ADJ
fuelectenerg-3309	185	20	variety	variety	NOUN
fuelectenerg-3309	185	21	of	of	ADP
fuelectenerg-3309	185	22	enumerating	enumerate	VERB
fuelectenerg-3309	185	23	methods	method	NOUN
fuelectenerg-3309	185	24	for	for	ADP
fuelectenerg-3309	185	25	p	p	PROPN
fuelectenerg-3309	185	26	(	(	PUNCT
fuelectenerg-3309	185	27	m	m	NOUN
fuelectenerg-3309	185	28	)	)	PUNCT
fuelectenerg-3309	185	29	,	,	PUNCT
fuelectenerg-3309	185	30	see	see	VERB
fuelectenerg-3309	185	31	theorem	theorem	ADJ
fuelectenerg-3309	185	32	(	(	PUNCT
fuelectenerg-3309	185	33	1	1	NUM
fuelectenerg-3309	185	34	)	)	PUNCT
fuelectenerg-3309	185	35	below	below	ADV
fuelectenerg-3309	185	36	.	.	PUNCT
fuelectenerg-3309	186	1	we	we	PRON
fuelectenerg-3309	186	2	notice	notice	VERB
fuelectenerg-3309	186	3	that	that	SCONJ
fuelectenerg-3309	186	4	the	the	DET
fuelectenerg-3309	186	5	lehmer	lehmer	NOUN
fuelectenerg-3309	186	6	code	code	NOUN
fuelectenerg-3309	186	7	of	of	ADP
fuelectenerg-3309	186	8	a	a	DET
fuelectenerg-3309	186	9	permutation	permutation	NOUN
fuelectenerg-3309	186	10	ρ	ρ	NOUN
fuelectenerg-3309	186	11	=	=	SYM
fuelectenerg-3309	186	12	(	(	PUNCT
fuelectenerg-3309	186	13	ρ1	ρ1	PROPN
fuelectenerg-3309	186	14	,	,	PUNCT
fuelectenerg-3309	186	15	....	....	PUNCT
fuelectenerg-3309	186	16	ρm	ρm	X
fuelectenerg-3309	186	17	)	)	PUNCT
fuelectenerg-3309	186	18	is	be	AUX
fuelectenerg-3309	186	19	a	a	DET
fuelectenerg-3309	186	20	sequence	sequence	NOUN
fuelectenerg-3309	186	21	of	of	ADP
fuelectenerg-3309	186	22	natural	natural	ADJ
fuelectenerg-3309	186	23	numbers	number	NOUN
fuelectenerg-3309	186	24	(	(	PUNCT
fuelectenerg-3309	186	25	l1	l1	PROPN
fuelectenerg-3309	186	26	,	,	PUNCT
fuelectenerg-3309	186	27	...	...	PUNCT
fuelectenerg-3309	186	28	,	,	PUNCT
fuelectenerg-3309	186	29	lm	lm	X
fuelectenerg-3309	186	30	)	)	PUNCT
fuelectenerg-3309	186	31	such	such	ADJ
fuelectenerg-3309	186	32	that	that	SCONJ
fuelectenerg-3309	186	33	li	li	PROPN
fuelectenerg-3309	186	34	is	be	AUX
fuelectenerg-3309	186	35	the	the	DET
fuelectenerg-3309	186	36	number	number	NOUN
fuelectenerg-3309	186	37	of	of	ADP
fuelectenerg-3309	186	38	all	all	DET
fuelectenerg-3309	186	39	elements	element	NOUN
fuelectenerg-3309	186	40	ρ1	ρ1	NOUN
fuelectenerg-3309	186	41	,	,	PUNCT
fuelectenerg-3309	186	42	...	...	PUNCT
fuelectenerg-3309	186	43	,	,	PUNCT
fuelectenerg-3309	186	44	ρi−1	ρi−1	PROPN
fuelectenerg-3309	186	45	which	which	PRON
fuelectenerg-3309	186	46	are	be	AUX
fuelectenerg-3309	186	47	less	less	ADJ
fuelectenerg-3309	186	48	than	than	ADP
fuelectenerg-3309	186	49	ρi	ρi	NOUN
fuelectenerg-3309	186	50	,	,	PUNCT
fuelectenerg-3309	186	51	i	i	NOUN
fuelectenerg-3309	186	52	=	=	NOUN
fuelectenerg-3309	186	53	1	1	NUM
fuelectenerg-3309	186	54	,	,	PUNCT
fuelectenerg-3309	186	55	...	...	PUNCT
fuelectenerg-3309	186	56	,	,	PUNCT
fuelectenerg-3309	186	57	m.	m.	NOUN
fuelectenerg-3309	186	58	244	244	NUM
fuelectenerg-3309	186	59	c.	c.	PROPN
fuelectenerg-3309	186	60	karanikas	karanikas	PROPN
fuelectenerg-3309	186	61	,	,	PUNCT
fuelectenerg-3309	186	62	n.	n.	PROPN
fuelectenerg-3309	186	63	atreas	atreas	PROPN
fuelectenerg-3309	186	64	enumeration	enumeration	PROPN
fuelectenerg-3309	186	65	and	and	CCONJ
fuelectenerg-3309	186	66	coding	code	VERB
fuelectenerg-3309	186	67	permutations	permutation	NOUN
fuelectenerg-3309	186	68	and	and	CCONJ
fuelectenerg-3309	186	69	reversible	reversible	ADJ
fuelectenerg-3309	186	70	logical	logical	ADJ
fuelectenerg-3309	186	71	circuits	circuit	NOUN
fuelectenerg-3309	186	72	245	245	NUM
fuelectenerg-3309	186	73	6	6	NUM
fuelectenerg-3309	186	74	n.	n.	NOUN
fuelectenerg-3309	186	75	atreas	atreas	PROPN
fuelectenerg-3309	186	76	and	and	CCONJ
fuelectenerg-3309	186	77	c.	c.	PROPN
fuelectenerg-3309	186	78	karanikas	karanikas	PROPN
fuelectenerg-3309	186	79	we	we	PRON
fuelectenerg-3309	186	80	may	may	AUX
fuelectenerg-3309	186	81	obtain	obtain	VERB
fuelectenerg-3309	186	82	various	various	ADJ
fuelectenerg-3309	186	83	enumerations	enumeration	NOUN
fuelectenerg-3309	186	84	of	of	ADP
fuelectenerg-3309	186	85	the	the	DET
fuelectenerg-3309	186	86	elements	element	NOUN
fuelectenerg-3309	186	87	of	of	ADP
fuelectenerg-3309	186	88	s(m	s(m	NOUN
fuelectenerg-3309	186	89	)	)	PUNCT
fuelectenerg-3309	186	90	(	(	PUNCT
fuelectenerg-3309	186	91	and	and	CCONJ
fuelectenerg-3309	186	92	hence	hence	ADV
fuelectenerg-3309	186	93	p	p	X
fuelectenerg-3309	186	94	(	(	PUNCT
fuelectenerg-3309	186	95	m	m	NOUN
fuelectenerg-3309	186	96	)	)	PUNCT
fuelectenerg-3309	186	97	as	as	ADV
fuelectenerg-3309	186	98	well	well	ADV
fuelectenerg-3309	186	99	)	)	PUNCT
fuelectenerg-3309	186	100	.	.	PUNCT
fuelectenerg-3309	187	1	indeed	indeed	ADV
fuelectenerg-3309	187	2	,	,	PUNCT
fuelectenerg-3309	187	3	let	let	VERB
fuelectenerg-3309	187	4	us	we	PRON
fuelectenerg-3309	187	5	fix	fix	VERB
fuelectenerg-3309	187	6	any	any	DET
fuelectenerg-3309	187	7	element	element	NOUN
fuelectenerg-3309	187	8	r	r	NOUN
fuelectenerg-3309	187	9	=	=	PUNCT
fuelectenerg-3309	187	10	(	(	PUNCT
fuelectenerg-3309	187	11	r1	r1	PROPN
fuelectenerg-3309	187	12	,	,	PUNCT
fuelectenerg-3309	187	13	r2	r2	PROPN
fuelectenerg-3309	187	14	,	,	PUNCT
fuelectenerg-3309	187	15	...	...	PUNCT
fuelectenerg-3309	187	16	,	,	PUNCT
fuelectenerg-3309	187	17	rm	rm	PROPN
fuelectenerg-3309	187	18	)	)	PUNCT
fuelectenerg-3309	187	19	∈	∈	PROPN
fuelectenerg-3309	187	20	r(m	r(m	PROPN
fuelectenerg-3309	187	21	)	)	PUNCT
fuelectenerg-3309	188	1	=	=	SYM
fuelectenerg-3309	188	2	p	p	X
fuelectenerg-3309	188	3	(	(	PUNCT
fuelectenerg-3309	188	4	1)×	1)×	NUM
fuelectenerg-3309	188	5	p	p	NOUN
fuelectenerg-3309	188	6	(	(	PUNCT
fuelectenerg-3309	188	7	2)×	2)×	NUM
fuelectenerg-3309	188	8	...	...	SYM
fuelectenerg-3309	188	9	×	×	NOUN
fuelectenerg-3309	188	10	p	p	X
fuelectenerg-3309	188	11	(	(	PUNCT
fuelectenerg-3309	188	12	m	m	NOUN
fuelectenerg-3309	188	13	)	)	PUNCT
fuelectenerg-3309	188	14	,	,	PUNCT
fuelectenerg-3309	188	15	(	(	PUNCT
fuelectenerg-3309	188	16	4	4	X
fuelectenerg-3309	188	17	)	)	PUNCT
fuelectenerg-3309	188	18	where	where	SCONJ
fuelectenerg-3309	188	19	ri	ri	NOUN
fuelectenerg-3309	188	20	=	=	PUNCT
fuelectenerg-3309	188	21	(	(	PUNCT
fuelectenerg-3309	188	22	ri,1	ri,1	PROPN
fuelectenerg-3309	188	23	,	,	PUNCT
fuelectenerg-3309	188	24	...	...	PUNCT
fuelectenerg-3309	188	25	ri	ri	NOUN
fuelectenerg-3309	188	26	,	,	PUNCT
fuelectenerg-3309	188	27	i	i	NOUN
fuelectenerg-3309	188	28	)	)	PUNCT
fuelectenerg-3309	188	29	∈	∈	PROPN
fuelectenerg-3309	189	1	p	p	X
fuelectenerg-3309	189	2	(	(	PUNCT
fuelectenerg-3309	189	3	i	i	PROPN
fuelectenerg-3309	189	4	)	)	PUNCT
fuelectenerg-3309	189	5	,	,	PUNCT
fuelectenerg-3309	189	6	i	i	PRON
fuelectenerg-3309	189	7	=	=	NOUN
fuelectenerg-3309	189	8	1	1	NUM
fuelectenerg-3309	189	9	,	,	PUNCT
fuelectenerg-3309	189	10	...	...	PUNCT
fuelectenerg-3309	189	11	,	,	PUNCT
fuelectenerg-3309	189	12	m.	m.	NOUN
fuelectenerg-3309	189	13	then	then	ADV
fuelectenerg-3309	189	14	we	we	PRON
fuelectenerg-3309	189	15	have	have	AUX
fuelectenerg-3309	189	16	:	:	PUNCT
fuelectenerg-3309	189	17	theorem	theorem	VERB
fuelectenerg-3309	189	18	1	1	NUM
fuelectenerg-3309	189	19	let	let	VERB
fuelectenerg-3309	189	20	s(m	s(m	PROPN
fuelectenerg-3309	189	21	)	)	PUNCT
fuelectenerg-3309	189	22	be	be	AUX
fuelectenerg-3309	189	23	defined	define	VERB
fuelectenerg-3309	189	24	in	in	ADP
fuelectenerg-3309	189	25	(	(	PUNCT
fuelectenerg-3309	189	26	1	1	NUM
fuelectenerg-3309	189	27	)	)	PUNCT
fuelectenerg-3309	189	28	and	and	CCONJ
fuelectenerg-3309	189	29	r	r	NOUN
fuelectenerg-3309	189	30	be	be	AUX
fuelectenerg-3309	189	31	a	a	DET
fuelectenerg-3309	189	32	fixed	fix	VERB
fuelectenerg-3309	189	33	element	element	NOUN
fuelectenerg-3309	189	34	of	of	ADP
fuelectenerg-3309	189	35	r(m	r(m	PROPN
fuelectenerg-3309	189	36	)	)	PUNCT
fuelectenerg-3309	189	37	as	as	ADP
fuelectenerg-3309	189	38	in	in	ADP
fuelectenerg-3309	189	39	(	(	PUNCT
fuelectenerg-3309	189	40	4	4	NUM
fuelectenerg-3309	189	41	)	)	PUNCT
fuelectenerg-3309	189	42	.	.	PUNCT
fuelectenerg-3309	190	1	for	for	ADP
fuelectenerg-3309	190	2	any	any	DET
fuelectenerg-3309	190	3	s	s	PROPN
fuelectenerg-3309	190	4	∈	∈	PROPN
fuelectenerg-3309	190	5	s(m	s(m	PROPN
fuelectenerg-3309	190	6	)	)	PUNCT
fuelectenerg-3309	190	7	we	we	PRON
fuelectenerg-3309	190	8	define	define	VERB
fuelectenerg-3309	190	9	wr	wr	PROPN
fuelectenerg-3309	190	10	,	,	PUNCT
fuelectenerg-3309	190	11	m(s	m(s	PROPN
fuelectenerg-3309	190	12	)	)	PUNCT
fuelectenerg-3309	190	13	=	=	PUNCT
fuelectenerg-3309	191	1	(	(	PUNCT
fuelectenerg-3309	191	2	r1,s1	r1,s1	PROPN
fuelectenerg-3309	191	3	,	,	PUNCT
fuelectenerg-3309	191	4	r2,s2	r2,s2	PROPN
fuelectenerg-3309	191	5	,	,	PUNCT
fuelectenerg-3309	191	6	...	...	PUNCT
fuelectenerg-3309	191	7	,	,	PUNCT
fuelectenerg-3309	191	8	rm	rm	PROPN
fuelectenerg-3309	191	9	,	,	PUNCT
fuelectenerg-3309	191	10	sm	sm	PROPN
fuelectenerg-3309	191	11	)	)	PUNCT
fuelectenerg-3309	191	12	then	then	ADV
fuelectenerg-3309	191	13	the	the	DET
fuelectenerg-3309	191	14	map	map	NOUN
fuelectenerg-3309	191	15	wr	wr	PROPN
fuelectenerg-3309	191	16	,	,	PUNCT
fuelectenerg-3309	191	17	m	m	VERB
fuelectenerg-3309	191	18	is	be	AUX
fuelectenerg-3309	191	19	onto	onto	ADP
fuelectenerg-3309	191	20	s(m	s(m	NOUN
fuelectenerg-3309	191	21	)	)	PUNCT
fuelectenerg-3309	191	22	.	.	PUNCT
fuelectenerg-3309	192	1	proof	proof	NOUN
fuelectenerg-3309	192	2	:	:	PUNCT
fuelectenerg-3309	192	3	let	let	VERB
fuelectenerg-3309	192	4	us	we	PRON
fuelectenerg-3309	192	5	fix	fix	VERB
fuelectenerg-3309	192	6	an	an	DET
fuelectenerg-3309	192	7	element	element	NOUN
fuelectenerg-3309	192	8	r	r	NOUN
fuelectenerg-3309	192	9	∈	∈	NOUN
fuelectenerg-3309	192	10	r(m	r(m	NOUN
fuelectenerg-3309	192	11	)	)	PUNCT
fuelectenerg-3309	192	12	.	.	PUNCT
fuelectenerg-3309	193	1	since	since	SCONJ
fuelectenerg-3309	193	2	ri	ri	PROPN
fuelectenerg-3309	193	3	,	,	PUNCT
fuelectenerg-3309	193	4	si	si	PROPN
fuelectenerg-3309	193	5	≤	≤	ADV
fuelectenerg-3309	193	6	i	i	PRON
fuelectenerg-3309	193	7	(	(	PUNCT
fuelectenerg-3309	193	8	due	due	ADP
fuelectenerg-3309	193	9	to	to	ADP
fuelectenerg-3309	193	10	the	the	DET
fuelectenerg-3309	193	11	fact	fact	NOUN
fuelectenerg-3309	193	12	that	that	SCONJ
fuelectenerg-3309	193	13	ri	ri	PROPN
fuelectenerg-3309	193	14	∈	∈	PROPN
fuelectenerg-3309	193	15	p	p	X
fuelectenerg-3309	193	16	(	(	PUNCT
fuelectenerg-3309	193	17	i	i	NOUN
fuelectenerg-3309	193	18	)	)	PUNCT
fuelectenerg-3309	193	19	)	)	PUNCT
fuelectenerg-3309	193	20	,	,	PUNCT
fuelectenerg-3309	193	21	we	we	PRON
fuelectenerg-3309	193	22	deduce	deduce	VERB
fuelectenerg-3309	193	23	that	that	DET
fuelectenerg-3309	193	24	wr	wr	NOUN
fuelectenerg-3309	193	25	,	,	PUNCT
fuelectenerg-3309	193	26	m(s	m(s	PROPN
fuelectenerg-3309	193	27	)	)	PUNCT
fuelectenerg-3309	193	28	∈	∈	PROPN
fuelectenerg-3309	193	29	s(m	s(m	PROPN
fuelectenerg-3309	193	30	)	)	PUNCT
fuelectenerg-3309	193	31	.	.	PUNCT
fuelectenerg-3309	194	1	also	also	ADV
fuelectenerg-3309	194	2	,	,	PUNCT
fuelectenerg-3309	194	3	the	the	DET
fuelectenerg-3309	194	4	fact	fact	NOUN
fuelectenerg-3309	194	5	that	that	SCONJ
fuelectenerg-3309	194	6	ri	ri	PROPN
fuelectenerg-3309	194	7	,	,	PUNCT
fuelectenerg-3309	194	8	j	j	PROPN
fuelectenerg-3309	194	9	≤	≤	PROPN
fuelectenerg-3309	195	1	i	i	PRON
fuelectenerg-3309	195	2	for	for	ADP
fuelectenerg-3309	195	3	any	any	DET
fuelectenerg-3309	195	4	j	j	NOUN
fuelectenerg-3309	195	5	=	=	SYM
fuelectenerg-3309	195	6	1	1	NUM
fuelectenerg-3309	195	7	,	,	PUNCT
fuelectenerg-3309	195	8	...	...	PUNCT
fuelectenerg-3309	195	9	,	,	PUNCT
fuelectenerg-3309	195	10	i	i	PRON
fuelectenerg-3309	195	11	implies	imply	VERB
fuelectenerg-3309	195	12	that	that	PRON
fuelectenerg-3309	195	13	wr	wr	NOUN
fuelectenerg-3309	195	14	,	,	PUNCT
fuelectenerg-3309	195	15	m	m	VERB
fuelectenerg-3309	195	16	is	be	AUX
fuelectenerg-3309	195	17	onto	onto	ADP
fuelectenerg-3309	195	18	s(m	s(m	NOUN
fuelectenerg-3309	195	19	)	)	PUNCT
fuelectenerg-3309	195	20	,	,	PUNCT
fuelectenerg-3309	195	21	because	because	SCONJ
fuelectenerg-3309	195	22	any	any	DET
fuelectenerg-3309	195	23	element	element	NOUN
fuelectenerg-3309	195	24	si	si	NOUN
fuelectenerg-3309	195	25	of	of	ADP
fuelectenerg-3309	195	26	s	s	PROPN
fuelectenerg-3309	195	27	=	=	PUNCT
fuelectenerg-3309	195	28	(	(	PUNCT
fuelectenerg-3309	195	29	s1	s1	PROPN
fuelectenerg-3309	195	30	,	,	PUNCT
fuelectenerg-3309	195	31	...	...	PUNCT
fuelectenerg-3309	195	32	,	,	PUNCT
fuelectenerg-3309	195	33	sm	sm	PROPN
fuelectenerg-3309	195	34	)	)	PUNCT
fuelectenerg-3309	195	35	can	can	AUX
fuelectenerg-3309	195	36	be	be	AUX
fuelectenerg-3309	195	37	written	write	VERB
fuelectenerg-3309	195	38	by	by	ADP
fuelectenerg-3309	195	39	si	si	X
fuelectenerg-3309	195	40	=	=	PROPN
fuelectenerg-3309	195	41	ri	ri	PROPN
fuelectenerg-3309	195	42	,	,	PUNCT
fuelectenerg-3309	195	43	a(i	a(i	PROPN
fuelectenerg-3309	195	44	)	)	PUNCT
fuelectenerg-3309	195	45	for	for	ADP
fuelectenerg-3309	195	46	some	some	DET
fuelectenerg-3309	195	47	index	index	NOUN
fuelectenerg-3309	195	48	a(i	a(i	NOUN
fuelectenerg-3309	195	49	)	)	PUNCT
fuelectenerg-3309	195	50	≤	≤	PUNCT
fuelectenerg-3309	196	1	i	i	PRON
fuelectenerg-3309	196	2	and	and	CCONJ
fuelectenerg-3309	196	3	so	so	ADV
fuelectenerg-3309	196	4	by	by	ADP
fuelectenerg-3309	196	5	defining	define	VERB
fuelectenerg-3309	196	6	a	a	DET
fuelectenerg-3309	196	7	=	=	X
fuelectenerg-3309	196	8	{	{	PUNCT
fuelectenerg-3309	196	9	a(i	a(i	PROPN
fuelectenerg-3309	196	10	)	)	PUNCT
fuelectenerg-3309	196	11	:	:	PUNCT
fuelectenerg-3309	197	1	i	i	NOUN
fuelectenerg-3309	197	2	=	=	NOUN
fuelectenerg-3309	197	3	1	1	NUM
fuelectenerg-3309	197	4	,	,	PUNCT
fuelectenerg-3309	197	5	...	...	PUNCT
fuelectenerg-3309	197	6	,	,	PUNCT
fuelectenerg-3309	197	7	m	m	AUX
fuelectenerg-3309	197	8	}	}	PUNCT
fuelectenerg-3309	197	9	we	we	PRON
fuelectenerg-3309	197	10	have	have	VERB
fuelectenerg-3309	197	11	wr	wr	PROPN
fuelectenerg-3309	197	12	,	,	PUNCT
fuelectenerg-3309	197	13	m(a	m(a	PROPN
fuelectenerg-3309	197	14	)	)	PUNCT
fuelectenerg-3309	197	15	=	=	VERB
fuelectenerg-3309	198	1	s.	s.	PROPN
fuelectenerg-3309	198	2	let	let	VERB
fuelectenerg-3309	198	3	u	u	PRON
fuelectenerg-3309	198	4	be	be	AUX
fuelectenerg-3309	198	5	as	as	ADP
fuelectenerg-3309	198	6	in	in	ADP
fuelectenerg-3309	198	7	(	(	PUNCT
fuelectenerg-3309	198	8	2	2	NUM
fuelectenerg-3309	198	9	)	)	PUNCT
fuelectenerg-3309	198	10	and	and	CCONJ
fuelectenerg-3309	198	11	wr	wr	PROPN
fuelectenerg-3309	198	12	,	,	PUNCT
fuelectenerg-3309	198	13	m	m	VERB
fuelectenerg-3309	198	14	be	be	VERB
fuelectenerg-3309	198	15	as	as	ADP
fuelectenerg-3309	198	16	in	in	ADP
fuelectenerg-3309	198	17	theorem	theorem	NOUN
fuelectenerg-3309	198	18	1	1	NUM
fuelectenerg-3309	198	19	.	.	PUNCT
fuelectenerg-3309	199	1	it	it	PRON
fuelectenerg-3309	199	2	is	be	AUX
fuelectenerg-3309	199	3	easy	easy	ADJ
fuelectenerg-3309	199	4	to	to	PART
fuelectenerg-3309	199	5	see	see	VERB
fuelectenerg-3309	199	6	that	that	SCONJ
fuelectenerg-3309	199	7	the	the	DET
fuelectenerg-3309	199	8	map	map	NOUN
fuelectenerg-3309	199	9	uwr	uwr	NOUN
fuelectenerg-3309	199	10	,	,	PUNCT
fuelectenerg-3309	199	11	mu−1	mu−1	PROPN
fuelectenerg-3309	199	12	:	:	PUNCT
fuelectenerg-3309	199	13	{	{	PUNCT
fuelectenerg-3309	199	14	0	0	NUM
fuelectenerg-3309	199	15	,	,	PUNCT
fuelectenerg-3309	199	16	...	...	PUNCT
fuelectenerg-3309	199	17	,	,	PUNCT
fuelectenerg-3309	199	18	m!−	m!−	VERB
fuelectenerg-3309	199	19	1	1	NUM
fuelectenerg-3309	199	20	}	}	PUNCT
fuelectenerg-3309	199	21	→	→	SYM
fuelectenerg-3309	199	22	{	{	PUNCT
fuelectenerg-3309	199	23	0	0	NUM
fuelectenerg-3309	199	24	,	,	PUNCT
fuelectenerg-3309	199	25	...	...	PUNCT
fuelectenerg-3309	199	26	,	,	PUNCT
fuelectenerg-3309	199	27	m!−	m!−	VERB
fuelectenerg-3309	199	28	1	1	NUM
fuelectenerg-3309	199	29	}	}	PUNCT
fuelectenerg-3309	199	30	provides	provide	VERB
fuelectenerg-3309	199	31	a	a	DET
fuelectenerg-3309	199	32	method	method	NOUN
fuelectenerg-3309	199	33	for	for	ADP
fuelectenerg-3309	199	34	shuffling	shuffle	VERB
fuelectenerg-3309	199	35	the	the	DET
fuelectenerg-3309	199	36	set	set	NOUN
fuelectenerg-3309	199	37	{	{	PUNCT
fuelectenerg-3309	199	38	0	0	NUM
fuelectenerg-3309	199	39	,	,	PUNCT
fuelectenerg-3309	199	40	...	...	PUNCT
fuelectenerg-3309	199	41	,	,	PUNCT
fuelectenerg-3309	199	42	m	m	PROPN
fuelectenerg-3309	199	43	!	!	PUNCT
fuelectenerg-3309	200	1	−	−	PROPN
fuelectenerg-3309	200	2	1	1	NUM
fuelectenerg-3309	200	3	}	}	PUNCT
fuelectenerg-3309	200	4	.	.	PUNCT
fuelectenerg-3309	201	1	by	by	ADP
fuelectenerg-3309	201	2	altering	alter	VERB
fuelectenerg-3309	201	3	the	the	DET
fuelectenerg-3309	201	4	selection	selection	NOUN
fuelectenerg-3309	201	5	of	of	ADP
fuelectenerg-3309	201	6	r	r	NOUN
fuelectenerg-3309	201	7	∈	∈	PROPN
fuelectenerg-3309	201	8	r(m	r(m	NOUN
fuelectenerg-3309	201	9	)	)	PUNCT
fuelectenerg-3309	201	10	in	in	ADP
fuelectenerg-3309	201	11	(	(	PUNCT
fuelectenerg-3309	201	12	4	4	X
fuelectenerg-3309	201	13	)	)	PUNCT
fuelectenerg-3309	201	14	we	we	PRON
fuelectenerg-3309	201	15	obtain	obtain	VERB
fuelectenerg-3309	201	16	a	a	DET
fuelectenerg-3309	201	17	different	different	ADJ
fuelectenerg-3309	201	18	shuffling	shuffling	NOUN
fuelectenerg-3309	201	19	.	.	PUNCT
fuelectenerg-3309	202	1	finally	finally	ADV
fuelectenerg-3309	202	2	,	,	PUNCT
fuelectenerg-3309	202	3	it	it	PRON
fuelectenerg-3309	202	4	is	be	AUX
fuelectenerg-3309	202	5	clear	clear	ADJ
fuelectenerg-3309	202	6	that	that	SCONJ
fuelectenerg-3309	202	7	the	the	DET
fuelectenerg-3309	202	8	class	class	NOUN
fuelectenerg-3309	202	9	of	of	ADP
fuelectenerg-3309	202	10	mappings	mapping	NOUN
fuelectenerg-3309	202	11	{	{	PUNCT
fuelectenerg-3309	202	12	qwr	qwr	NOUN
fuelectenerg-3309	202	13	,	,	PUNCT
fuelectenerg-3309	202	14	mu−1	mu−1	PROPN
fuelectenerg-3309	202	15	:	:	PUNCT
fuelectenerg-3309	202	16	r	r	NOUN
fuelectenerg-3309	202	17	∈	∈	PROPN
fuelectenerg-3309	202	18	r(m	r(m	NOUN
fuelectenerg-3309	202	19	)	)	PUNCT
fuelectenerg-3309	202	20	}	}	PUNCT
fuelectenerg-3309	202	21	provides	provide	VERB
fuelectenerg-3309	202	22	a	a	DET
fuelectenerg-3309	202	23	great	great	ADJ
fuelectenerg-3309	202	24	variety	variety	NOUN
fuelectenerg-3309	202	25	of	of	ADP
fuelectenerg-3309	202	26	enumeration	enumeration	NOUN
fuelectenerg-3309	202	27	/	/	SYM
fuelectenerg-3309	202	28	shuffling	shuffle	VERB
fuelectenerg-3309	202	29	methods	method	NOUN
fuelectenerg-3309	202	30	for	for	ADP
fuelectenerg-3309	202	31	the	the	DET
fuelectenerg-3309	202	32	set	set	NOUN
fuelectenerg-3309	202	33	of	of	ADP
fuelectenerg-3309	202	34	permutations	permutation	NOUN
fuelectenerg-3309	202	35	p	p	X
fuelectenerg-3309	202	36	(	(	PUNCT
fuelectenerg-3309	202	37	m	m	NOUN
fuelectenerg-3309	202	38	)	)	PUNCT
fuelectenerg-3309	202	39	.	.	PUNCT
fuelectenerg-3309	203	1	example	example	NOUN
fuelectenerg-3309	203	2	3	3	NUM
fuelectenerg-3309	203	3	for	for	ADP
fuelectenerg-3309	203	4	m	m	NOUN
fuelectenerg-3309	203	5	=	=	NOUN
fuelectenerg-3309	203	6	4	4	NUM
fuelectenerg-3309	203	7	and	and	CCONJ
fuelectenerg-3309	203	8	r	r	NOUN
fuelectenerg-3309	203	9	=	=	SYM
fuelectenerg-3309	203	10	{	{	PUNCT
fuelectenerg-3309	203	11	(	(	PUNCT
fuelectenerg-3309	203	12	1	1	NUM
fuelectenerg-3309	203	13	)	)	PUNCT
fuelectenerg-3309	203	14	,	,	PUNCT
fuelectenerg-3309	203	15	(	(	PUNCT
fuelectenerg-3309	203	16	2	2	NUM
fuelectenerg-3309	203	17	,	,	PUNCT
fuelectenerg-3309	203	18	1	1	NUM
fuelectenerg-3309	203	19	)	)	PUNCT
fuelectenerg-3309	203	20	,	,	PUNCT
fuelectenerg-3309	203	21	(	(	PUNCT
fuelectenerg-3309	203	22	2	2	NUM
fuelectenerg-3309	203	23	,	,	PUNCT
fuelectenerg-3309	203	24	1	1	NUM
fuelectenerg-3309	203	25	,	,	PUNCT
fuelectenerg-3309	203	26	3	3	NUM
fuelectenerg-3309	203	27	)	)	PUNCT
fuelectenerg-3309	203	28	,	,	PUNCT
fuelectenerg-3309	203	29	(	(	PUNCT
fuelectenerg-3309	203	30	4	4	NUM
fuelectenerg-3309	203	31	,	,	PUNCT
fuelectenerg-3309	203	32	2	2	NUM
fuelectenerg-3309	203	33	,	,	PUNCT
fuelectenerg-3309	203	34	1	1	NUM
fuelectenerg-3309	203	35	,	,	PUNCT
fuelectenerg-3309	203	36	3	3	NUM
fuelectenerg-3309	203	37	)	)	PUNCT
fuelectenerg-3309	203	38	}	}	PUNCT
fuelectenerg-3309	203	39	,	,	PUNCT
fuelectenerg-3309	203	40	then	then	ADV
fuelectenerg-3309	203	41	by	by	ADP
fuelectenerg-3309	203	42	using	use	VERB
fuelectenerg-3309	203	43	theorem	theorem	NOUN
fuelectenerg-3309	203	44	1	1	NUM
fuelectenerg-3309	203	45	,	,	PUNCT
fuelectenerg-3309	203	46	the	the	DET
fuelectenerg-3309	203	47	lexicographical	lexicographical	ADJ
fuelectenerg-3309	203	48	order	order	NOUN
fuelectenerg-3309	203	49	of	of	ADP
fuelectenerg-3309	203	50	s(4	s(4	NOUN
fuelectenerg-3309	203	51	)	)	PUNCT
fuelectenerg-3309	203	52	(	(	PUNCT
fuelectenerg-3309	203	53	see	see	VERB
fuelectenerg-3309	203	54	example	example	NOUN
fuelectenerg-3309	203	55	2	2	NUM
fuelectenerg-3309	203	56	)	)	PUNCT
fuelectenerg-3309	203	57	is	be	AUX
fuelectenerg-3309	203	58	shuffled	shuffle	VERB
fuelectenerg-3309	203	59	to	to	ADP
fuelectenerg-3309	203	60	:	:	PUNCT
fuelectenerg-3309	203	61	{	{	PUNCT
fuelectenerg-3309	203	62	(	(	PUNCT
fuelectenerg-3309	203	63	1	1	NUM
fuelectenerg-3309	203	64	,	,	PUNCT
fuelectenerg-3309	203	65	2	2	NUM
fuelectenerg-3309	203	66	,	,	PUNCT
fuelectenerg-3309	203	67	2	2	NUM
fuelectenerg-3309	203	68	,	,	PUNCT
fuelectenerg-3309	203	69	4	4	NUM
fuelectenerg-3309	203	70	)	)	PUNCT
fuelectenerg-3309	203	71	,	,	PUNCT
fuelectenerg-3309	203	72	(	(	PUNCT
fuelectenerg-3309	203	73	1	1	NUM
fuelectenerg-3309	203	74	,	,	PUNCT
fuelectenerg-3309	203	75	2	2	NUM
fuelectenerg-3309	203	76	,	,	PUNCT
fuelectenerg-3309	203	77	2	2	NUM
fuelectenerg-3309	203	78	,	,	PUNCT
fuelectenerg-3309	203	79	2	2	NUM
fuelectenerg-3309	203	80	)	)	PUNCT
fuelectenerg-3309	203	81	,	,	PUNCT
fuelectenerg-3309	203	82	(	(	PUNCT
fuelectenerg-3309	203	83	1	1	NUM
fuelectenerg-3309	203	84	,	,	PUNCT
fuelectenerg-3309	203	85	2	2	NUM
fuelectenerg-3309	203	86	,	,	PUNCT
fuelectenerg-3309	203	87	2	2	NUM
fuelectenerg-3309	203	88	,	,	PUNCT
fuelectenerg-3309	203	89	1	1	NUM
fuelectenerg-3309	203	90	)	)	PUNCT
fuelectenerg-3309	203	91	,	,	PUNCT
fuelectenerg-3309	203	92	(	(	PUNCT
fuelectenerg-3309	203	93	1	1	NUM
fuelectenerg-3309	203	94	,	,	PUNCT
fuelectenerg-3309	203	95	2	2	NUM
fuelectenerg-3309	203	96	,	,	PUNCT
fuelectenerg-3309	203	97	2	2	NUM
fuelectenerg-3309	203	98	,	,	PUNCT
fuelectenerg-3309	203	99	3	3	NUM
fuelectenerg-3309	203	100	)	)	PUNCT
fuelectenerg-3309	203	101	,	,	PUNCT
fuelectenerg-3309	203	102	(	(	PUNCT
fuelectenerg-3309	203	103	1	1	NUM
fuelectenerg-3309	203	104	,	,	PUNCT
fuelectenerg-3309	203	105	2	2	NUM
fuelectenerg-3309	203	106	,	,	PUNCT
fuelectenerg-3309	203	107	1	1	NUM
fuelectenerg-3309	203	108	,	,	PUNCT
fuelectenerg-3309	203	109	4	4	NUM
fuelectenerg-3309	203	110	)	)	PUNCT
fuelectenerg-3309	203	111	,	,	PUNCT
fuelectenerg-3309	203	112	(	(	PUNCT
fuelectenerg-3309	203	113	1	1	NUM
fuelectenerg-3309	203	114	,	,	PUNCT
fuelectenerg-3309	203	115	2	2	NUM
fuelectenerg-3309	203	116	,	,	PUNCT
fuelectenerg-3309	203	117	1	1	NUM
fuelectenerg-3309	203	118	,	,	PUNCT
fuelectenerg-3309	203	119	2	2	NUM
fuelectenerg-3309	203	120	)	)	PUNCT
fuelectenerg-3309	203	121	,	,	PUNCT
fuelectenerg-3309	203	122	(	(	PUNCT
fuelectenerg-3309	203	123	1	1	NUM
fuelectenerg-3309	203	124	,	,	PUNCT
fuelectenerg-3309	203	125	2	2	NUM
fuelectenerg-3309	203	126	,	,	PUNCT
fuelectenerg-3309	203	127	1	1	NUM
fuelectenerg-3309	203	128	,	,	PUNCT
fuelectenerg-3309	203	129	1	1	NUM
fuelectenerg-3309	203	130	)	)	PUNCT
fuelectenerg-3309	203	131	,	,	PUNCT
fuelectenerg-3309	203	132	(	(	PUNCT
fuelectenerg-3309	203	133	1	1	NUM
fuelectenerg-3309	203	134	,	,	PUNCT
fuelectenerg-3309	203	135	2	2	NUM
fuelectenerg-3309	203	136	,	,	PUNCT
fuelectenerg-3309	203	137	1	1	NUM
fuelectenerg-3309	203	138	,	,	PUNCT
fuelectenerg-3309	203	139	3	3	NUM
fuelectenerg-3309	203	140	)	)	PUNCT
fuelectenerg-3309	203	141	,	,	PUNCT
fuelectenerg-3309	203	142	(	(	PUNCT
fuelectenerg-3309	203	143	1	1	NUM
fuelectenerg-3309	203	144	,	,	PUNCT
fuelectenerg-3309	203	145	2	2	NUM
fuelectenerg-3309	203	146	,	,	PUNCT
fuelectenerg-3309	203	147	3	3	NUM
fuelectenerg-3309	203	148	,	,	PUNCT
fuelectenerg-3309	203	149	4	4	NUM
fuelectenerg-3309	203	150	)	)	PUNCT
fuelectenerg-3309	203	151	,	,	PUNCT
fuelectenerg-3309	203	152	(	(	PUNCT
fuelectenerg-3309	203	153	1	1	NUM
fuelectenerg-3309	203	154	,	,	PUNCT
fuelectenerg-3309	203	155	2	2	NUM
fuelectenerg-3309	203	156	,	,	PUNCT
fuelectenerg-3309	203	157	3	3	NUM
fuelectenerg-3309	203	158	,	,	PUNCT
fuelectenerg-3309	203	159	2	2	NUM
fuelectenerg-3309	203	160	)	)	PUNCT
fuelectenerg-3309	203	161	,	,	PUNCT
fuelectenerg-3309	203	162	(	(	PUNCT
fuelectenerg-3309	203	163	1	1	NUM
fuelectenerg-3309	203	164	,	,	PUNCT
fuelectenerg-3309	203	165	2	2	NUM
fuelectenerg-3309	203	166	,	,	PUNCT
fuelectenerg-3309	203	167	3	3	NUM
fuelectenerg-3309	203	168	,	,	PUNCT
fuelectenerg-3309	203	169	1	1	NUM
fuelectenerg-3309	203	170	)	)	PUNCT
fuelectenerg-3309	203	171	,	,	PUNCT
fuelectenerg-3309	203	172	(	(	PUNCT
fuelectenerg-3309	203	173	1	1	NUM
fuelectenerg-3309	203	174	,	,	PUNCT
fuelectenerg-3309	203	175	2	2	NUM
fuelectenerg-3309	203	176	,	,	PUNCT
fuelectenerg-3309	203	177	3	3	NUM
fuelectenerg-3309	203	178	,	,	PUNCT
fuelectenerg-3309	203	179	3	3	NUM
fuelectenerg-3309	203	180	)	)	PUNCT
fuelectenerg-3309	203	181	,	,	PUNCT
fuelectenerg-3309	203	182	(	(	PUNCT
fuelectenerg-3309	203	183	1	1	NUM
fuelectenerg-3309	203	184	,	,	PUNCT
fuelectenerg-3309	203	185	1	1	NUM
fuelectenerg-3309	203	186	,	,	PUNCT
fuelectenerg-3309	203	187	2	2	NUM
fuelectenerg-3309	203	188	,	,	PUNCT
fuelectenerg-3309	203	189	4	4	NUM
fuelectenerg-3309	203	190	)	)	PUNCT
fuelectenerg-3309	203	191	,	,	PUNCT
fuelectenerg-3309	203	192	(	(	PUNCT
fuelectenerg-3309	203	193	1	1	NUM
fuelectenerg-3309	203	194	,	,	PUNCT
fuelectenerg-3309	203	195	1	1	NUM
fuelectenerg-3309	203	196	,	,	PUNCT
fuelectenerg-3309	203	197	2	2	NUM
fuelectenerg-3309	203	198	,	,	PUNCT
fuelectenerg-3309	203	199	2	2	NUM
fuelectenerg-3309	203	200	)	)	PUNCT
fuelectenerg-3309	203	201	,	,	PUNCT
fuelectenerg-3309	203	202	(	(	PUNCT
fuelectenerg-3309	203	203	1	1	NUM
fuelectenerg-3309	203	204	,	,	PUNCT
fuelectenerg-3309	203	205	1	1	NUM
fuelectenerg-3309	203	206	,	,	PUNCT
fuelectenerg-3309	203	207	2	2	NUM
fuelectenerg-3309	203	208	,	,	PUNCT
fuelectenerg-3309	203	209	1	1	NUM
fuelectenerg-3309	203	210	)	)	PUNCT
fuelectenerg-3309	203	211	,	,	PUNCT
fuelectenerg-3309	203	212	(	(	PUNCT
fuelectenerg-3309	203	213	1	1	NUM
fuelectenerg-3309	203	214	,	,	PUNCT
fuelectenerg-3309	203	215	1	1	NUM
fuelectenerg-3309	203	216	,	,	PUNCT
fuelectenerg-3309	203	217	2	2	NUM
fuelectenerg-3309	203	218	,	,	PUNCT
fuelectenerg-3309	203	219	3	3	NUM
fuelectenerg-3309	203	220	)	)	PUNCT
fuelectenerg-3309	203	221	,	,	PUNCT
fuelectenerg-3309	203	222	(	(	PUNCT
fuelectenerg-3309	203	223	1	1	NUM
fuelectenerg-3309	203	224	,	,	PUNCT
fuelectenerg-3309	203	225	1	1	NUM
fuelectenerg-3309	203	226	,	,	PUNCT
fuelectenerg-3309	203	227	1	1	NUM
fuelectenerg-3309	203	228	,	,	PUNCT
fuelectenerg-3309	203	229	4	4	NUM
fuelectenerg-3309	203	230	)	)	PUNCT
fuelectenerg-3309	203	231	,	,	PUNCT
fuelectenerg-3309	203	232	(	(	PUNCT
fuelectenerg-3309	203	233	1	1	NUM
fuelectenerg-3309	203	234	,	,	PUNCT
fuelectenerg-3309	203	235	1	1	NUM
fuelectenerg-3309	203	236	,	,	PUNCT
fuelectenerg-3309	203	237	1	1	NUM
fuelectenerg-3309	203	238	,	,	PUNCT
fuelectenerg-3309	203	239	2	2	NUM
fuelectenerg-3309	203	240	)	)	PUNCT
fuelectenerg-3309	203	241	,	,	PUNCT
fuelectenerg-3309	203	242	(	(	PUNCT
fuelectenerg-3309	203	243	1	1	NUM
fuelectenerg-3309	203	244	,	,	PUNCT
fuelectenerg-3309	203	245	1	1	NUM
fuelectenerg-3309	203	246	,	,	PUNCT
fuelectenerg-3309	203	247	1	1	NUM
fuelectenerg-3309	203	248	,	,	PUNCT
fuelectenerg-3309	203	249	1	1	NUM
fuelectenerg-3309	203	250	)	)	PUNCT
fuelectenerg-3309	203	251	,	,	PUNCT
fuelectenerg-3309	203	252	(	(	PUNCT
fuelectenerg-3309	203	253	1	1	NUM
fuelectenerg-3309	203	254	,	,	PUNCT
fuelectenerg-3309	203	255	1	1	NUM
fuelectenerg-3309	203	256	,	,	PUNCT
fuelectenerg-3309	203	257	1	1	NUM
fuelectenerg-3309	203	258	,	,	PUNCT
fuelectenerg-3309	203	259	3	3	NUM
fuelectenerg-3309	203	260	)	)	PUNCT
fuelectenerg-3309	203	261	,	,	PUNCT
fuelectenerg-3309	203	262	(	(	PUNCT
fuelectenerg-3309	203	263	1	1	NUM
fuelectenerg-3309	203	264	,	,	PUNCT
fuelectenerg-3309	203	265	1	1	NUM
fuelectenerg-3309	203	266	,	,	PUNCT
fuelectenerg-3309	203	267	3	3	NUM
fuelectenerg-3309	203	268	,	,	PUNCT
fuelectenerg-3309	203	269	4	4	NUM
fuelectenerg-3309	203	270	)	)	PUNCT
fuelectenerg-3309	203	271	,	,	PUNCT
fuelectenerg-3309	203	272	(	(	PUNCT
fuelectenerg-3309	203	273	1	1	NUM
fuelectenerg-3309	203	274	,	,	PUNCT
fuelectenerg-3309	203	275	1	1	NUM
fuelectenerg-3309	203	276	,	,	PUNCT
fuelectenerg-3309	203	277	3	3	NUM
fuelectenerg-3309	203	278	,	,	PUNCT
fuelectenerg-3309	203	279	2	2	NUM
fuelectenerg-3309	203	280	)	)	PUNCT
fuelectenerg-3309	203	281	,	,	PUNCT
fuelectenerg-3309	203	282	(	(	PUNCT
fuelectenerg-3309	203	283	1	1	NUM
fuelectenerg-3309	203	284	,	,	PUNCT
fuelectenerg-3309	203	285	1	1	NUM
fuelectenerg-3309	203	286	,	,	PUNCT
fuelectenerg-3309	203	287	3	3	NUM
fuelectenerg-3309	203	288	,	,	PUNCT
fuelectenerg-3309	203	289	1	1	NUM
fuelectenerg-3309	203	290	)	)	PUNCT
fuelectenerg-3309	203	291	,	,	PUNCT
fuelectenerg-3309	203	292	(	(	PUNCT
fuelectenerg-3309	203	293	1	1	NUM
fuelectenerg-3309	203	294	,	,	PUNCT
fuelectenerg-3309	203	295	1	1	NUM
fuelectenerg-3309	203	296	,	,	PUNCT
fuelectenerg-3309	203	297	3	3	NUM
fuelectenerg-3309	203	298	,	,	PUNCT
fuelectenerg-3309	203	299	3	3	NUM
fuelectenerg-3309	203	300	)	)	PUNCT
fuelectenerg-3309	203	301	}	}	PUNCT
fuelectenerg-3309	203	302	.	.	PUNCT
fuelectenerg-3309	204	1	246	246	NUM
fuelectenerg-3309	204	2	c.	c.	PROPN
fuelectenerg-3309	204	3	karanikas	karanikas	PROPN
fuelectenerg-3309	204	4	,	,	PUNCT
fuelectenerg-3309	204	5	n.	n.	PROPN
fuelectenerg-3309	204	6	atreas	atreas	PROPN
fuelectenerg-3309	204	7	enumeration	enumeration	PROPN
fuelectenerg-3309	204	8	and	and	CCONJ
fuelectenerg-3309	204	9	coding	code	VERB
fuelectenerg-3309	204	10	permutations	permutation	NOUN
fuelectenerg-3309	204	11	and	and	CCONJ
fuelectenerg-3309	204	12	reversible	reversible	ADJ
fuelectenerg-3309	204	13	logical	logical	ADJ
fuelectenerg-3309	204	14	circuits	circuit	NOUN
fuelectenerg-3309	204	15	247	247	NUM
fuelectenerg-3309	204	16	6	6	NUM
fuelectenerg-3309	204	17	n.	n.	NOUN
fuelectenerg-3309	204	18	atreas	atreas	PROPN
fuelectenerg-3309	204	19	and	and	CCONJ
fuelectenerg-3309	204	20	c.	c.	PROPN
fuelectenerg-3309	204	21	karanikas	karanikas	PROPN
fuelectenerg-3309	204	22	we	we	PRON
fuelectenerg-3309	204	23	may	may	AUX
fuelectenerg-3309	204	24	obtain	obtain	VERB
fuelectenerg-3309	204	25	various	various	ADJ
fuelectenerg-3309	204	26	enumerations	enumeration	NOUN
fuelectenerg-3309	204	27	of	of	ADP
fuelectenerg-3309	204	28	the	the	DET
fuelectenerg-3309	204	29	elements	element	NOUN
fuelectenerg-3309	204	30	of	of	ADP
fuelectenerg-3309	204	31	s(m	s(m	NOUN
fuelectenerg-3309	204	32	)	)	PUNCT
fuelectenerg-3309	204	33	(	(	PUNCT
fuelectenerg-3309	204	34	and	and	CCONJ
fuelectenerg-3309	204	35	hence	hence	ADV
fuelectenerg-3309	204	36	p	p	X
fuelectenerg-3309	204	37	(	(	PUNCT
fuelectenerg-3309	204	38	m	m	NOUN
fuelectenerg-3309	204	39	)	)	PUNCT
fuelectenerg-3309	204	40	as	as	ADV
fuelectenerg-3309	204	41	well	well	ADV
fuelectenerg-3309	204	42	)	)	PUNCT
fuelectenerg-3309	204	43	.	.	PUNCT
fuelectenerg-3309	205	1	indeed	indeed	ADV
fuelectenerg-3309	205	2	,	,	PUNCT
fuelectenerg-3309	205	3	let	let	VERB
fuelectenerg-3309	205	4	us	we	PRON
fuelectenerg-3309	205	5	fix	fix	VERB
fuelectenerg-3309	205	6	any	any	DET
fuelectenerg-3309	205	7	element	element	NOUN
fuelectenerg-3309	205	8	r	r	NOUN
fuelectenerg-3309	205	9	=	=	PUNCT
fuelectenerg-3309	205	10	(	(	PUNCT
fuelectenerg-3309	205	11	r1	r1	PROPN
fuelectenerg-3309	205	12	,	,	PUNCT
fuelectenerg-3309	205	13	r2	r2	PROPN
fuelectenerg-3309	205	14	,	,	PUNCT
fuelectenerg-3309	205	15	...	...	PUNCT
fuelectenerg-3309	205	16	,	,	PUNCT
fuelectenerg-3309	205	17	rm	rm	PROPN
fuelectenerg-3309	205	18	)	)	PUNCT
fuelectenerg-3309	205	19	∈	∈	PROPN
fuelectenerg-3309	205	20	r(m	r(m	PROPN
fuelectenerg-3309	205	21	)	)	PUNCT
fuelectenerg-3309	206	1	=	=	SYM
fuelectenerg-3309	206	2	p	p	X
fuelectenerg-3309	206	3	(	(	PUNCT
fuelectenerg-3309	206	4	1)×	1)×	NUM
fuelectenerg-3309	206	5	p	p	NOUN
fuelectenerg-3309	206	6	(	(	PUNCT
fuelectenerg-3309	206	7	2)×	2)×	NUM
fuelectenerg-3309	206	8	...	...	SYM
fuelectenerg-3309	206	9	×	×	NOUN
fuelectenerg-3309	206	10	p	p	X
fuelectenerg-3309	206	11	(	(	PUNCT
fuelectenerg-3309	206	12	m	m	NOUN
fuelectenerg-3309	206	13	)	)	PUNCT
fuelectenerg-3309	206	14	,	,	PUNCT
fuelectenerg-3309	206	15	(	(	PUNCT
fuelectenerg-3309	206	16	4	4	X
fuelectenerg-3309	206	17	)	)	PUNCT
fuelectenerg-3309	206	18	where	where	SCONJ
fuelectenerg-3309	206	19	ri	ri	NOUN
fuelectenerg-3309	206	20	=	=	PUNCT
fuelectenerg-3309	206	21	(	(	PUNCT
fuelectenerg-3309	206	22	ri,1	ri,1	PROPN
fuelectenerg-3309	206	23	,	,	PUNCT
fuelectenerg-3309	206	24	...	...	PUNCT
fuelectenerg-3309	206	25	ri	ri	NOUN
fuelectenerg-3309	206	26	,	,	PUNCT
fuelectenerg-3309	206	27	i	i	NOUN
fuelectenerg-3309	206	28	)	)	PUNCT
fuelectenerg-3309	206	29	∈	∈	PROPN
fuelectenerg-3309	207	1	p	p	X
fuelectenerg-3309	207	2	(	(	PUNCT
fuelectenerg-3309	207	3	i	i	PROPN
fuelectenerg-3309	207	4	)	)	PUNCT
fuelectenerg-3309	207	5	,	,	PUNCT
fuelectenerg-3309	207	6	i	i	PRON
fuelectenerg-3309	207	7	=	=	NOUN
fuelectenerg-3309	207	8	1	1	NUM
fuelectenerg-3309	207	9	,	,	PUNCT
fuelectenerg-3309	207	10	...	...	PUNCT
fuelectenerg-3309	207	11	,	,	PUNCT
fuelectenerg-3309	207	12	m.	m.	NOUN
fuelectenerg-3309	207	13	then	then	ADV
fuelectenerg-3309	207	14	we	we	PRON
fuelectenerg-3309	207	15	have	have	AUX
fuelectenerg-3309	207	16	:	:	PUNCT
fuelectenerg-3309	207	17	theorem	theorem	VERB
fuelectenerg-3309	207	18	1	1	NUM
fuelectenerg-3309	207	19	let	let	VERB
fuelectenerg-3309	207	20	s(m	s(m	PROPN
fuelectenerg-3309	207	21	)	)	PUNCT
fuelectenerg-3309	207	22	be	be	AUX
fuelectenerg-3309	207	23	defined	define	VERB
fuelectenerg-3309	207	24	in	in	ADP
fuelectenerg-3309	207	25	(	(	PUNCT
fuelectenerg-3309	207	26	1	1	NUM
fuelectenerg-3309	207	27	)	)	PUNCT
fuelectenerg-3309	207	28	and	and	CCONJ
fuelectenerg-3309	207	29	r	r	NOUN
fuelectenerg-3309	207	30	be	be	AUX
fuelectenerg-3309	207	31	a	a	DET
fuelectenerg-3309	207	32	fixed	fix	VERB
fuelectenerg-3309	207	33	element	element	NOUN
fuelectenerg-3309	207	34	of	of	ADP
fuelectenerg-3309	207	35	r(m	r(m	PROPN
fuelectenerg-3309	207	36	)	)	PUNCT
fuelectenerg-3309	207	37	as	as	ADP
fuelectenerg-3309	207	38	in	in	ADP
fuelectenerg-3309	207	39	(	(	PUNCT
fuelectenerg-3309	207	40	4	4	NUM
fuelectenerg-3309	207	41	)	)	PUNCT
fuelectenerg-3309	207	42	.	.	PUNCT
fuelectenerg-3309	208	1	for	for	ADP
fuelectenerg-3309	208	2	any	any	DET
fuelectenerg-3309	208	3	s	s	PROPN
fuelectenerg-3309	208	4	∈	∈	PROPN
fuelectenerg-3309	208	5	s(m	s(m	PROPN
fuelectenerg-3309	208	6	)	)	PUNCT
fuelectenerg-3309	208	7	we	we	PRON
fuelectenerg-3309	208	8	define	define	VERB
fuelectenerg-3309	208	9	wr	wr	PROPN
fuelectenerg-3309	208	10	,	,	PUNCT
fuelectenerg-3309	208	11	m(s	m(s	PROPN
fuelectenerg-3309	208	12	)	)	PUNCT
fuelectenerg-3309	208	13	=	=	PUNCT
fuelectenerg-3309	209	1	(	(	PUNCT
fuelectenerg-3309	209	2	r1,s1	r1,s1	PROPN
fuelectenerg-3309	209	3	,	,	PUNCT
fuelectenerg-3309	209	4	r2,s2	r2,s2	PROPN
fuelectenerg-3309	209	5	,	,	PUNCT
fuelectenerg-3309	209	6	...	...	PUNCT
fuelectenerg-3309	209	7	,	,	PUNCT
fuelectenerg-3309	209	8	rm	rm	PROPN
fuelectenerg-3309	209	9	,	,	PUNCT
fuelectenerg-3309	209	10	sm	sm	PROPN
fuelectenerg-3309	209	11	)	)	PUNCT
fuelectenerg-3309	209	12	then	then	ADV
fuelectenerg-3309	209	13	the	the	DET
fuelectenerg-3309	209	14	map	map	NOUN
fuelectenerg-3309	209	15	wr	wr	PROPN
fuelectenerg-3309	209	16	,	,	PUNCT
fuelectenerg-3309	209	17	m	m	VERB
fuelectenerg-3309	209	18	is	be	AUX
fuelectenerg-3309	209	19	onto	onto	ADP
fuelectenerg-3309	209	20	s(m	s(m	NOUN
fuelectenerg-3309	209	21	)	)	PUNCT
fuelectenerg-3309	209	22	.	.	PUNCT
fuelectenerg-3309	210	1	proof	proof	NOUN
fuelectenerg-3309	210	2	:	:	PUNCT
fuelectenerg-3309	210	3	let	let	VERB
fuelectenerg-3309	210	4	us	we	PRON
fuelectenerg-3309	210	5	fix	fix	VERB
fuelectenerg-3309	210	6	an	an	DET
fuelectenerg-3309	210	7	element	element	NOUN
fuelectenerg-3309	210	8	r	r	NOUN
fuelectenerg-3309	210	9	∈	∈	NOUN
fuelectenerg-3309	210	10	r(m	r(m	NOUN
fuelectenerg-3309	210	11	)	)	PUNCT
fuelectenerg-3309	210	12	.	.	PUNCT
fuelectenerg-3309	211	1	since	since	SCONJ
fuelectenerg-3309	211	2	ri	ri	PROPN
fuelectenerg-3309	211	3	,	,	PUNCT
fuelectenerg-3309	211	4	si	si	PROPN
fuelectenerg-3309	211	5	≤	≤	ADV
fuelectenerg-3309	211	6	i	i	PRON
fuelectenerg-3309	211	7	(	(	PUNCT
fuelectenerg-3309	211	8	due	due	ADP
fuelectenerg-3309	211	9	to	to	ADP
fuelectenerg-3309	211	10	the	the	DET
fuelectenerg-3309	211	11	fact	fact	NOUN
fuelectenerg-3309	211	12	that	that	SCONJ
fuelectenerg-3309	211	13	ri	ri	PROPN
fuelectenerg-3309	211	14	∈	∈	PROPN
fuelectenerg-3309	211	15	p	p	X
fuelectenerg-3309	211	16	(	(	PUNCT
fuelectenerg-3309	211	17	i	i	NOUN
fuelectenerg-3309	211	18	)	)	PUNCT
fuelectenerg-3309	211	19	)	)	PUNCT
fuelectenerg-3309	211	20	,	,	PUNCT
fuelectenerg-3309	211	21	we	we	PRON
fuelectenerg-3309	211	22	deduce	deduce	VERB
fuelectenerg-3309	211	23	that	that	DET
fuelectenerg-3309	211	24	wr	wr	NOUN
fuelectenerg-3309	211	25	,	,	PUNCT
fuelectenerg-3309	211	26	m(s	m(s	PROPN
fuelectenerg-3309	211	27	)	)	PUNCT
fuelectenerg-3309	211	28	∈	∈	PROPN
fuelectenerg-3309	211	29	s(m	s(m	PROPN
fuelectenerg-3309	211	30	)	)	PUNCT
fuelectenerg-3309	211	31	.	.	PUNCT
fuelectenerg-3309	212	1	also	also	ADV
fuelectenerg-3309	212	2	,	,	PUNCT
fuelectenerg-3309	212	3	the	the	DET
fuelectenerg-3309	212	4	fact	fact	NOUN
fuelectenerg-3309	212	5	that	that	SCONJ
fuelectenerg-3309	212	6	ri	ri	PROPN
fuelectenerg-3309	212	7	,	,	PUNCT
fuelectenerg-3309	212	8	j	j	PROPN
fuelectenerg-3309	212	9	≤	≤	PROPN
fuelectenerg-3309	213	1	i	i	PRON
fuelectenerg-3309	213	2	for	for	ADP
fuelectenerg-3309	213	3	any	any	DET
fuelectenerg-3309	213	4	j	j	NOUN
fuelectenerg-3309	213	5	=	=	SYM
fuelectenerg-3309	213	6	1	1	NUM
fuelectenerg-3309	213	7	,	,	PUNCT
fuelectenerg-3309	213	8	...	...	PUNCT
fuelectenerg-3309	213	9	,	,	PUNCT
fuelectenerg-3309	213	10	i	i	PRON
fuelectenerg-3309	213	11	implies	imply	VERB
fuelectenerg-3309	213	12	that	that	PRON
fuelectenerg-3309	213	13	wr	wr	NOUN
fuelectenerg-3309	213	14	,	,	PUNCT
fuelectenerg-3309	213	15	m	m	VERB
fuelectenerg-3309	213	16	is	be	AUX
fuelectenerg-3309	213	17	onto	onto	ADP
fuelectenerg-3309	213	18	s(m	s(m	NOUN
fuelectenerg-3309	213	19	)	)	PUNCT
fuelectenerg-3309	213	20	,	,	PUNCT
fuelectenerg-3309	213	21	because	because	SCONJ
fuelectenerg-3309	213	22	any	any	DET
fuelectenerg-3309	213	23	element	element	NOUN
fuelectenerg-3309	213	24	si	si	NOUN
fuelectenerg-3309	213	25	of	of	ADP
fuelectenerg-3309	213	26	s	s	PROPN
fuelectenerg-3309	213	27	=	=	PUNCT
fuelectenerg-3309	213	28	(	(	PUNCT
fuelectenerg-3309	213	29	s1	s1	PROPN
fuelectenerg-3309	213	30	,	,	PUNCT
fuelectenerg-3309	213	31	...	...	PUNCT
fuelectenerg-3309	213	32	,	,	PUNCT
fuelectenerg-3309	213	33	sm	sm	PROPN
fuelectenerg-3309	213	34	)	)	PUNCT
fuelectenerg-3309	213	35	can	can	AUX
fuelectenerg-3309	213	36	be	be	AUX
fuelectenerg-3309	213	37	written	write	VERB
fuelectenerg-3309	213	38	by	by	ADP
fuelectenerg-3309	213	39	si	si	X
fuelectenerg-3309	213	40	=	=	PROPN
fuelectenerg-3309	213	41	ri	ri	PROPN
fuelectenerg-3309	213	42	,	,	PUNCT
fuelectenerg-3309	213	43	a(i	a(i	PROPN
fuelectenerg-3309	213	44	)	)	PUNCT
fuelectenerg-3309	213	45	for	for	ADP
fuelectenerg-3309	213	46	some	some	DET
fuelectenerg-3309	213	47	index	index	NOUN
fuelectenerg-3309	213	48	a(i	a(i	NOUN
fuelectenerg-3309	213	49	)	)	PUNCT
fuelectenerg-3309	213	50	≤	≤	PUNCT
fuelectenerg-3309	214	1	i	i	PRON
fuelectenerg-3309	214	2	and	and	CCONJ
fuelectenerg-3309	214	3	so	so	ADV
fuelectenerg-3309	214	4	by	by	ADP
fuelectenerg-3309	214	5	defining	define	VERB
fuelectenerg-3309	214	6	a	a	DET
fuelectenerg-3309	214	7	=	=	X
fuelectenerg-3309	214	8	{	{	PUNCT
fuelectenerg-3309	214	9	a(i	a(i	PROPN
fuelectenerg-3309	214	10	)	)	PUNCT
fuelectenerg-3309	214	11	:	:	PUNCT
fuelectenerg-3309	215	1	i	i	NOUN
fuelectenerg-3309	215	2	=	=	NOUN
fuelectenerg-3309	215	3	1	1	NUM
fuelectenerg-3309	215	4	,	,	PUNCT
fuelectenerg-3309	215	5	...	...	PUNCT
fuelectenerg-3309	215	6	,	,	PUNCT
fuelectenerg-3309	215	7	m	m	AUX
fuelectenerg-3309	215	8	}	}	PUNCT
fuelectenerg-3309	215	9	we	we	PRON
fuelectenerg-3309	215	10	have	have	VERB
fuelectenerg-3309	215	11	wr	wr	PROPN
fuelectenerg-3309	215	12	,	,	PUNCT
fuelectenerg-3309	215	13	m(a	m(a	PROPN
fuelectenerg-3309	215	14	)	)	PUNCT
fuelectenerg-3309	215	15	=	=	VERB
fuelectenerg-3309	216	1	s.	s.	PROPN
fuelectenerg-3309	216	2	let	let	VERB
fuelectenerg-3309	216	3	u	u	PRON
fuelectenerg-3309	216	4	be	be	AUX
fuelectenerg-3309	216	5	as	as	ADP
fuelectenerg-3309	216	6	in	in	ADP
fuelectenerg-3309	216	7	(	(	PUNCT
fuelectenerg-3309	216	8	2	2	NUM
fuelectenerg-3309	216	9	)	)	PUNCT
fuelectenerg-3309	216	10	and	and	CCONJ
fuelectenerg-3309	216	11	wr	wr	PROPN
fuelectenerg-3309	216	12	,	,	PUNCT
fuelectenerg-3309	216	13	m	m	VERB
fuelectenerg-3309	216	14	be	be	VERB
fuelectenerg-3309	216	15	as	as	ADP
fuelectenerg-3309	216	16	in	in	ADP
fuelectenerg-3309	216	17	theorem	theorem	NOUN
fuelectenerg-3309	216	18	1	1	NUM
fuelectenerg-3309	216	19	.	.	PUNCT
fuelectenerg-3309	217	1	it	it	PRON
fuelectenerg-3309	217	2	is	be	AUX
fuelectenerg-3309	217	3	easy	easy	ADJ
fuelectenerg-3309	217	4	to	to	PART
fuelectenerg-3309	217	5	see	see	VERB
fuelectenerg-3309	217	6	that	that	SCONJ
fuelectenerg-3309	217	7	the	the	DET
fuelectenerg-3309	217	8	map	map	NOUN
fuelectenerg-3309	217	9	uwr	uwr	NOUN
fuelectenerg-3309	217	10	,	,	PUNCT
fuelectenerg-3309	217	11	mu−1	mu−1	PROPN
fuelectenerg-3309	217	12	:	:	PUNCT
fuelectenerg-3309	217	13	{	{	PUNCT
fuelectenerg-3309	217	14	0	0	NUM
fuelectenerg-3309	217	15	,	,	PUNCT
fuelectenerg-3309	217	16	...	...	PUNCT
fuelectenerg-3309	217	17	,	,	PUNCT
fuelectenerg-3309	217	18	m!−	m!−	VERB
fuelectenerg-3309	217	19	1	1	NUM
fuelectenerg-3309	217	20	}	}	PUNCT
fuelectenerg-3309	217	21	→	→	SYM
fuelectenerg-3309	217	22	{	{	PUNCT
fuelectenerg-3309	217	23	0	0	NUM
fuelectenerg-3309	217	24	,	,	PUNCT
fuelectenerg-3309	217	25	...	...	PUNCT
fuelectenerg-3309	217	26	,	,	PUNCT
fuelectenerg-3309	217	27	m!−	m!−	VERB
fuelectenerg-3309	217	28	1	1	NUM
fuelectenerg-3309	217	29	}	}	PUNCT
fuelectenerg-3309	217	30	provides	provide	VERB
fuelectenerg-3309	217	31	a	a	DET
fuelectenerg-3309	217	32	method	method	NOUN
fuelectenerg-3309	217	33	for	for	ADP
fuelectenerg-3309	217	34	shuffling	shuffle	VERB
fuelectenerg-3309	217	35	the	the	DET
fuelectenerg-3309	217	36	set	set	NOUN
fuelectenerg-3309	217	37	{	{	PUNCT
fuelectenerg-3309	217	38	0	0	NUM
fuelectenerg-3309	217	39	,	,	PUNCT
fuelectenerg-3309	217	40	...	...	PUNCT
fuelectenerg-3309	217	41	,	,	PUNCT
fuelectenerg-3309	217	42	m	m	PROPN
fuelectenerg-3309	217	43	!	!	PUNCT
fuelectenerg-3309	218	1	−	−	PROPN
fuelectenerg-3309	218	2	1	1	NUM
fuelectenerg-3309	218	3	}	}	PUNCT
fuelectenerg-3309	218	4	.	.	PUNCT
fuelectenerg-3309	219	1	by	by	ADP
fuelectenerg-3309	219	2	altering	alter	VERB
fuelectenerg-3309	219	3	the	the	DET
fuelectenerg-3309	219	4	selection	selection	NOUN
fuelectenerg-3309	219	5	of	of	ADP
fuelectenerg-3309	219	6	r	r	NOUN
fuelectenerg-3309	219	7	∈	∈	PROPN
fuelectenerg-3309	219	8	r(m	r(m	NOUN
fuelectenerg-3309	219	9	)	)	PUNCT
fuelectenerg-3309	219	10	in	in	ADP
fuelectenerg-3309	219	11	(	(	PUNCT
fuelectenerg-3309	219	12	4	4	X
fuelectenerg-3309	219	13	)	)	PUNCT
fuelectenerg-3309	219	14	we	we	PRON
fuelectenerg-3309	219	15	obtain	obtain	VERB
fuelectenerg-3309	219	16	a	a	DET
fuelectenerg-3309	219	17	different	different	ADJ
fuelectenerg-3309	219	18	shuffling	shuffling	NOUN
fuelectenerg-3309	219	19	.	.	PUNCT
fuelectenerg-3309	220	1	finally	finally	ADV
fuelectenerg-3309	220	2	,	,	PUNCT
fuelectenerg-3309	220	3	it	it	PRON
fuelectenerg-3309	220	4	is	be	AUX
fuelectenerg-3309	220	5	clear	clear	ADJ
fuelectenerg-3309	220	6	that	that	SCONJ
fuelectenerg-3309	220	7	the	the	DET
fuelectenerg-3309	220	8	class	class	NOUN
fuelectenerg-3309	220	9	of	of	ADP
fuelectenerg-3309	220	10	mappings	mapping	NOUN
fuelectenerg-3309	220	11	{	{	PUNCT
fuelectenerg-3309	220	12	qwr	qwr	NOUN
fuelectenerg-3309	220	13	,	,	PUNCT
fuelectenerg-3309	220	14	mu−1	mu−1	PROPN
fuelectenerg-3309	220	15	:	:	PUNCT
fuelectenerg-3309	220	16	r	r	NOUN
fuelectenerg-3309	220	17	∈	∈	PROPN
fuelectenerg-3309	220	18	r(m	r(m	NOUN
fuelectenerg-3309	220	19	)	)	PUNCT
fuelectenerg-3309	220	20	}	}	PUNCT
fuelectenerg-3309	220	21	provides	provide	VERB
fuelectenerg-3309	220	22	a	a	DET
fuelectenerg-3309	220	23	great	great	ADJ
fuelectenerg-3309	220	24	variety	variety	NOUN
fuelectenerg-3309	220	25	of	of	ADP
fuelectenerg-3309	220	26	enumeration	enumeration	NOUN
fuelectenerg-3309	220	27	/	/	SYM
fuelectenerg-3309	220	28	shuffling	shuffle	VERB
fuelectenerg-3309	220	29	methods	method	NOUN
fuelectenerg-3309	220	30	for	for	ADP
fuelectenerg-3309	220	31	the	the	DET
fuelectenerg-3309	220	32	set	set	NOUN
fuelectenerg-3309	220	33	of	of	ADP
fuelectenerg-3309	220	34	permutations	permutation	NOUN
fuelectenerg-3309	220	35	p	p	X
fuelectenerg-3309	220	36	(	(	PUNCT
fuelectenerg-3309	220	37	m	m	NOUN
fuelectenerg-3309	220	38	)	)	PUNCT
fuelectenerg-3309	220	39	.	.	PUNCT
fuelectenerg-3309	221	1	example	example	NOUN
fuelectenerg-3309	221	2	3	3	NUM
fuelectenerg-3309	221	3	for	for	ADP
fuelectenerg-3309	221	4	m	m	NOUN
fuelectenerg-3309	221	5	=	=	NOUN
fuelectenerg-3309	221	6	4	4	NUM
fuelectenerg-3309	221	7	and	and	CCONJ
fuelectenerg-3309	221	8	r	r	NOUN
fuelectenerg-3309	221	9	=	=	SYM
fuelectenerg-3309	221	10	{	{	PUNCT
fuelectenerg-3309	221	11	(	(	PUNCT
fuelectenerg-3309	221	12	1	1	NUM
fuelectenerg-3309	221	13	)	)	PUNCT
fuelectenerg-3309	221	14	,	,	PUNCT
fuelectenerg-3309	221	15	(	(	PUNCT
fuelectenerg-3309	221	16	2	2	NUM
fuelectenerg-3309	221	17	,	,	PUNCT
fuelectenerg-3309	221	18	1	1	NUM
fuelectenerg-3309	221	19	)	)	PUNCT
fuelectenerg-3309	221	20	,	,	PUNCT
fuelectenerg-3309	221	21	(	(	PUNCT
fuelectenerg-3309	221	22	2	2	NUM
fuelectenerg-3309	221	23	,	,	PUNCT
fuelectenerg-3309	221	24	1	1	NUM
fuelectenerg-3309	221	25	,	,	PUNCT
fuelectenerg-3309	221	26	3	3	NUM
fuelectenerg-3309	221	27	)	)	PUNCT
fuelectenerg-3309	221	28	,	,	PUNCT
fuelectenerg-3309	221	29	(	(	PUNCT
fuelectenerg-3309	221	30	4	4	NUM
fuelectenerg-3309	221	31	,	,	PUNCT
fuelectenerg-3309	221	32	2	2	NUM
fuelectenerg-3309	221	33	,	,	PUNCT
fuelectenerg-3309	221	34	1	1	NUM
fuelectenerg-3309	221	35	,	,	PUNCT
fuelectenerg-3309	221	36	3	3	NUM
fuelectenerg-3309	221	37	)	)	PUNCT
fuelectenerg-3309	221	38	}	}	PUNCT
fuelectenerg-3309	221	39	,	,	PUNCT
fuelectenerg-3309	221	40	then	then	ADV
fuelectenerg-3309	221	41	by	by	ADP
fuelectenerg-3309	221	42	using	use	VERB
fuelectenerg-3309	221	43	theorem	theorem	NOUN
fuelectenerg-3309	221	44	1	1	NUM
fuelectenerg-3309	221	45	,	,	PUNCT
fuelectenerg-3309	221	46	the	the	DET
fuelectenerg-3309	221	47	lexicographical	lexicographical	ADJ
fuelectenerg-3309	221	48	order	order	NOUN
fuelectenerg-3309	221	49	of	of	ADP
fuelectenerg-3309	221	50	s(4	s(4	NOUN
fuelectenerg-3309	221	51	)	)	PUNCT
fuelectenerg-3309	221	52	(	(	PUNCT
fuelectenerg-3309	221	53	see	see	VERB
fuelectenerg-3309	221	54	example	example	NOUN
fuelectenerg-3309	221	55	2	2	NUM
fuelectenerg-3309	221	56	)	)	PUNCT
fuelectenerg-3309	221	57	is	be	AUX
fuelectenerg-3309	221	58	shuffled	shuffle	VERB
fuelectenerg-3309	221	59	to	to	ADP
fuelectenerg-3309	221	60	:	:	PUNCT
fuelectenerg-3309	221	61	{	{	PUNCT
fuelectenerg-3309	221	62	(	(	PUNCT
fuelectenerg-3309	221	63	1	1	NUM
fuelectenerg-3309	221	64	,	,	PUNCT
fuelectenerg-3309	221	65	2	2	NUM
fuelectenerg-3309	221	66	,	,	PUNCT
fuelectenerg-3309	221	67	2	2	NUM
fuelectenerg-3309	221	68	,	,	PUNCT
fuelectenerg-3309	221	69	4	4	NUM
fuelectenerg-3309	221	70	)	)	PUNCT
fuelectenerg-3309	221	71	,	,	PUNCT
fuelectenerg-3309	221	72	(	(	PUNCT
fuelectenerg-3309	221	73	1	1	NUM
fuelectenerg-3309	221	74	,	,	PUNCT
fuelectenerg-3309	221	75	2	2	NUM
fuelectenerg-3309	221	76	,	,	PUNCT
fuelectenerg-3309	221	77	2	2	NUM
fuelectenerg-3309	221	78	,	,	PUNCT
fuelectenerg-3309	221	79	2	2	NUM
fuelectenerg-3309	221	80	)	)	PUNCT
fuelectenerg-3309	221	81	,	,	PUNCT
fuelectenerg-3309	221	82	(	(	PUNCT
fuelectenerg-3309	221	83	1	1	NUM
fuelectenerg-3309	221	84	,	,	PUNCT
fuelectenerg-3309	221	85	2	2	NUM
fuelectenerg-3309	221	86	,	,	PUNCT
fuelectenerg-3309	221	87	2	2	NUM
fuelectenerg-3309	221	88	,	,	PUNCT
fuelectenerg-3309	221	89	1	1	NUM
fuelectenerg-3309	221	90	)	)	PUNCT
fuelectenerg-3309	221	91	,	,	PUNCT
fuelectenerg-3309	221	92	(	(	PUNCT
fuelectenerg-3309	221	93	1	1	NUM
fuelectenerg-3309	221	94	,	,	PUNCT
fuelectenerg-3309	221	95	2	2	NUM
fuelectenerg-3309	221	96	,	,	PUNCT
fuelectenerg-3309	221	97	2	2	NUM
fuelectenerg-3309	221	98	,	,	PUNCT
fuelectenerg-3309	221	99	3	3	NUM
fuelectenerg-3309	221	100	)	)	PUNCT
fuelectenerg-3309	221	101	,	,	PUNCT
fuelectenerg-3309	221	102	(	(	PUNCT
fuelectenerg-3309	221	103	1	1	NUM
fuelectenerg-3309	221	104	,	,	PUNCT
fuelectenerg-3309	221	105	2	2	NUM
fuelectenerg-3309	221	106	,	,	PUNCT
fuelectenerg-3309	221	107	1	1	NUM
fuelectenerg-3309	221	108	,	,	PUNCT
fuelectenerg-3309	221	109	4	4	NUM
fuelectenerg-3309	221	110	)	)	PUNCT
fuelectenerg-3309	221	111	,	,	PUNCT
fuelectenerg-3309	221	112	(	(	PUNCT
fuelectenerg-3309	221	113	1	1	NUM
fuelectenerg-3309	221	114	,	,	PUNCT
fuelectenerg-3309	221	115	2	2	NUM
fuelectenerg-3309	221	116	,	,	PUNCT
fuelectenerg-3309	221	117	1	1	NUM
fuelectenerg-3309	221	118	,	,	PUNCT
fuelectenerg-3309	221	119	2	2	NUM
fuelectenerg-3309	221	120	)	)	PUNCT
fuelectenerg-3309	221	121	,	,	PUNCT
fuelectenerg-3309	221	122	(	(	PUNCT
fuelectenerg-3309	221	123	1	1	NUM
fuelectenerg-3309	221	124	,	,	PUNCT
fuelectenerg-3309	221	125	2	2	NUM
fuelectenerg-3309	221	126	,	,	PUNCT
fuelectenerg-3309	221	127	1	1	NUM
fuelectenerg-3309	221	128	,	,	PUNCT
fuelectenerg-3309	221	129	1	1	NUM
fuelectenerg-3309	221	130	)	)	PUNCT
fuelectenerg-3309	221	131	,	,	PUNCT
fuelectenerg-3309	221	132	(	(	PUNCT
fuelectenerg-3309	221	133	1	1	NUM
fuelectenerg-3309	221	134	,	,	PUNCT
fuelectenerg-3309	221	135	2	2	NUM
fuelectenerg-3309	221	136	,	,	PUNCT
fuelectenerg-3309	221	137	1	1	NUM
fuelectenerg-3309	221	138	,	,	PUNCT
fuelectenerg-3309	221	139	3	3	NUM
fuelectenerg-3309	221	140	)	)	PUNCT
fuelectenerg-3309	221	141	,	,	PUNCT
fuelectenerg-3309	221	142	(	(	PUNCT
fuelectenerg-3309	221	143	1	1	NUM
fuelectenerg-3309	221	144	,	,	PUNCT
fuelectenerg-3309	221	145	2	2	NUM
fuelectenerg-3309	221	146	,	,	PUNCT
fuelectenerg-3309	221	147	3	3	NUM
fuelectenerg-3309	221	148	,	,	PUNCT
fuelectenerg-3309	221	149	4	4	NUM
fuelectenerg-3309	221	150	)	)	PUNCT
fuelectenerg-3309	221	151	,	,	PUNCT
fuelectenerg-3309	221	152	(	(	PUNCT
fuelectenerg-3309	221	153	1	1	NUM
fuelectenerg-3309	221	154	,	,	PUNCT
fuelectenerg-3309	221	155	2	2	NUM
fuelectenerg-3309	221	156	,	,	PUNCT
fuelectenerg-3309	221	157	3	3	NUM
fuelectenerg-3309	221	158	,	,	PUNCT
fuelectenerg-3309	221	159	2	2	NUM
fuelectenerg-3309	221	160	)	)	PUNCT
fuelectenerg-3309	221	161	,	,	PUNCT
fuelectenerg-3309	221	162	(	(	PUNCT
fuelectenerg-3309	221	163	1	1	NUM
fuelectenerg-3309	221	164	,	,	PUNCT
fuelectenerg-3309	221	165	2	2	NUM
fuelectenerg-3309	221	166	,	,	PUNCT
fuelectenerg-3309	221	167	3	3	NUM
fuelectenerg-3309	221	168	,	,	PUNCT
fuelectenerg-3309	221	169	1	1	NUM
fuelectenerg-3309	221	170	)	)	PUNCT
fuelectenerg-3309	221	171	,	,	PUNCT
fuelectenerg-3309	221	172	(	(	PUNCT
fuelectenerg-3309	221	173	1	1	NUM
fuelectenerg-3309	221	174	,	,	PUNCT
fuelectenerg-3309	221	175	2	2	NUM
fuelectenerg-3309	221	176	,	,	PUNCT
fuelectenerg-3309	221	177	3	3	NUM
fuelectenerg-3309	221	178	,	,	PUNCT
fuelectenerg-3309	221	179	3	3	NUM
fuelectenerg-3309	221	180	)	)	PUNCT
fuelectenerg-3309	221	181	,	,	PUNCT
fuelectenerg-3309	221	182	(	(	PUNCT
fuelectenerg-3309	221	183	1	1	NUM
fuelectenerg-3309	221	184	,	,	PUNCT
fuelectenerg-3309	221	185	1	1	NUM
fuelectenerg-3309	221	186	,	,	PUNCT
fuelectenerg-3309	221	187	2	2	NUM
fuelectenerg-3309	221	188	,	,	PUNCT
fuelectenerg-3309	221	189	4	4	NUM
fuelectenerg-3309	221	190	)	)	PUNCT
fuelectenerg-3309	221	191	,	,	PUNCT
fuelectenerg-3309	221	192	(	(	PUNCT
fuelectenerg-3309	221	193	1	1	NUM
fuelectenerg-3309	221	194	,	,	PUNCT
fuelectenerg-3309	221	195	1	1	NUM
fuelectenerg-3309	221	196	,	,	PUNCT
fuelectenerg-3309	221	197	2	2	NUM
fuelectenerg-3309	221	198	,	,	PUNCT
fuelectenerg-3309	221	199	2	2	NUM
fuelectenerg-3309	221	200	)	)	PUNCT
fuelectenerg-3309	221	201	,	,	PUNCT
fuelectenerg-3309	221	202	(	(	PUNCT
fuelectenerg-3309	221	203	1	1	NUM
fuelectenerg-3309	221	204	,	,	PUNCT
fuelectenerg-3309	221	205	1	1	NUM
fuelectenerg-3309	221	206	,	,	PUNCT
fuelectenerg-3309	221	207	2	2	NUM
fuelectenerg-3309	221	208	,	,	PUNCT
fuelectenerg-3309	221	209	1	1	NUM
fuelectenerg-3309	221	210	)	)	PUNCT
fuelectenerg-3309	221	211	,	,	PUNCT
fuelectenerg-3309	221	212	(	(	PUNCT
fuelectenerg-3309	221	213	1	1	NUM
fuelectenerg-3309	221	214	,	,	PUNCT
fuelectenerg-3309	221	215	1	1	NUM
fuelectenerg-3309	221	216	,	,	PUNCT
fuelectenerg-3309	221	217	2	2	NUM
fuelectenerg-3309	221	218	,	,	PUNCT
fuelectenerg-3309	221	219	3	3	NUM
fuelectenerg-3309	221	220	)	)	PUNCT
fuelectenerg-3309	221	221	,	,	PUNCT
fuelectenerg-3309	221	222	(	(	PUNCT
fuelectenerg-3309	221	223	1	1	NUM
fuelectenerg-3309	221	224	,	,	PUNCT
fuelectenerg-3309	221	225	1	1	NUM
fuelectenerg-3309	221	226	,	,	PUNCT
fuelectenerg-3309	221	227	1	1	NUM
fuelectenerg-3309	221	228	,	,	PUNCT
fuelectenerg-3309	221	229	4	4	NUM
fuelectenerg-3309	221	230	)	)	PUNCT
fuelectenerg-3309	221	231	,	,	PUNCT
fuelectenerg-3309	221	232	(	(	PUNCT
fuelectenerg-3309	221	233	1	1	NUM
fuelectenerg-3309	221	234	,	,	PUNCT
fuelectenerg-3309	221	235	1	1	NUM
fuelectenerg-3309	221	236	,	,	PUNCT
fuelectenerg-3309	221	237	1	1	NUM
fuelectenerg-3309	221	238	,	,	PUNCT
fuelectenerg-3309	221	239	2	2	NUM
fuelectenerg-3309	221	240	)	)	PUNCT
fuelectenerg-3309	221	241	,	,	PUNCT
fuelectenerg-3309	221	242	(	(	PUNCT
fuelectenerg-3309	221	243	1	1	NUM
fuelectenerg-3309	221	244	,	,	PUNCT
fuelectenerg-3309	221	245	1	1	NUM
fuelectenerg-3309	221	246	,	,	PUNCT
fuelectenerg-3309	221	247	1	1	NUM
fuelectenerg-3309	221	248	,	,	PUNCT
fuelectenerg-3309	221	249	1	1	NUM
fuelectenerg-3309	221	250	)	)	PUNCT
fuelectenerg-3309	221	251	,	,	PUNCT
fuelectenerg-3309	221	252	(	(	PUNCT
fuelectenerg-3309	221	253	1	1	NUM
fuelectenerg-3309	221	254	,	,	PUNCT
fuelectenerg-3309	221	255	1	1	NUM
fuelectenerg-3309	221	256	,	,	PUNCT
fuelectenerg-3309	221	257	1	1	NUM
fuelectenerg-3309	221	258	,	,	PUNCT
fuelectenerg-3309	221	259	3	3	NUM
fuelectenerg-3309	221	260	)	)	PUNCT
fuelectenerg-3309	221	261	,	,	PUNCT
fuelectenerg-3309	221	262	(	(	PUNCT
fuelectenerg-3309	221	263	1	1	NUM
fuelectenerg-3309	221	264	,	,	PUNCT
fuelectenerg-3309	221	265	1	1	NUM
fuelectenerg-3309	221	266	,	,	PUNCT
fuelectenerg-3309	221	267	3	3	NUM
fuelectenerg-3309	221	268	,	,	PUNCT
fuelectenerg-3309	221	269	4	4	NUM
fuelectenerg-3309	221	270	)	)	PUNCT
fuelectenerg-3309	221	271	,	,	PUNCT
fuelectenerg-3309	221	272	(	(	PUNCT
fuelectenerg-3309	221	273	1	1	NUM
fuelectenerg-3309	221	274	,	,	PUNCT
fuelectenerg-3309	221	275	1	1	NUM
fuelectenerg-3309	221	276	,	,	PUNCT
fuelectenerg-3309	221	277	3	3	NUM
fuelectenerg-3309	221	278	,	,	PUNCT
fuelectenerg-3309	221	279	2	2	NUM
fuelectenerg-3309	221	280	)	)	PUNCT
fuelectenerg-3309	221	281	,	,	PUNCT
fuelectenerg-3309	221	282	(	(	PUNCT
fuelectenerg-3309	221	283	1	1	NUM
fuelectenerg-3309	221	284	,	,	PUNCT
fuelectenerg-3309	221	285	1	1	NUM
fuelectenerg-3309	221	286	,	,	PUNCT
fuelectenerg-3309	221	287	3	3	NUM
fuelectenerg-3309	221	288	,	,	PUNCT
fuelectenerg-3309	221	289	1	1	NUM
fuelectenerg-3309	221	290	)	)	PUNCT
fuelectenerg-3309	221	291	,	,	PUNCT
fuelectenerg-3309	221	292	(	(	PUNCT
fuelectenerg-3309	221	293	1	1	NUM
fuelectenerg-3309	221	294	,	,	PUNCT
fuelectenerg-3309	221	295	1	1	NUM
fuelectenerg-3309	221	296	,	,	PUNCT
fuelectenerg-3309	221	297	3	3	NUM
fuelectenerg-3309	221	298	,	,	PUNCT
fuelectenerg-3309	221	299	3	3	NUM
fuelectenerg-3309	221	300	)	)	PUNCT
fuelectenerg-3309	221	301	}	}	PUNCT
fuelectenerg-3309	221	302	.	.	PUNCT
fuelectenerg-3309	222	1	enumeration	enumeration	NOUN
fuelectenerg-3309	222	2	and	and	CCONJ
fuelectenerg-3309	222	3	coding	code	VERB
fuelectenerg-3309	222	4	permutations	permutation	NOUN
fuelectenerg-3309	222	5	and	and	CCONJ
fuelectenerg-3309	222	6	reversible	reversible	ADJ
fuelectenerg-3309	222	7	logical	logical	ADJ
fuelectenerg-3309	222	8	circuits	circuit	NOUN
fuelectenerg-3309	222	9	7	7	NUM
fuelectenerg-3309	222	10	if	if	SCONJ
fuelectenerg-3309	222	11	q	q	NOUN
fuelectenerg-3309	222	12	is	be	AUX
fuelectenerg-3309	222	13	defined	define	VERB
fuelectenerg-3309	222	14	in	in	ADP
fuelectenerg-3309	222	15	(	(	PUNCT
fuelectenerg-3309	222	16	3	3	NUM
fuelectenerg-3309	222	17	)	)	PUNCT
fuelectenerg-3309	222	18	,	,	PUNCT
fuelectenerg-3309	222	19	then	then	ADV
fuelectenerg-3309	222	20	by	by	ADP
fuelectenerg-3309	222	21	using	use	VERB
fuelectenerg-3309	222	22	the	the	DET
fuelectenerg-3309	222	23	composition	composition	NOUN
fuelectenerg-3309	222	24	map	map	NOUN
fuelectenerg-3309	222	25	q−1wr,4u	q−1wr,4u	ADJ
fuelectenerg-3309	222	26	−1	−1	NOUN
fuelectenerg-3309	222	27	we	we	PRON
fuelectenerg-3309	222	28	obtain	obtain	VERB
fuelectenerg-3309	222	29	the	the	DET
fuelectenerg-3309	222	30	following	follow	VERB
fuelectenerg-3309	222	31	enumeration	enumeration	NOUN
fuelectenerg-3309	222	32	of	of	ADP
fuelectenerg-3309	222	33	the	the	DET
fuelectenerg-3309	222	34	set	set	NOUN
fuelectenerg-3309	222	35	p	p	NOUN
fuelectenerg-3309	222	36	(	(	PUNCT
fuelectenerg-3309	222	37	4	4	NUM
fuelectenerg-3309	222	38	):	):	PUNCT
fuelectenerg-3309	222	39	{	{	PUNCT
fuelectenerg-3309	222	40	(	(	PUNCT
fuelectenerg-3309	222	41	1	1	NUM
fuelectenerg-3309	222	42	,	,	PUNCT
fuelectenerg-3309	222	43	2	2	NUM
fuelectenerg-3309	222	44	,	,	PUNCT
fuelectenerg-3309	222	45	3	3	NUM
fuelectenerg-3309	222	46	,	,	PUNCT
fuelectenerg-3309	222	47	4	4	NUM
fuelectenerg-3309	222	48	)	)	PUNCT
fuelectenerg-3309	222	49	,	,	PUNCT
fuelectenerg-3309	222	50	(	(	PUNCT
fuelectenerg-3309	222	51	1	1	NUM
fuelectenerg-3309	222	52	,	,	PUNCT
fuelectenerg-3309	222	53	4	4	NUM
fuelectenerg-3309	222	54	,	,	PUNCT
fuelectenerg-3309	222	55	2	2	NUM
fuelectenerg-3309	222	56	,	,	PUNCT
fuelectenerg-3309	222	57	3	3	NUM
fuelectenerg-3309	222	58	)	)	PUNCT
fuelectenerg-3309	222	59	,	,	PUNCT
fuelectenerg-3309	222	60	(	(	PUNCT
fuelectenerg-3309	222	61	4	4	NUM
fuelectenerg-3309	222	62	,	,	PUNCT
fuelectenerg-3309	222	63	1	1	NUM
fuelectenerg-3309	222	64	,	,	PUNCT
fuelectenerg-3309	222	65	2	2	NUM
fuelectenerg-3309	222	66	,	,	PUNCT
fuelectenerg-3309	222	67	3	3	NUM
fuelectenerg-3309	222	68	)	)	PUNCT
fuelectenerg-3309	222	69	,	,	PUNCT
fuelectenerg-3309	222	70	(	(	PUNCT
fuelectenerg-3309	222	71	1	1	NUM
fuelectenerg-3309	222	72	,	,	PUNCT
fuelectenerg-3309	222	73	2	2	NUM
fuelectenerg-3309	222	74	,	,	PUNCT
fuelectenerg-3309	222	75	4	4	NUM
fuelectenerg-3309	222	76	,	,	PUNCT
fuelectenerg-3309	222	77	3	3	NUM
fuelectenerg-3309	222	78	)	)	PUNCT
fuelectenerg-3309	222	79	,	,	PUNCT
fuelectenerg-3309	222	80	(	(	PUNCT
fuelectenerg-3309	222	81	2	2	NUM
fuelectenerg-3309	222	82	,	,	PUNCT
fuelectenerg-3309	222	83	3	3	NUM
fuelectenerg-3309	222	84	,	,	PUNCT
fuelectenerg-3309	222	85	1	1	NUM
fuelectenerg-3309	222	86	,	,	PUNCT
fuelectenerg-3309	222	87	4	4	NUM
fuelectenerg-3309	222	88	)	)	PUNCT
fuelectenerg-3309	222	89	,	,	PUNCT
fuelectenerg-3309	222	90	(	(	PUNCT
fuelectenerg-3309	222	91	2	2	NUM
fuelectenerg-3309	222	92	,	,	PUNCT
fuelectenerg-3309	222	93	4	4	NUM
fuelectenerg-3309	222	94	,	,	PUNCT
fuelectenerg-3309	222	95	3	3	NUM
fuelectenerg-3309	222	96	,	,	PUNCT
fuelectenerg-3309	222	97	1	1	NUM
fuelectenerg-3309	222	98	)	)	PUNCT
fuelectenerg-3309	222	99	,	,	PUNCT
fuelectenerg-3309	222	100	(	(	PUNCT
fuelectenerg-3309	222	101	4	4	NUM
fuelectenerg-3309	222	102	,	,	PUNCT
fuelectenerg-3309	222	103	2	2	NUM
fuelectenerg-3309	222	104	,	,	PUNCT
fuelectenerg-3309	222	105	3	3	NUM
fuelectenerg-3309	222	106	,	,	PUNCT
fuelectenerg-3309	222	107	1	1	NUM
fuelectenerg-3309	222	108	)	)	PUNCT
fuelectenerg-3309	222	109	,	,	PUNCT
fuelectenerg-3309	222	110	(	(	PUNCT
fuelectenerg-3309	222	111	2	2	NUM
fuelectenerg-3309	222	112	,	,	PUNCT
fuelectenerg-3309	222	113	3	3	NUM
fuelectenerg-3309	222	114	,	,	PUNCT
fuelectenerg-3309	222	115	4	4	NUM
fuelectenerg-3309	222	116	,	,	PUNCT
fuelectenerg-3309	222	117	1	1	NUM
fuelectenerg-3309	222	118	)	)	PUNCT
fuelectenerg-3309	222	119	,	,	PUNCT
fuelectenerg-3309	222	120	(	(	PUNCT
fuelectenerg-3309	222	121	3	3	NUM
fuelectenerg-3309	222	122	,	,	PUNCT
fuelectenerg-3309	222	123	2	2	NUM
fuelectenerg-3309	222	124	,	,	PUNCT
fuelectenerg-3309	222	125	1	1	NUM
fuelectenerg-3309	222	126	,	,	PUNCT
fuelectenerg-3309	222	127	4	4	NUM
fuelectenerg-3309	222	128	)	)	PUNCT
fuelectenerg-3309	222	129	,	,	PUNCT
fuelectenerg-3309	222	130	(	(	PUNCT
fuelectenerg-3309	222	131	3	3	NUM
fuelectenerg-3309	222	132	,	,	PUNCT
fuelectenerg-3309	222	133	4	4	NUM
fuelectenerg-3309	222	134	,	,	PUNCT
fuelectenerg-3309	222	135	2	2	NUM
fuelectenerg-3309	222	136	,	,	PUNCT
fuelectenerg-3309	222	137	1	1	NUM
fuelectenerg-3309	222	138	)	)	PUNCT
fuelectenerg-3309	222	139	,	,	PUNCT
fuelectenerg-3309	222	140	(	(	PUNCT
fuelectenerg-3309	222	141	4	4	NUM
fuelectenerg-3309	222	142	,	,	PUNCT
fuelectenerg-3309	222	143	3	3	NUM
fuelectenerg-3309	222	144	,	,	PUNCT
fuelectenerg-3309	222	145	2	2	NUM
fuelectenerg-3309	222	146	,	,	PUNCT
fuelectenerg-3309	222	147	1	1	NUM
fuelectenerg-3309	222	148	)	)	PUNCT
fuelectenerg-3309	222	149	,	,	PUNCT
fuelectenerg-3309	222	150	(	(	PUNCT
fuelectenerg-3309	222	151	3	3	NUM
fuelectenerg-3309	222	152	,	,	PUNCT
fuelectenerg-3309	222	153	2	2	NUM
fuelectenerg-3309	222	154	,	,	PUNCT
fuelectenerg-3309	222	155	4	4	NUM
fuelectenerg-3309	222	156	,	,	PUNCT
fuelectenerg-3309	222	157	1	1	NUM
fuelectenerg-3309	222	158	)	)	PUNCT
fuelectenerg-3309	222	159	,	,	PUNCT
fuelectenerg-3309	222	160	(	(	PUNCT
fuelectenerg-3309	222	161	2	2	NUM
fuelectenerg-3309	222	162	,	,	PUNCT
fuelectenerg-3309	222	163	1	1	NUM
fuelectenerg-3309	222	164	,	,	PUNCT
fuelectenerg-3309	222	165	3	3	NUM
fuelectenerg-3309	222	166	,	,	PUNCT
fuelectenerg-3309	222	167	4	4	NUM
fuelectenerg-3309	222	168	)	)	PUNCT
fuelectenerg-3309	222	169	,	,	PUNCT
fuelectenerg-3309	222	170	(	(	PUNCT
fuelectenerg-3309	222	171	2	2	NUM
fuelectenerg-3309	222	172	,	,	PUNCT
fuelectenerg-3309	222	173	4	4	NUM
fuelectenerg-3309	222	174	,	,	PUNCT
fuelectenerg-3309	222	175	1	1	NUM
fuelectenerg-3309	222	176	,	,	PUNCT
fuelectenerg-3309	222	177	3	3	NUM
fuelectenerg-3309	222	178	)	)	PUNCT
fuelectenerg-3309	222	179	,	,	PUNCT
fuelectenerg-3309	222	180	(	(	PUNCT
fuelectenerg-3309	222	181	4	4	NUM
fuelectenerg-3309	222	182	,	,	PUNCT
fuelectenerg-3309	222	183	2	2	NUM
fuelectenerg-3309	222	184	,	,	PUNCT
fuelectenerg-3309	222	185	1	1	NUM
fuelectenerg-3309	222	186	,	,	PUNCT
fuelectenerg-3309	222	187	3	3	NUM
fuelectenerg-3309	222	188	)	)	PUNCT
fuelectenerg-3309	222	189	,	,	PUNCT
fuelectenerg-3309	222	190	(	(	PUNCT
fuelectenerg-3309	222	191	2	2	NUM
fuelectenerg-3309	222	192	,	,	PUNCT
fuelectenerg-3309	222	193	1	1	NUM
fuelectenerg-3309	222	194	,	,	PUNCT
fuelectenerg-3309	222	195	4	4	NUM
fuelectenerg-3309	222	196	,	,	PUNCT
fuelectenerg-3309	222	197	3	3	NUM
fuelectenerg-3309	222	198	)	)	PUNCT
fuelectenerg-3309	222	199	,	,	PUNCT
fuelectenerg-3309	222	200	(	(	PUNCT
fuelectenerg-3309	222	201	1	1	NUM
fuelectenerg-3309	222	202	,	,	PUNCT
fuelectenerg-3309	222	203	3	3	NUM
fuelectenerg-3309	222	204	,	,	PUNCT
fuelectenerg-3309	222	205	2	2	NUM
fuelectenerg-3309	222	206	,	,	PUNCT
fuelectenerg-3309	222	207	4	4	NUM
fuelectenerg-3309	222	208	)	)	PUNCT
fuelectenerg-3309	222	209	,	,	PUNCT
fuelectenerg-3309	222	210	(	(	PUNCT
fuelectenerg-3309	222	211	1	1	NUM
fuelectenerg-3309	222	212	,	,	PUNCT
fuelectenerg-3309	222	213	4	4	NUM
fuelectenerg-3309	222	214	,	,	PUNCT
fuelectenerg-3309	222	215	3	3	NUM
fuelectenerg-3309	222	216	,	,	PUNCT
fuelectenerg-3309	222	217	2	2	NUM
fuelectenerg-3309	222	218	)	)	PUNCT
fuelectenerg-3309	222	219	,	,	PUNCT
fuelectenerg-3309	222	220	(	(	PUNCT
fuelectenerg-3309	222	221	4	4	NUM
fuelectenerg-3309	222	222	,	,	PUNCT
fuelectenerg-3309	222	223	1	1	NUM
fuelectenerg-3309	222	224	,	,	PUNCT
fuelectenerg-3309	222	225	3	3	NUM
fuelectenerg-3309	222	226	,	,	PUNCT
fuelectenerg-3309	222	227	2	2	NUM
fuelectenerg-3309	222	228	)	)	PUNCT
fuelectenerg-3309	222	229	,	,	PUNCT
fuelectenerg-3309	222	230	(	(	PUNCT
fuelectenerg-3309	222	231	1	1	NUM
fuelectenerg-3309	222	232	,	,	PUNCT
fuelectenerg-3309	222	233	3	3	NUM
fuelectenerg-3309	222	234	,	,	PUNCT
fuelectenerg-3309	222	235	4	4	NUM
fuelectenerg-3309	222	236	,	,	PUNCT
fuelectenerg-3309	222	237	2	2	NUM
fuelectenerg-3309	222	238	)	)	PUNCT
fuelectenerg-3309	222	239	,	,	PUNCT
fuelectenerg-3309	222	240	(	(	PUNCT
fuelectenerg-3309	222	241	3	3	NUM
fuelectenerg-3309	222	242	,	,	PUNCT
fuelectenerg-3309	222	243	1	1	NUM
fuelectenerg-3309	222	244	,	,	PUNCT
fuelectenerg-3309	222	245	2	2	NUM
fuelectenerg-3309	222	246	,	,	PUNCT
fuelectenerg-3309	222	247	4	4	NUM
fuelectenerg-3309	222	248	)	)	PUNCT
fuelectenerg-3309	222	249	,	,	PUNCT
fuelectenerg-3309	222	250	(	(	PUNCT
fuelectenerg-3309	222	251	3	3	NUM
fuelectenerg-3309	222	252	,	,	PUNCT
fuelectenerg-3309	222	253	4	4	NUM
fuelectenerg-3309	222	254	,	,	PUNCT
fuelectenerg-3309	222	255	1	1	NUM
fuelectenerg-3309	222	256	,	,	PUNCT
fuelectenerg-3309	222	257	2	2	NUM
fuelectenerg-3309	222	258	)	)	PUNCT
fuelectenerg-3309	222	259	,	,	PUNCT
fuelectenerg-3309	222	260	(	(	PUNCT
fuelectenerg-3309	222	261	4	4	NUM
fuelectenerg-3309	222	262	,	,	PUNCT
fuelectenerg-3309	222	263	3	3	NUM
fuelectenerg-3309	222	264	,	,	PUNCT
fuelectenerg-3309	222	265	1	1	NUM
fuelectenerg-3309	222	266	,	,	PUNCT
fuelectenerg-3309	222	267	2	2	NUM
fuelectenerg-3309	222	268	)	)	PUNCT
fuelectenerg-3309	222	269	,	,	PUNCT
fuelectenerg-3309	222	270	(	(	PUNCT
fuelectenerg-3309	222	271	3	3	NUM
fuelectenerg-3309	222	272	,	,	PUNCT
fuelectenerg-3309	222	273	1	1	NUM
fuelectenerg-3309	222	274	,	,	PUNCT
fuelectenerg-3309	222	275	4	4	NUM
fuelectenerg-3309	222	276	,	,	PUNCT
fuelectenerg-3309	222	277	2	2	NUM
fuelectenerg-3309	222	278	)	)	PUNCT
fuelectenerg-3309	222	279	}	}	PUNCT
fuelectenerg-3309	222	280	.	.	PUNCT
fuelectenerg-3309	223	1	3	3	NUM
fuelectenerg-3309	223	2	a	a	DET
fuelectenerg-3309	223	3	class	class	NOUN
fuelectenerg-3309	223	4	of	of	ADP
fuelectenerg-3309	223	5	boolean	boolean	ADJ
fuelectenerg-3309	223	6	matrices	matrix	NOUN
fuelectenerg-3309	223	7	coded	code	VERB
fuelectenerg-3309	223	8	by	by	ADP
fuelectenerg-3309	223	9	permutations	permutation	NOUN
fuelectenerg-3309	223	10	and	and	CCONJ
fuelectenerg-3309	223	11	a	a	DET
fuelectenerg-3309	223	12	class	class	NOUN
fuelectenerg-3309	223	13	of	of	ADP
fuelectenerg-3309	223	14	bijection	bijection	NOUN
fuelectenerg-3309	223	15	maps	map	NOUN
fuelectenerg-3309	223	16	before	before	SCONJ
fuelectenerg-3309	223	17	we	we	PRON
fuelectenerg-3309	223	18	introduce	introduce	VERB
fuelectenerg-3309	223	19	a	a	DET
fuelectenerg-3309	223	20	class	class	NOUN
fuelectenerg-3309	223	21	of	of	ADP
fuelectenerg-3309	223	22	bijection	bijection	NOUN
fuelectenerg-3309	223	23	maps	map	NOUN
fuelectenerg-3309	223	24	on	on	ADP
fuelectenerg-3309	223	25	{	{	PUNCT
fuelectenerg-3309	223	26	0	0	NUM
fuelectenerg-3309	223	27	,	,	PUNCT
fuelectenerg-3309	223	28	1	1	NUM
fuelectenerg-3309	223	29	,	,	PUNCT
fuelectenerg-3309	223	30	...	...	PUNCT
fuelectenerg-3309	223	31	,	,	PUNCT
fuelectenerg-3309	223	32	qm−1	qm−1	NOUN
fuelectenerg-3309	223	33	}	}	PUNCT
fuelectenerg-3309	223	34	for	for	ADP
fuelectenerg-3309	223	35	any	any	DET
fuelectenerg-3309	223	36	pair	pair	NOUN
fuelectenerg-3309	223	37	of	of	ADP
fuelectenerg-3309	223	38	natural	natural	ADJ
fuelectenerg-3309	223	39	numbers	number	NOUN
fuelectenerg-3309	223	40	m	m	ADP
fuelectenerg-3309	223	41	,	,	PUNCT
fuelectenerg-3309	223	42	q	q	X
fuelectenerg-3309	223	43	≥	≥	NOUN
fuelectenerg-3309	223	44	2	2	NUM
fuelectenerg-3309	223	45	,	,	PUNCT
fuelectenerg-3309	223	46	we	we	PRON
fuelectenerg-3309	223	47	present	present	VERB
fuelectenerg-3309	223	48	as	as	ADP
fuelectenerg-3309	223	49	in	in	ADP
fuelectenerg-3309	223	50	[	[	X
fuelectenerg-3309	223	51	2	2	NUM
fuelectenerg-3309	223	52	]	]	PUNCT
fuelectenerg-3309	223	53	a	a	DET
fuelectenerg-3309	223	54	class	class	NOUN
fuelectenerg-3309	223	55	of	of	ADP
fuelectenerg-3309	223	56	sparse	sparse	ADJ
fuelectenerg-3309	223	57	boolean	boolean	ADJ
fuelectenerg-3309	223	58	matrices	matrix	NOUN
fuelectenerg-3309	223	59	and	and	CCONJ
fuelectenerg-3309	223	60	their	their	PRON
fuelectenerg-3309	223	61	properties	property	NOUN
fuelectenerg-3309	223	62	.	.	PUNCT
fuelectenerg-3309	224	1	definition	definition	NOUN
fuelectenerg-3309	224	2	1	1	NUM
fuelectenerg-3309	224	3	for	for	ADP
fuelectenerg-3309	224	4	any	any	DET
fuelectenerg-3309	224	5	natural	natural	ADJ
fuelectenerg-3309	224	6	number	number	NOUN
fuelectenerg-3309	224	7	m	m	PROPN
fuelectenerg-3309	224	8	≥	≥	NOUN
fuelectenerg-3309	224	9	2	2	NUM
fuelectenerg-3309	224	10	we	we	PRON
fuelectenerg-3309	224	11	define	define	VERB
fuelectenerg-3309	224	12	by	by	ADP
fuelectenerg-3309	224	13	zm	zm	PROPN
fuelectenerg-3309	224	14	the	the	DET
fuelectenerg-3309	224	15	class	class	NOUN
fuelectenerg-3309	224	16	of	of	ADP
fuelectenerg-3309	224	17	all	all	DET
fuelectenerg-3309	224	18	m×m	m×m	ADJ
fuelectenerg-3309	224	19	boolean	boolean	ADJ
fuelectenerg-3309	224	20	matrices	matrix	NOUN
fuelectenerg-3309	224	21	whose	whose	DET
fuelectenerg-3309	224	22	row	row	NOUN
fuelectenerg-3309	224	23	vectors	vector	NOUN
fuelectenerg-3309	224	24	zi	zi	NOUN
fuelectenerg-3309	224	25	satisfy	satisfy	PROPN
fuelectenerg-3309	224	26	zi	zi	PROPN
fuelectenerg-3309	224	27	⊙	⊙	PROPN
fuelectenerg-3309	224	28	zj	zj	PROPN
fuelectenerg-3309	224	29	=	=	PROPN
fuelectenerg-3309	224	30	cij	cij	PROPN
fuelectenerg-3309	224	31	zmax{i	zmax{i	PROPN
fuelectenerg-3309	224	32	,	,	PUNCT
fuelectenerg-3309	224	33	j	j	NOUN
fuelectenerg-3309	224	34	}	}	PUNCT
fuelectenerg-3309	224	35	:	:	PUNCT
fuelectenerg-3309	224	36	cij	cij	PROPN
fuelectenerg-3309	224	37	∈	∈	PROPN
fuelectenerg-3309	224	38	{	{	PUNCT
fuelectenerg-3309	224	39	0	0	NUM
fuelectenerg-3309	224	40	,	,	PUNCT
fuelectenerg-3309	224	41	1	1	NUM
fuelectenerg-3309	224	42	}	}	PUNCT
fuelectenerg-3309	224	43	,	,	PUNCT
fuelectenerg-3309	224	44	i	i	PRON
fuelectenerg-3309	224	45	,	,	PUNCT
fuelectenerg-3309	224	46	j	j	PROPN
fuelectenerg-3309	224	47	=	=	SYM
fuelectenerg-3309	224	48	1	1	NUM
fuelectenerg-3309	224	49	,	,	PUNCT
fuelectenerg-3309	224	50	...	...	PUNCT
fuelectenerg-3309	224	51	,	,	PUNCT
fuelectenerg-3309	224	52	m	m	PROPN
fuelectenerg-3309	224	53	,	,	PUNCT
fuelectenerg-3309	224	54	where	where	SCONJ
fuelectenerg-3309	224	55	⊙	⊙	PROPN
fuelectenerg-3309	224	56	is	be	AUX
fuelectenerg-3309	224	57	the	the	DET
fuelectenerg-3309	224	58	usual	usual	ADJ
fuelectenerg-3309	224	59	hadamard	hadamard	ADJ
fuelectenerg-3309	224	60	product	product	NOUN
fuelectenerg-3309	224	61	operation	operation	NOUN
fuelectenerg-3309	224	62	.	.	PUNCT
fuelectenerg-3309	225	1	then	then	ADV
fuelectenerg-3309	225	2	the	the	DET
fuelectenerg-3309	225	3	following	following	ADJ
fuelectenerg-3309	225	4	result	result	NOUN
fuelectenerg-3309	225	5	is	be	AUX
fuelectenerg-3309	225	6	straightforward	straightforward	ADJ
fuelectenerg-3309	225	7	:	:	PUNCT
fuelectenerg-3309	225	8	lemma	lemma	PROPN
fuelectenerg-3309	225	9	1	1	NUM
fuelectenerg-3309	226	1	[	[	X
fuelectenerg-3309	226	2	2	2	NUM
fuelectenerg-3309	226	3	]	]	PUNCT
fuelectenerg-3309	226	4	let	let	VERB
fuelectenerg-3309	226	5	a	a	PRON
fuelectenerg-3309	226	6	be	be	AUX
fuelectenerg-3309	226	7	an	an	DET
fuelectenerg-3309	226	8	m	m	NOUN
fuelectenerg-3309	226	9	×m	×m	NOUN
fuelectenerg-3309	226	10	boolean	boolean	ADJ
fuelectenerg-3309	226	11	matrix	matrix	NOUN
fuelectenerg-3309	226	12	and	and	CCONJ
fuelectenerg-3309	226	13	let	let	VERB
fuelectenerg-3309	226	14	1	1	NUM
fuelectenerg-3309	226	15	≤	≤	NUM
fuelectenerg-3309	227	1	i	i	PRON
fuelectenerg-3309	227	2	<	<	X
fuelectenerg-3309	227	3	j	j	PROPN
fuelectenerg-3309	227	4	≤	≤	PROPN
fuelectenerg-3309	227	5	m.	m.	NOUN
fuelectenerg-3309	227	6	then	then	ADV
fuelectenerg-3309	227	7	a	a	DET
fuelectenerg-3309	227	8	∈	∈	PROPN
fuelectenerg-3309	227	9	zm	zm	NOUN
fuelectenerg-3309	227	10	if	if	SCONJ
fuelectenerg-3309	227	11	and	and	CCONJ
fuelectenerg-3309	227	12	only	only	ADV
fuelectenerg-3309	227	13	if	if	SCONJ
fuelectenerg-3309	227	14	supp{aj	supp{aj	NUM
fuelectenerg-3309	227	15	}	}	PUNCT
fuelectenerg-3309	227	16	⊂	⊂	NOUN
fuelectenerg-3309	227	17	supp{ai	supp{ai	ADJ
fuelectenerg-3309	227	18	}	}	PUNCT
fuelectenerg-3309	227	19	or	or	CCONJ
fuelectenerg-3309	227	20	supp{ai}∩supp{aj	supp{ai}∩supp{aj	ADV
fuelectenerg-3309	227	21	}	}	PUNCT
fuelectenerg-3309	227	22	=	=	PUNCT
fuelectenerg-3309	227	23	∅.	∅.	ADP
fuelectenerg-3309	227	24	here	here	ADV
fuelectenerg-3309	227	25	,	,	PUNCT
fuelectenerg-3309	227	26	supp{aj	supp{aj	PROPN
fuelectenerg-3309	227	27	}	}	PUNCT
fuelectenerg-3309	227	28	denotes	denote	VERB
fuelectenerg-3309	227	29	the	the	DET
fuelectenerg-3309	227	30	set	set	NOUN
fuelectenerg-3309	227	31	of	of	ADP
fuelectenerg-3309	227	32	all	all	DET
fuelectenerg-3309	227	33	non	non	ADJ
fuelectenerg-3309	227	34	zero	zero	NUM
fuelectenerg-3309	227	35	entries	entry	NOUN
fuelectenerg-3309	227	36	of	of	ADP
fuelectenerg-3309	227	37	the	the	DET
fuelectenerg-3309	227	38	row	row	NOUN
fuelectenerg-3309	227	39	aj	aj	PROPN
fuelectenerg-3309	227	40	.	.	PUNCT
fuelectenerg-3309	228	1	in	in	ADP
fuelectenerg-3309	228	2	[	[	X
fuelectenerg-3309	228	3	2	2	X
fuelectenerg-3309	228	4	]	]	PUNCT
fuelectenerg-3309	228	5	we	we	PRON
fuelectenerg-3309	228	6	proved	prove	VERB
fuelectenerg-3309	228	7	the	the	DET
fuelectenerg-3309	228	8	following	following	NOUN
fuelectenerg-3309	228	9	:	:	PUNCT
fuelectenerg-3309	228	10	proposition	proposition	NOUN
fuelectenerg-3309	228	11	2	2	NUM
fuelectenerg-3309	228	12	let	let	VERB
fuelectenerg-3309	228	13	p	p	PROPN
fuelectenerg-3309	228	14	(	(	PUNCT
fuelectenerg-3309	228	15	m	m	NOUN
fuelectenerg-3309	228	16	)	)	PUNCT
fuelectenerg-3309	228	17	and	and	CCONJ
fuelectenerg-3309	228	18	s(m	s(m	PROPN
fuelectenerg-3309	228	19	)	)	PUNCT
fuelectenerg-3309	228	20	be	be	AUX
fuelectenerg-3309	228	21	defined	define	VERB
fuelectenerg-3309	228	22	in	in	ADP
fuelectenerg-3309	228	23	section	section	NOUN
fuelectenerg-3309	228	24	2	2	NUM
fuelectenerg-3309	228	25	.	.	PUNCT
fuelectenerg-3309	229	1	then	then	ADV
fuelectenerg-3309	229	2	every	every	DET
fuelectenerg-3309	229	3	matrix	matrix	NOUN
fuelectenerg-3309	229	4	in	in	ADP
fuelectenerg-3309	229	5	the	the	DET
fuelectenerg-3309	229	6	class	class	NOUN
fuelectenerg-3309	229	7	zm	zm	PROPN
fuelectenerg-3309	229	8	is	be	AUX
fuelectenerg-3309	229	9	uniquely	uniquely	ADV
fuelectenerg-3309	229	10	identified	identify	VERB
fuelectenerg-3309	229	11	by	by	ADP
fuelectenerg-3309	229	12	a	a	DET
fuelectenerg-3309	229	13	pair	pair	NOUN
fuelectenerg-3309	229	14	(	(	PUNCT
fuelectenerg-3309	229	15	ρ	ρ	PROPN
fuelectenerg-3309	229	16	,	,	PUNCT
fuelectenerg-3309	229	17	s	s	PART
fuelectenerg-3309	229	18	)	)	PUNCT
fuelectenerg-3309	229	19	∈	∈	PROPN
fuelectenerg-3309	229	20	p	p	NOUN
fuelectenerg-3309	229	21	(	(	PUNCT
fuelectenerg-3309	229	22	m)×s(m	m)×s(m	NOUN
fuelectenerg-3309	229	23	)	)	PUNCT
fuelectenerg-3309	229	24	.	.	PUNCT
fuelectenerg-3309	230	1	using	use	VERB
fuelectenerg-3309	230	2	the	the	DET
fuelectenerg-3309	230	3	above	above	ADJ
fuelectenerg-3309	230	4	observations	observation	NOUN
fuelectenerg-3309	230	5	we	we	PRON
fuelectenerg-3309	230	6	may	may	AUX
fuelectenerg-3309	230	7	easily	easily	ADV
fuelectenerg-3309	230	8	construct	construct	VERB
fuelectenerg-3309	230	9	elements	element	NOUN
fuelectenerg-3309	230	10	in	in	ADP
fuelectenerg-3309	230	11	the	the	DET
fuelectenerg-3309	230	12	above	above	ADJ
fuelectenerg-3309	230	13	class	class	NOUN
fuelectenerg-3309	230	14	of	of	ADP
fuelectenerg-3309	230	15	zm	zm	PROPN
fuelectenerg-3309	230	16	matrices	matrix	NOUN
fuelectenerg-3309	230	17	.	.	PUNCT
fuelectenerg-3309	231	1	indeed	indeed	ADV
fuelectenerg-3309	231	2	,	,	PUNCT
fuelectenerg-3309	231	3	let	let	VERB
fuelectenerg-3309	231	4	us	we	PRON
fuelectenerg-3309	231	5	fix	fix	VERB
fuelectenerg-3309	231	6	a	a	DET
fuelectenerg-3309	231	7	pair	pair	NOUN
fuelectenerg-3309	231	8	(	(	PUNCT
fuelectenerg-3309	231	9	ρ	ρ	PROPN
fuelectenerg-3309	231	10	,	,	PUNCT
fuelectenerg-3309	231	11	s	s	PART
fuelectenerg-3309	231	12	)	)	PUNCT
fuelectenerg-3309	231	13	∈	∈	PROPN
fuelectenerg-3309	232	1	p	p	X
fuelectenerg-3309	232	2	(	(	PUNCT
fuelectenerg-3309	232	3	m	m	NOUN
fuelectenerg-3309	232	4	)	)	PUNCT
fuelectenerg-3309	232	5	×	×	PROPN
fuelectenerg-3309	232	6	s(m	s(m	PROPN
fuelectenerg-3309	232	7	)	)	PUNCT
fuelectenerg-3309	232	8	which	which	PRON
fuelectenerg-3309	232	9	determines	determine	VERB
fuelectenerg-3309	232	10	a	a	DET
fuelectenerg-3309	232	11	matrix	matrix	NOUN
fuelectenerg-3309	232	12	z	z	NOUN
fuelectenerg-3309	232	13	∈	∈	PROPN
fuelectenerg-3309	232	14	zm	zm	PROPN
fuelectenerg-3309	232	15	in	in	ADP
fuelectenerg-3309	232	16	a	a	DET
fuelectenerg-3309	232	17	unique	unique	ADJ
fuelectenerg-3309	232	18	way	way	NOUN
fuelectenerg-3309	232	19	.	.	PUNCT
fuelectenerg-3309	233	1	from	from	ADP
fuelectenerg-3309	233	2	the	the	DET
fuelectenerg-3309	233	3	pair	pair	NOUN
fuelectenerg-3309	233	4	(	(	PUNCT
fuelectenerg-3309	233	5	ρ	ρ	PROPN
fuelectenerg-3309	233	6	,	,	PUNCT
fuelectenerg-3309	233	7	s	s	PART
fuelectenerg-3309	233	8	)	)	PUNCT
fuelectenerg-3309	233	9	we	we	PRON
fuelectenerg-3309	233	10	may	may	AUX
fuelectenerg-3309	233	11	construct	construct	VERB
fuelectenerg-3309	233	12	z	z	PROPN
fuelectenerg-3309	233	13	in	in	ADP
fuelectenerg-3309	233	14	the	the	DET
fuelectenerg-3309	233	15	following	follow	VERB
fuelectenerg-3309	233	16	manner	manner	NOUN
fuelectenerg-3309	233	17	:	:	PUNCT
fuelectenerg-3309	233	18	246	246	NUM
fuelectenerg-3309	233	19	c.	c.	PROPN
fuelectenerg-3309	233	20	karanikas	karanikas	PROPN
fuelectenerg-3309	233	21	,	,	PUNCT
fuelectenerg-3309	233	22	n.	n.	PROPN
fuelectenerg-3309	233	23	atreas	atreas	PROPN
fuelectenerg-3309	233	24	enumeration	enumeration	PROPN
fuelectenerg-3309	233	25	and	and	CCONJ
fuelectenerg-3309	233	26	coding	code	VERB
fuelectenerg-3309	233	27	permutations	permutation	NOUN
fuelectenerg-3309	233	28	and	and	CCONJ
fuelectenerg-3309	233	29	reversible	reversible	ADJ
fuelectenerg-3309	233	30	logical	logical	ADJ
fuelectenerg-3309	233	31	circuits	circuit	NOUN
fuelectenerg-3309	233	32	247	247	NUM
fuelectenerg-3309	233	33	8	8	NUM
fuelectenerg-3309	233	34	n.	n.	NOUN
fuelectenerg-3309	233	35	atreas	atreas	PROPN
fuelectenerg-3309	233	36	and	and	CCONJ
fuelectenerg-3309	233	37	c.	c.	PROPN
fuelectenerg-3309	233	38	karanikas	karanikas	PROPN
fuelectenerg-3309	233	39	(	(	PUNCT
fuelectenerg-3309	233	40	i	i	NOUN
fuelectenerg-3309	233	41	)	)	PUNCT
fuelectenerg-3309	233	42	first	first	ADV
fuelectenerg-3309	233	43	,	,	PUNCT
fuelectenerg-3309	233	44	we	we	PRON
fuelectenerg-3309	233	45	use	use	VERB
fuelectenerg-3309	233	46	ρ	ρ	NOUN
fuelectenerg-3309	233	47	to	to	PART
fuelectenerg-3309	233	48	permute	permute	VERB
fuelectenerg-3309	233	49	the	the	DET
fuelectenerg-3309	233	50	rows	row	NOUN
fuelectenerg-3309	233	51	of	of	ADP
fuelectenerg-3309	233	52	the	the	DET
fuelectenerg-3309	233	53	identity	identity	NOUN
fuelectenerg-3309	233	54	matrix	matrix	NOUN
fuelectenerg-3309	234	1	i	i	PRON
fuelectenerg-3309	234	2	m	m	VERB
fuelectenerg-3309	235	1	and	and	CCONJ
fuelectenerg-3309	235	2	so	so	ADV
fuelectenerg-3309	235	3	we	we	PRON
fuelectenerg-3309	235	4	construct	construct	VERB
fuelectenerg-3309	235	5	an	an	DET
fuelectenerg-3309	235	6	m×m	m×m	ADJ
fuelectenerg-3309	235	7	permutation	permutation	NOUN
fuelectenerg-3309	235	8	matrix	matrix	NOUN
fuelectenerg-3309	235	9	,	,	PUNCT
fuelectenerg-3309	235	10	say	say	VERB
fuelectenerg-3309	235	11	z1	z1	PROPN
fuelectenerg-3309	235	12	.	.	PUNCT
fuelectenerg-3309	235	13	(	(	PUNCT
fuelectenerg-3309	235	14	ii	ii	NOUN
fuelectenerg-3309	235	15	)	)	PUNCT
fuelectenerg-3309	235	16	starting	start	VERB
fuelectenerg-3309	235	17	with	with	ADP
fuelectenerg-3309	235	18	the	the	DET
fuelectenerg-3309	235	19	above	above	ADJ
fuelectenerg-3309	235	20	matrix	matrix	NOUN
fuelectenerg-3309	235	21	z1	z1	NOUN
fuelectenerg-3309	235	22	,	,	PUNCT
fuelectenerg-3309	235	23	we	we	PRON
fuelectenerg-3309	235	24	construct	construct	VERB
fuelectenerg-3309	235	25	a	a	DET
fuelectenerg-3309	235	26	sequence	sequence	NOUN
fuelectenerg-3309	235	27	{	{	PUNCT
fuelectenerg-3309	235	28	zi}mi=2	zi}mi=2	PROPN
fuelectenerg-3309	235	29	of	of	ADP
fuelectenerg-3309	235	30	m	m	PROPN
fuelectenerg-3309	235	31	×	×	PROPN
fuelectenerg-3309	235	32	m	m	NOUN
fuelectenerg-3309	235	33	matrices	matrix	NOUN
fuelectenerg-3309	235	34	iteratively	iteratively	ADV
fuelectenerg-3309	235	35	,	,	PUNCT
fuelectenerg-3309	235	36	by	by	ADP
fuelectenerg-3309	235	37	using	use	VERB
fuelectenerg-3309	235	38	s	s	PROPN
fuelectenerg-3309	235	39	∈	∈	PROPN
fuelectenerg-3309	235	40	s(m	s(m	PROPN
fuelectenerg-3309	235	41	)	)	PUNCT
fuelectenerg-3309	235	42	.	.	PUNCT
fuelectenerg-3309	236	1	in	in	ADP
fuelectenerg-3309	236	2	the	the	DET
fuelectenerg-3309	236	3	ith	ith	ADJ
fuelectenerg-3309	236	4	step	step	NOUN
fuelectenerg-3309	236	5	of	of	ADP
fuelectenerg-3309	236	6	this	this	DET
fuelectenerg-3309	236	7	iteration	iteration	NOUN
fuelectenerg-3309	236	8	,	,	PUNCT
fuelectenerg-3309	236	9	a	a	DET
fuelectenerg-3309	236	10	matrix	matrix	NOUN
fuelectenerg-3309	236	11	zi	zi	NOUN
fuelectenerg-3309	236	12	is	be	AUX
fuelectenerg-3309	236	13	constructed	construct	VERB
fuelectenerg-3309	236	14	from	from	ADP
fuelectenerg-3309	236	15	the	the	DET
fuelectenerg-3309	236	16	matrix	matrix	NOUN
fuelectenerg-3309	236	17	zi−1	zi−1	NOUN
fuelectenerg-3309	236	18	based	base	VERB
fuelectenerg-3309	236	19	on	on	ADP
fuelectenerg-3309	236	20	the	the	DET
fuelectenerg-3309	236	21	following	follow	VERB
fuelectenerg-3309	236	22	rule	rule	NOUN
fuelectenerg-3309	236	23	:	:	PUNCT
fuelectenerg-3309	236	24	(	(	PUNCT
fuelectenerg-3309	236	25	a	a	X
fuelectenerg-3309	236	26	)	)	PUNCT
fuelectenerg-3309	236	27	if	if	SCONJ
fuelectenerg-3309	236	28	si	si	X
fuelectenerg-3309	236	29	=	=	SYM
fuelectenerg-3309	236	30	i	i	PROPN
fuelectenerg-3309	236	31	,	,	PUNCT
fuelectenerg-3309	236	32	define	define	VERB
fuelectenerg-3309	236	33	zi	zi	NOUN
fuelectenerg-3309	236	34	=	=	PUNCT
fuelectenerg-3309	236	35	zi−1	zi−1	PROPN
fuelectenerg-3309	236	36	.	.	PUNCT
fuelectenerg-3309	237	1	(	(	PUNCT
fuelectenerg-3309	237	2	a	a	X
fuelectenerg-3309	237	3	)	)	PUNCT
fuelectenerg-3309	237	4	if	if	SCONJ
fuelectenerg-3309	237	5	si	si	PROPN
fuelectenerg-3309	237	6	<	<	X
fuelectenerg-3309	237	7	i	i	PROPN
fuelectenerg-3309	237	8	,	,	PUNCT
fuelectenerg-3309	237	9	define	define	VERB
fuelectenerg-3309	237	10	zi	zi	NOUN
fuelectenerg-3309	237	11	by	by	ADP
fuelectenerg-3309	237	12	replacing	replace	VERB
fuelectenerg-3309	237	13	only	only	ADV
fuelectenerg-3309	237	14	the	the	DET
fuelectenerg-3309	237	15	si	si	NOUN
fuelectenerg-3309	237	16	-	-	PUNCT
fuelectenerg-3309	237	17	row	row	NOUN
fuelectenerg-3309	237	18	of	of	ADP
fuelectenerg-3309	237	19	zi−1	zi−1	PROPN
fuelectenerg-3309	237	20	with	with	ADP
fuelectenerg-3309	237	21	the	the	DET
fuelectenerg-3309	237	22	sum	sum	NOUN
fuelectenerg-3309	237	23	of	of	ADP
fuelectenerg-3309	237	24	the	the	DET
fuelectenerg-3309	237	25	i	i	NOUN
fuelectenerg-3309	237	26	-	-	PUNCT
fuelectenerg-3309	237	27	row	row	NOUN
fuelectenerg-3309	237	28	and	and	CCONJ
fuelectenerg-3309	237	29	si	si	NOUN
fuelectenerg-3309	237	30	-	-	PUNCT
fuelectenerg-3309	237	31	row	row	NOUN
fuelectenerg-3309	237	32	of	of	ADP
fuelectenerg-3309	237	33	zi−1	zi−1	PROPN
fuelectenerg-3309	237	34	.	.	PUNCT
fuelectenerg-3309	238	1	(	(	PUNCT
fuelectenerg-3309	238	2	iii	iii	NOUN
fuelectenerg-3309	238	3	)	)	PUNCT
fuelectenerg-3309	238	4	execute	execute	NOUN
fuelectenerg-3309	238	5	step	step	NOUN
fuelectenerg-3309	238	6	(	(	PUNCT
fuelectenerg-3309	238	7	ii	ii	NOUN
fuelectenerg-3309	238	8	)	)	PUNCT
fuelectenerg-3309	238	9	for	for	ADP
fuelectenerg-3309	238	10	any	any	DET
fuelectenerg-3309	238	11	i	i	NOUN
fuelectenerg-3309	238	12	=	=	NOUN
fuelectenerg-3309	238	13	2	2	NUM
fuelectenerg-3309	238	14	,	,	PUNCT
fuelectenerg-3309	238	15	...	...	PUNCT
fuelectenerg-3309	238	16	,	,	PUNCT
fuelectenerg-3309	238	17	m.	m.	NOUN
fuelectenerg-3309	238	18	then	then	ADV
fuelectenerg-3309	238	19	z	z	PROPN
fuelectenerg-3309	239	1	=	=	SYM
fuelectenerg-3309	239	2	zm	zm	PROPN
fuelectenerg-3309	239	3	is	be	AUX
fuelectenerg-3309	239	4	a	a	DET
fuelectenerg-3309	239	5	matrix	matrix	NOUN
fuelectenerg-3309	239	6	in	in	ADP
fuelectenerg-3309	239	7	the	the	DET
fuelectenerg-3309	239	8	class	class	NOUN
fuelectenerg-3309	239	9	zm	zm	PROPN
fuelectenerg-3309	239	10	.	.	PUNCT
fuelectenerg-3309	239	11	example	example	NOUN
fuelectenerg-3309	239	12	4	4	NUM
fuelectenerg-3309	239	13	let	let	VERB
fuelectenerg-3309	239	14	m	m	VERB
fuelectenerg-3309	239	15	=	=	SYM
fuelectenerg-3309	239	16	5	5	NUM
fuelectenerg-3309	239	17	,	,	PUNCT
fuelectenerg-3309	239	18	ρ	ρ	NOUN
fuelectenerg-3309	239	19	=	=	SYM
fuelectenerg-3309	239	20	(	(	PUNCT
fuelectenerg-3309	239	21	4	4	NUM
fuelectenerg-3309	239	22	,	,	PUNCT
fuelectenerg-3309	239	23	1	1	NUM
fuelectenerg-3309	239	24	,	,	PUNCT
fuelectenerg-3309	239	25	2	2	NUM
fuelectenerg-3309	239	26	,	,	PUNCT
fuelectenerg-3309	239	27	5	5	NUM
fuelectenerg-3309	239	28	,	,	PUNCT
fuelectenerg-3309	239	29	3	3	NUM
fuelectenerg-3309	239	30	)	)	PUNCT
fuelectenerg-3309	239	31	and	and	CCONJ
fuelectenerg-3309	239	32	s	s	VERB
fuelectenerg-3309	239	33	=	=	X
fuelectenerg-3309	239	34	(	(	PUNCT
fuelectenerg-3309	239	35	1	1	NUM
fuelectenerg-3309	239	36	,	,	PUNCT
fuelectenerg-3309	239	37	1	1	NUM
fuelectenerg-3309	239	38	,	,	PUNCT
fuelectenerg-3309	239	39	3	3	NUM
fuelectenerg-3309	239	40	,	,	PUNCT
fuelectenerg-3309	239	41	1	1	NUM
fuelectenerg-3309	239	42	,	,	PUNCT
fuelectenerg-3309	239	43	3	3	NUM
fuelectenerg-3309	239	44	)	)	PUNCT
fuelectenerg-3309	239	45	.	.	PUNCT
fuelectenerg-3309	240	1	then	then	ADV
fuelectenerg-3309	240	2	the	the	DET
fuelectenerg-3309	240	3	element	element	NOUN
fuelectenerg-3309	240	4	z	z	PROPN
fuelectenerg-3309	240	5	∈	∈	PROPN
fuelectenerg-3309	240	6	z5	z5	NOUN
fuelectenerg-3309	240	7	associated	associate	VERB
fuelectenerg-3309	240	8	with	with	ADP
fuelectenerg-3309	240	9	the	the	DET
fuelectenerg-3309	240	10	above	above	ADJ
fuelectenerg-3309	240	11	pair	pair	NOUN
fuelectenerg-3309	240	12	(	(	PUNCT
fuelectenerg-3309	240	13	ρ	ρ	PROPN
fuelectenerg-3309	240	14	,	,	PUNCT
fuelectenerg-3309	240	15	s	s	PART
fuelectenerg-3309	240	16	)	)	PUNCT
fuelectenerg-3309	240	17	is	be	AUX
fuelectenerg-3309	240	18	the	the	DET
fuelectenerg-3309	240	19	following	follow	VERB
fuelectenerg-3309	240	20	z	z	NOUN
fuelectenerg-3309	240	21	=	=	SYM
fuelectenerg-3309	240	22			NOUN
fuelectenerg-3309	240	23			PROPN
fuelectenerg-3309	240	24	1	1	NUM
fuelectenerg-3309	240	25	0	0	NUM
fuelectenerg-3309	240	26	0	0	NUM
fuelectenerg-3309	240	27	1	1	NUM
fuelectenerg-3309	240	28	1	1	NUM
fuelectenerg-3309	240	29	1	1	NUM
fuelectenerg-3309	240	30	0	0	NUM
fuelectenerg-3309	240	31	0	0	NUM
fuelectenerg-3309	240	32	0	0	NUM
fuelectenerg-3309	240	33	0	0	NUM
fuelectenerg-3309	240	34	0	0	NUM
fuelectenerg-3309	240	35	1	1	NUM
fuelectenerg-3309	240	36	1	1	NUM
fuelectenerg-3309	240	37	0	0	NUM
fuelectenerg-3309	240	38	0	0	NUM
fuelectenerg-3309	240	39	0	0	NUM
fuelectenerg-3309	240	40	0	0	NUM
fuelectenerg-3309	240	41	0	0	NUM
fuelectenerg-3309	240	42	0	0	NUM
fuelectenerg-3309	240	43	1	1	NUM
fuelectenerg-3309	240	44	0	0	NUM
fuelectenerg-3309	240	45	0	0	NUM
fuelectenerg-3309	240	46	1	1	NUM
fuelectenerg-3309	240	47	0	0	NUM
fuelectenerg-3309	240	48	0	0	NUM
fuelectenerg-3309	240	49			PROPN
fuelectenerg-3309	241	1			NOUN
fuelectenerg-3309	241	2	.	.	PUNCT
fuelectenerg-3309	242	1	it	it	PRON
fuelectenerg-3309	242	2	is	be	AUX
fuelectenerg-3309	242	3	remarkable	remarkable	ADJ
fuelectenerg-3309	242	4	that	that	SCONJ
fuelectenerg-3309	242	5	any	any	DET
fuelectenerg-3309	242	6	matrix	matrix	NOUN
fuelectenerg-3309	242	7	z	z	NOUN
fuelectenerg-3309	242	8	in	in	ADP
fuelectenerg-3309	242	9	the	the	DET
fuelectenerg-3309	242	10	class	class	NOUN
fuelectenerg-3309	242	11	zm	zm	PROPN
fuelectenerg-3309	242	12	(	(	PUNCT
fuelectenerg-3309	242	13	which	which	PRON
fuelectenerg-3309	242	14	depends	depend	VERB
fuelectenerg-3309	242	15	only	only	ADV
fuelectenerg-3309	242	16	on	on	ADP
fuelectenerg-3309	242	17	a	a	DET
fuelectenerg-3309	242	18	pair	pair	NOUN
fuelectenerg-3309	242	19	(	(	PUNCT
fuelectenerg-3309	242	20	ρ	ρ	PROPN
fuelectenerg-3309	242	21	,	,	PUNCT
fuelectenerg-3309	242	22	s	s	PART
fuelectenerg-3309	242	23	)	)	PUNCT
fuelectenerg-3309	242	24	)	)	PUNCT
fuelectenerg-3309	242	25	is	be	AUX
fuelectenerg-3309	242	26	invertible	invertible	ADJ
fuelectenerg-3309	242	27	and	and	CCONJ
fuelectenerg-3309	242	28	the	the	DET
fuelectenerg-3309	242	29	entries	entry	NOUN
fuelectenerg-3309	242	30	of	of	ADP
fuelectenerg-3309	242	31	inverse	inverse	ADJ
fuelectenerg-3309	242	32	matrix	matrix	NOUN
fuelectenerg-3309	242	33	z−1	z−1	NUM
fuelectenerg-3309	242	34	are	be	AUX
fuelectenerg-3309	242	35	immediately	immediately	ADV
fuelectenerg-3309	242	36	computed	compute	VERB
fuelectenerg-3309	242	37	by	by	ADP
fuelectenerg-3309	242	38	the	the	DET
fuelectenerg-3309	242	39	above	above	ADJ
fuelectenerg-3309	242	40	pair	pair	NOUN
fuelectenerg-3309	242	41	(	(	PUNCT
fuelectenerg-3309	242	42	ρ	ρ	PROPN
fuelectenerg-3309	242	43	,	,	PUNCT
fuelectenerg-3309	242	44	s	s	PART
fuelectenerg-3309	242	45	):	):	PUNCT
fuelectenerg-3309	242	46	z−1	z−1	PROPN
fuelectenerg-3309	242	47	i	i	PROPN
fuelectenerg-3309	242	48	,	,	PUNCT
fuelectenerg-3309	242	49	j	j	PROPN
fuelectenerg-3309	242	50	=	=	SYM
fuelectenerg-3309	242	51			NUM
fuelectenerg-3309	242	52			NOUN
fuelectenerg-3309	243	1	1	1	NUM
fuelectenerg-3309	243	2	i	i	NOUN
fuelectenerg-3309	243	3	=	=	SYM
fuelectenerg-3309	243	4	ρ(j	ρ(j	PROPN
fuelectenerg-3309	243	5	)	)	PUNCT
fuelectenerg-3309	243	6	−1	−1	NOUN
fuelectenerg-3309	243	7	,	,	PUNCT
fuelectenerg-3309	243	8	i	i	PRON
fuelectenerg-3309	243	9	=	=	PUNCT
fuelectenerg-3309	243	10	ρ(s(j	ρ(s(j	PROPN
fuelectenerg-3309	243	11	)	)	PUNCT
fuelectenerg-3309	243	12	)	)	PUNCT
fuelectenerg-3309	243	13	and	and	CCONJ
fuelectenerg-3309	243	14	s(j	s(j	PROPN
fuelectenerg-3309	243	15	)	)	PUNCT
fuelectenerg-3309	244	1	<	<	X
fuelectenerg-3309	244	2	j	j	PROPN
fuelectenerg-3309	244	3	0	0	PUNCT
fuelectenerg-3309	245	1	otherwise	otherwise	ADV
fuelectenerg-3309	245	2	,	,	PUNCT
fuelectenerg-3309	245	3	i	i	PRON
fuelectenerg-3309	245	4	,	,	PUNCT
fuelectenerg-3309	245	5	j	j	PROPN
fuelectenerg-3309	245	6	=	=	SYM
fuelectenerg-3309	245	7	1	1	NUM
fuelectenerg-3309	245	8	,	,	PUNCT
fuelectenerg-3309	245	9	...	...	PUNCT
fuelectenerg-3309	245	10	,	,	PUNCT
fuelectenerg-3309	245	11	m.	m.	NOUN
fuelectenerg-3309	245	12	(	(	PUNCT
fuelectenerg-3309	245	13	5	5	NUM
fuelectenerg-3309	245	14	)	)	PUNCT
fuelectenerg-3309	245	15	example	example	NOUN
fuelectenerg-3309	245	16	5	5	NUM
fuelectenerg-3309	245	17	if	if	SCONJ
fuelectenerg-3309	245	18	z	z	PROPN
fuelectenerg-3309	245	19	∈	∈	PROPN
fuelectenerg-3309	245	20	z5	z5	NOUN
fuelectenerg-3309	245	21	is	be	AUX
fuelectenerg-3309	245	22	as	as	ADP
fuelectenerg-3309	245	23	in	in	ADP
fuelectenerg-3309	245	24	example	example	NOUN
fuelectenerg-3309	245	25	(	(	PUNCT
fuelectenerg-3309	245	26	4	4	NUM
fuelectenerg-3309	245	27	)	)	PUNCT
fuelectenerg-3309	245	28	,	,	PUNCT
fuelectenerg-3309	245	29	then	then	ADV
fuelectenerg-3309	245	30	the	the	DET
fuelectenerg-3309	245	31	inverse	inverse	NOUN
fuelectenerg-3309	245	32	matrix	matrix	NOUN
fuelectenerg-3309	245	33	of	of	ADP
fuelectenerg-3309	245	34	z	z	PROPN
fuelectenerg-3309	245	35	is	be	AUX
fuelectenerg-3309	245	36	calculated	calculate	VERB
fuelectenerg-3309	245	37	directly	directly	ADV
fuelectenerg-3309	245	38	from	from	ADP
fuelectenerg-3309	245	39	(	(	PUNCT
fuelectenerg-3309	245	40	5	5	NUM
fuelectenerg-3309	245	41	):	):	PUNCT
fuelectenerg-3309	246	1	z−1	z−1	PROPN
fuelectenerg-3309	246	2	=	=	SYM
fuelectenerg-3309	246	3			NOUN
fuelectenerg-3309	246	4			NOUN
fuelectenerg-3309	246	5	0	0	NUM
fuelectenerg-3309	246	6	1	1	NUM
fuelectenerg-3309	246	7	0	0	NUM
fuelectenerg-3309	246	8	0	0	NUM
fuelectenerg-3309	246	9	0	0	NUM
fuelectenerg-3309	246	10	0	0	NUM
fuelectenerg-3309	246	11	0	0	NUM
fuelectenerg-3309	246	12	1	1	NUM
fuelectenerg-3309	246	13	0	0	NUM
fuelectenerg-3309	246	14	−1	−1	NOUN
fuelectenerg-3309	246	15	0	0	NUM
fuelectenerg-3309	246	16	0	0	NUM
fuelectenerg-3309	246	17	0	0	NUM
fuelectenerg-3309	246	18	0	0	NUM
fuelectenerg-3309	246	19	1	1	NUM
fuelectenerg-3309	246	20	1	1	NUM
fuelectenerg-3309	246	21	−1	−1	NOUN
fuelectenerg-3309	246	22	0	0	NUM
fuelectenerg-3309	246	23	−1	−1	NOUN
fuelectenerg-3309	246	24	0	0	NUM
fuelectenerg-3309	246	25	0	0	NUM
fuelectenerg-3309	246	26	0	0	NUM
fuelectenerg-3309	246	27	0	0	NUM
fuelectenerg-3309	246	28	1	1	NUM
fuelectenerg-3309	246	29	0	0	NUM
fuelectenerg-3309	246	30			PROPN
fuelectenerg-3309	247	1			NOUN
fuelectenerg-3309	247	2	.	.	PUNCT
fuelectenerg-3309	248	1	248	248	NUM
fuelectenerg-3309	248	2	c.	c.	PROPN
fuelectenerg-3309	248	3	karanikas	karanikas	PROPN
fuelectenerg-3309	248	4	,	,	PUNCT
fuelectenerg-3309	248	5	n.	n.	PROPN
fuelectenerg-3309	248	6	atreas	atreas	PROPN
fuelectenerg-3309	248	7	enumeration	enumeration	PROPN
fuelectenerg-3309	248	8	and	and	CCONJ
fuelectenerg-3309	248	9	coding	code	VERB
fuelectenerg-3309	248	10	permutations	permutation	NOUN
fuelectenerg-3309	248	11	and	and	CCONJ
fuelectenerg-3309	248	12	reversible	reversible	ADJ
fuelectenerg-3309	248	13	logical	logical	ADJ
fuelectenerg-3309	248	14	circuits	circuit	NOUN
fuelectenerg-3309	248	15	249	249	NUM
fuelectenerg-3309	248	16	8	8	NUM
fuelectenerg-3309	248	17	n.	n.	PROPN
fuelectenerg-3309	248	18	atreas	atreas	PROPN
fuelectenerg-3309	248	19	and	and	CCONJ
fuelectenerg-3309	248	20	c.	c.	PROPN
fuelectenerg-3309	248	21	karanikas	karanikas	PROPN
fuelectenerg-3309	248	22	(	(	PUNCT
fuelectenerg-3309	248	23	i	i	NOUN
fuelectenerg-3309	248	24	)	)	PUNCT
fuelectenerg-3309	248	25	first	first	ADV
fuelectenerg-3309	248	26	,	,	PUNCT
fuelectenerg-3309	248	27	we	we	PRON
fuelectenerg-3309	248	28	use	use	VERB
fuelectenerg-3309	248	29	ρ	ρ	NOUN
fuelectenerg-3309	248	30	to	to	PART
fuelectenerg-3309	248	31	permute	permute	VERB
fuelectenerg-3309	248	32	the	the	DET
fuelectenerg-3309	248	33	rows	row	NOUN
fuelectenerg-3309	248	34	of	of	ADP
fuelectenerg-3309	248	35	the	the	DET
fuelectenerg-3309	248	36	identity	identity	NOUN
fuelectenerg-3309	248	37	matrix	matrix	NOUN
fuelectenerg-3309	249	1	i	i	PRON
fuelectenerg-3309	249	2	m	m	VERB
fuelectenerg-3309	250	1	and	and	CCONJ
fuelectenerg-3309	250	2	so	so	ADV
fuelectenerg-3309	250	3	we	we	PRON
fuelectenerg-3309	250	4	construct	construct	VERB
fuelectenerg-3309	250	5	an	an	DET
fuelectenerg-3309	250	6	m×m	m×m	ADJ
fuelectenerg-3309	250	7	permutation	permutation	NOUN
fuelectenerg-3309	250	8	matrix	matrix	NOUN
fuelectenerg-3309	250	9	,	,	PUNCT
fuelectenerg-3309	250	10	say	say	VERB
fuelectenerg-3309	250	11	z1	z1	PROPN
fuelectenerg-3309	250	12	.	.	PUNCT
fuelectenerg-3309	250	13	(	(	PUNCT
fuelectenerg-3309	250	14	ii	ii	NOUN
fuelectenerg-3309	250	15	)	)	PUNCT
fuelectenerg-3309	250	16	starting	start	VERB
fuelectenerg-3309	250	17	with	with	ADP
fuelectenerg-3309	250	18	the	the	DET
fuelectenerg-3309	250	19	above	above	ADJ
fuelectenerg-3309	250	20	matrix	matrix	NOUN
fuelectenerg-3309	250	21	z1	z1	NOUN
fuelectenerg-3309	250	22	,	,	PUNCT
fuelectenerg-3309	250	23	we	we	PRON
fuelectenerg-3309	250	24	construct	construct	VERB
fuelectenerg-3309	250	25	a	a	DET
fuelectenerg-3309	250	26	sequence	sequence	NOUN
fuelectenerg-3309	250	27	{	{	PUNCT
fuelectenerg-3309	250	28	zi}mi=2	zi}mi=2	PROPN
fuelectenerg-3309	250	29	of	of	ADP
fuelectenerg-3309	250	30	m	m	PROPN
fuelectenerg-3309	250	31	×	×	PROPN
fuelectenerg-3309	250	32	m	m	NOUN
fuelectenerg-3309	250	33	matrices	matrix	NOUN
fuelectenerg-3309	250	34	iteratively	iteratively	ADV
fuelectenerg-3309	250	35	,	,	PUNCT
fuelectenerg-3309	250	36	by	by	ADP
fuelectenerg-3309	250	37	using	use	VERB
fuelectenerg-3309	250	38	s	s	PROPN
fuelectenerg-3309	250	39	∈	∈	PROPN
fuelectenerg-3309	250	40	s(m	s(m	PROPN
fuelectenerg-3309	250	41	)	)	PUNCT
fuelectenerg-3309	250	42	.	.	PUNCT
fuelectenerg-3309	251	1	in	in	ADP
fuelectenerg-3309	251	2	the	the	DET
fuelectenerg-3309	251	3	ith	ith	ADJ
fuelectenerg-3309	251	4	step	step	NOUN
fuelectenerg-3309	251	5	of	of	ADP
fuelectenerg-3309	251	6	this	this	DET
fuelectenerg-3309	251	7	iteration	iteration	NOUN
fuelectenerg-3309	251	8	,	,	PUNCT
fuelectenerg-3309	251	9	a	a	DET
fuelectenerg-3309	251	10	matrix	matrix	NOUN
fuelectenerg-3309	251	11	zi	zi	NOUN
fuelectenerg-3309	251	12	is	be	AUX
fuelectenerg-3309	251	13	constructed	construct	VERB
fuelectenerg-3309	251	14	from	from	ADP
fuelectenerg-3309	251	15	the	the	DET
fuelectenerg-3309	251	16	matrix	matrix	NOUN
fuelectenerg-3309	251	17	zi−1	zi−1	NOUN
fuelectenerg-3309	251	18	based	base	VERB
fuelectenerg-3309	251	19	on	on	ADP
fuelectenerg-3309	251	20	the	the	DET
fuelectenerg-3309	251	21	following	follow	VERB
fuelectenerg-3309	251	22	rule	rule	NOUN
fuelectenerg-3309	251	23	:	:	PUNCT
fuelectenerg-3309	251	24	(	(	PUNCT
fuelectenerg-3309	251	25	a	a	X
fuelectenerg-3309	251	26	)	)	PUNCT
fuelectenerg-3309	251	27	if	if	SCONJ
fuelectenerg-3309	251	28	si	si	X
fuelectenerg-3309	251	29	=	=	SYM
fuelectenerg-3309	251	30	i	i	PROPN
fuelectenerg-3309	251	31	,	,	PUNCT
fuelectenerg-3309	251	32	define	define	VERB
fuelectenerg-3309	251	33	zi	zi	NOUN
fuelectenerg-3309	251	34	=	=	PUNCT
fuelectenerg-3309	251	35	zi−1	zi−1	PROPN
fuelectenerg-3309	251	36	.	.	PUNCT
fuelectenerg-3309	252	1	(	(	PUNCT
fuelectenerg-3309	252	2	a	a	X
fuelectenerg-3309	252	3	)	)	PUNCT
fuelectenerg-3309	252	4	if	if	SCONJ
fuelectenerg-3309	252	5	si	si	PROPN
fuelectenerg-3309	252	6	<	<	X
fuelectenerg-3309	252	7	i	i	PROPN
fuelectenerg-3309	252	8	,	,	PUNCT
fuelectenerg-3309	252	9	define	define	VERB
fuelectenerg-3309	252	10	zi	zi	NOUN
fuelectenerg-3309	252	11	by	by	ADP
fuelectenerg-3309	252	12	replacing	replace	VERB
fuelectenerg-3309	252	13	only	only	ADV
fuelectenerg-3309	252	14	the	the	DET
fuelectenerg-3309	252	15	si	si	NOUN
fuelectenerg-3309	252	16	-	-	PUNCT
fuelectenerg-3309	252	17	row	row	NOUN
fuelectenerg-3309	252	18	of	of	ADP
fuelectenerg-3309	252	19	zi−1	zi−1	PROPN
fuelectenerg-3309	252	20	with	with	ADP
fuelectenerg-3309	252	21	the	the	DET
fuelectenerg-3309	252	22	sum	sum	NOUN
fuelectenerg-3309	252	23	of	of	ADP
fuelectenerg-3309	252	24	the	the	DET
fuelectenerg-3309	252	25	i	i	NOUN
fuelectenerg-3309	252	26	-	-	PUNCT
fuelectenerg-3309	252	27	row	row	NOUN
fuelectenerg-3309	252	28	and	and	CCONJ
fuelectenerg-3309	252	29	si	si	NOUN
fuelectenerg-3309	252	30	-	-	PUNCT
fuelectenerg-3309	252	31	row	row	NOUN
fuelectenerg-3309	252	32	of	of	ADP
fuelectenerg-3309	252	33	zi−1	zi−1	PROPN
fuelectenerg-3309	252	34	.	.	PUNCT
fuelectenerg-3309	253	1	(	(	PUNCT
fuelectenerg-3309	253	2	iii	iii	NOUN
fuelectenerg-3309	253	3	)	)	PUNCT
fuelectenerg-3309	253	4	execute	execute	NOUN
fuelectenerg-3309	253	5	step	step	NOUN
fuelectenerg-3309	253	6	(	(	PUNCT
fuelectenerg-3309	253	7	ii	ii	NOUN
fuelectenerg-3309	253	8	)	)	PUNCT
fuelectenerg-3309	253	9	for	for	ADP
fuelectenerg-3309	253	10	any	any	DET
fuelectenerg-3309	253	11	i	i	NOUN
fuelectenerg-3309	253	12	=	=	NOUN
fuelectenerg-3309	253	13	2	2	NUM
fuelectenerg-3309	253	14	,	,	PUNCT
fuelectenerg-3309	253	15	...	...	PUNCT
fuelectenerg-3309	253	16	,	,	PUNCT
fuelectenerg-3309	253	17	m.	m.	NOUN
fuelectenerg-3309	253	18	then	then	ADV
fuelectenerg-3309	253	19	z	z	PROPN
fuelectenerg-3309	254	1	=	=	SYM
fuelectenerg-3309	254	2	zm	zm	PROPN
fuelectenerg-3309	254	3	is	be	AUX
fuelectenerg-3309	254	4	a	a	DET
fuelectenerg-3309	254	5	matrix	matrix	NOUN
fuelectenerg-3309	254	6	in	in	ADP
fuelectenerg-3309	254	7	the	the	DET
fuelectenerg-3309	254	8	class	class	NOUN
fuelectenerg-3309	254	9	zm	zm	PROPN
fuelectenerg-3309	254	10	.	.	PUNCT
fuelectenerg-3309	254	11	example	example	NOUN
fuelectenerg-3309	254	12	4	4	NUM
fuelectenerg-3309	254	13	let	let	VERB
fuelectenerg-3309	254	14	m	m	VERB
fuelectenerg-3309	254	15	=	=	SYM
fuelectenerg-3309	254	16	5	5	NUM
fuelectenerg-3309	254	17	,	,	PUNCT
fuelectenerg-3309	254	18	ρ	ρ	NOUN
fuelectenerg-3309	254	19	=	=	SYM
fuelectenerg-3309	254	20	(	(	PUNCT
fuelectenerg-3309	254	21	4	4	NUM
fuelectenerg-3309	254	22	,	,	PUNCT
fuelectenerg-3309	254	23	1	1	NUM
fuelectenerg-3309	254	24	,	,	PUNCT
fuelectenerg-3309	254	25	2	2	NUM
fuelectenerg-3309	254	26	,	,	PUNCT
fuelectenerg-3309	254	27	5	5	NUM
fuelectenerg-3309	254	28	,	,	PUNCT
fuelectenerg-3309	254	29	3	3	NUM
fuelectenerg-3309	254	30	)	)	PUNCT
fuelectenerg-3309	254	31	and	and	CCONJ
fuelectenerg-3309	254	32	s	s	VERB
fuelectenerg-3309	254	33	=	=	X
fuelectenerg-3309	254	34	(	(	PUNCT
fuelectenerg-3309	254	35	1	1	NUM
fuelectenerg-3309	254	36	,	,	PUNCT
fuelectenerg-3309	254	37	1	1	NUM
fuelectenerg-3309	254	38	,	,	PUNCT
fuelectenerg-3309	254	39	3	3	NUM
fuelectenerg-3309	254	40	,	,	PUNCT
fuelectenerg-3309	254	41	1	1	NUM
fuelectenerg-3309	254	42	,	,	PUNCT
fuelectenerg-3309	254	43	3	3	NUM
fuelectenerg-3309	254	44	)	)	PUNCT
fuelectenerg-3309	254	45	.	.	PUNCT
fuelectenerg-3309	255	1	then	then	ADV
fuelectenerg-3309	255	2	the	the	DET
fuelectenerg-3309	255	3	element	element	NOUN
fuelectenerg-3309	255	4	z	z	PROPN
fuelectenerg-3309	255	5	∈	∈	PROPN
fuelectenerg-3309	255	6	z5	z5	NOUN
fuelectenerg-3309	255	7	associated	associate	VERB
fuelectenerg-3309	255	8	with	with	ADP
fuelectenerg-3309	255	9	the	the	DET
fuelectenerg-3309	255	10	above	above	ADJ
fuelectenerg-3309	255	11	pair	pair	NOUN
fuelectenerg-3309	255	12	(	(	PUNCT
fuelectenerg-3309	255	13	ρ	ρ	PROPN
fuelectenerg-3309	255	14	,	,	PUNCT
fuelectenerg-3309	255	15	s	s	PART
fuelectenerg-3309	255	16	)	)	PUNCT
fuelectenerg-3309	255	17	is	be	AUX
fuelectenerg-3309	255	18	the	the	DET
fuelectenerg-3309	255	19	following	follow	VERB
fuelectenerg-3309	255	20	z	z	NOUN
fuelectenerg-3309	255	21	=	=	SYM
fuelectenerg-3309	255	22			NOUN
fuelectenerg-3309	255	23			PROPN
fuelectenerg-3309	255	24	1	1	NUM
fuelectenerg-3309	255	25	0	0	NUM
fuelectenerg-3309	255	26	0	0	NUM
fuelectenerg-3309	255	27	1	1	NUM
fuelectenerg-3309	255	28	1	1	NUM
fuelectenerg-3309	255	29	1	1	NUM
fuelectenerg-3309	255	30	0	0	NUM
fuelectenerg-3309	255	31	0	0	NUM
fuelectenerg-3309	255	32	0	0	NUM
fuelectenerg-3309	255	33	0	0	NUM
fuelectenerg-3309	255	34	0	0	NUM
fuelectenerg-3309	255	35	1	1	NUM
fuelectenerg-3309	255	36	1	1	NUM
fuelectenerg-3309	255	37	0	0	NUM
fuelectenerg-3309	255	38	0	0	NUM
fuelectenerg-3309	255	39	0	0	NUM
fuelectenerg-3309	255	40	0	0	NUM
fuelectenerg-3309	255	41	0	0	NUM
fuelectenerg-3309	255	42	0	0	NUM
fuelectenerg-3309	255	43	1	1	NUM
fuelectenerg-3309	255	44	0	0	NUM
fuelectenerg-3309	255	45	0	0	NUM
fuelectenerg-3309	255	46	1	1	NUM
fuelectenerg-3309	255	47	0	0	NUM
fuelectenerg-3309	255	48	0	0	NUM
fuelectenerg-3309	255	49			PROPN
fuelectenerg-3309	256	1			NOUN
fuelectenerg-3309	256	2	.	.	PUNCT
fuelectenerg-3309	257	1	it	it	PRON
fuelectenerg-3309	257	2	is	be	AUX
fuelectenerg-3309	257	3	remarkable	remarkable	ADJ
fuelectenerg-3309	257	4	that	that	SCONJ
fuelectenerg-3309	257	5	any	any	DET
fuelectenerg-3309	257	6	matrix	matrix	NOUN
fuelectenerg-3309	257	7	z	z	NOUN
fuelectenerg-3309	257	8	in	in	ADP
fuelectenerg-3309	257	9	the	the	DET
fuelectenerg-3309	257	10	class	class	NOUN
fuelectenerg-3309	257	11	zm	zm	PROPN
fuelectenerg-3309	257	12	(	(	PUNCT
fuelectenerg-3309	257	13	which	which	PRON
fuelectenerg-3309	257	14	depends	depend	VERB
fuelectenerg-3309	257	15	only	only	ADV
fuelectenerg-3309	257	16	on	on	ADP
fuelectenerg-3309	257	17	a	a	DET
fuelectenerg-3309	257	18	pair	pair	NOUN
fuelectenerg-3309	257	19	(	(	PUNCT
fuelectenerg-3309	257	20	ρ	ρ	PROPN
fuelectenerg-3309	257	21	,	,	PUNCT
fuelectenerg-3309	257	22	s	s	PART
fuelectenerg-3309	257	23	)	)	PUNCT
fuelectenerg-3309	257	24	)	)	PUNCT
fuelectenerg-3309	257	25	is	be	AUX
fuelectenerg-3309	257	26	invertible	invertible	ADJ
fuelectenerg-3309	257	27	and	and	CCONJ
fuelectenerg-3309	257	28	the	the	DET
fuelectenerg-3309	257	29	entries	entry	NOUN
fuelectenerg-3309	257	30	of	of	ADP
fuelectenerg-3309	257	31	inverse	inverse	ADJ
fuelectenerg-3309	257	32	matrix	matrix	NOUN
fuelectenerg-3309	257	33	z−1	z−1	NUM
fuelectenerg-3309	257	34	are	be	AUX
fuelectenerg-3309	257	35	immediately	immediately	ADV
fuelectenerg-3309	257	36	computed	compute	VERB
fuelectenerg-3309	257	37	by	by	ADP
fuelectenerg-3309	257	38	the	the	DET
fuelectenerg-3309	257	39	above	above	ADJ
fuelectenerg-3309	257	40	pair	pair	NOUN
fuelectenerg-3309	257	41	(	(	PUNCT
fuelectenerg-3309	257	42	ρ	ρ	PROPN
fuelectenerg-3309	257	43	,	,	PUNCT
fuelectenerg-3309	257	44	s	s	PART
fuelectenerg-3309	257	45	):	):	PUNCT
fuelectenerg-3309	257	46	z−1	z−1	PROPN
fuelectenerg-3309	257	47	i	i	PROPN
fuelectenerg-3309	257	48	,	,	PUNCT
fuelectenerg-3309	257	49	j	j	PROPN
fuelectenerg-3309	257	50	=	=	SYM
fuelectenerg-3309	257	51			NUM
fuelectenerg-3309	257	52			NOUN
fuelectenerg-3309	258	1	1	1	NUM
fuelectenerg-3309	258	2	i	i	NOUN
fuelectenerg-3309	258	3	=	=	SYM
fuelectenerg-3309	258	4	ρ(j	ρ(j	PROPN
fuelectenerg-3309	258	5	)	)	PUNCT
fuelectenerg-3309	258	6	−1	−1	NOUN
fuelectenerg-3309	258	7	,	,	PUNCT
fuelectenerg-3309	258	8	i	i	PRON
fuelectenerg-3309	258	9	=	=	PUNCT
fuelectenerg-3309	258	10	ρ(s(j	ρ(s(j	PROPN
fuelectenerg-3309	258	11	)	)	PUNCT
fuelectenerg-3309	258	12	)	)	PUNCT
fuelectenerg-3309	258	13	and	and	CCONJ
fuelectenerg-3309	258	14	s(j	s(j	PROPN
fuelectenerg-3309	258	15	)	)	PUNCT
fuelectenerg-3309	259	1	<	<	X
fuelectenerg-3309	259	2	j	j	PROPN
fuelectenerg-3309	259	3	0	0	PUNCT
fuelectenerg-3309	260	1	otherwise	otherwise	ADV
fuelectenerg-3309	260	2	,	,	PUNCT
fuelectenerg-3309	260	3	i	i	PRON
fuelectenerg-3309	260	4	,	,	PUNCT
fuelectenerg-3309	260	5	j	j	PROPN
fuelectenerg-3309	260	6	=	=	SYM
fuelectenerg-3309	260	7	1	1	NUM
fuelectenerg-3309	260	8	,	,	PUNCT
fuelectenerg-3309	260	9	...	...	PUNCT
fuelectenerg-3309	260	10	,	,	PUNCT
fuelectenerg-3309	260	11	m.	m.	NOUN
fuelectenerg-3309	260	12	(	(	PUNCT
fuelectenerg-3309	260	13	5	5	NUM
fuelectenerg-3309	260	14	)	)	PUNCT
fuelectenerg-3309	260	15	example	example	NOUN
fuelectenerg-3309	260	16	5	5	NUM
fuelectenerg-3309	260	17	if	if	SCONJ
fuelectenerg-3309	260	18	z	z	PROPN
fuelectenerg-3309	260	19	∈	∈	PROPN
fuelectenerg-3309	260	20	z5	z5	NOUN
fuelectenerg-3309	260	21	is	be	AUX
fuelectenerg-3309	260	22	as	as	ADP
fuelectenerg-3309	260	23	in	in	ADP
fuelectenerg-3309	260	24	example	example	NOUN
fuelectenerg-3309	260	25	(	(	PUNCT
fuelectenerg-3309	260	26	4	4	NUM
fuelectenerg-3309	260	27	)	)	PUNCT
fuelectenerg-3309	260	28	,	,	PUNCT
fuelectenerg-3309	260	29	then	then	ADV
fuelectenerg-3309	260	30	the	the	DET
fuelectenerg-3309	260	31	inverse	inverse	NOUN
fuelectenerg-3309	260	32	matrix	matrix	NOUN
fuelectenerg-3309	260	33	of	of	ADP
fuelectenerg-3309	260	34	z	z	PROPN
fuelectenerg-3309	260	35	is	be	AUX
fuelectenerg-3309	260	36	calculated	calculate	VERB
fuelectenerg-3309	260	37	directly	directly	ADV
fuelectenerg-3309	260	38	from	from	ADP
fuelectenerg-3309	260	39	(	(	PUNCT
fuelectenerg-3309	260	40	5	5	NUM
fuelectenerg-3309	260	41	):	):	PUNCT
fuelectenerg-3309	261	1	z−1	z−1	PROPN
fuelectenerg-3309	261	2	=	=	SYM
fuelectenerg-3309	261	3			NOUN
fuelectenerg-3309	261	4			NOUN
fuelectenerg-3309	261	5	0	0	NUM
fuelectenerg-3309	261	6	1	1	NUM
fuelectenerg-3309	261	7	0	0	NUM
fuelectenerg-3309	261	8	0	0	NUM
fuelectenerg-3309	261	9	0	0	NUM
fuelectenerg-3309	261	10	0	0	NUM
fuelectenerg-3309	261	11	0	0	NUM
fuelectenerg-3309	261	12	1	1	NUM
fuelectenerg-3309	261	13	0	0	NUM
fuelectenerg-3309	261	14	−1	−1	NOUN
fuelectenerg-3309	261	15	0	0	NUM
fuelectenerg-3309	261	16	0	0	NUM
fuelectenerg-3309	261	17	0	0	NUM
fuelectenerg-3309	261	18	0	0	NUM
fuelectenerg-3309	261	19	1	1	NUM
fuelectenerg-3309	261	20	1	1	NUM
fuelectenerg-3309	261	21	−1	−1	NOUN
fuelectenerg-3309	261	22	0	0	NUM
fuelectenerg-3309	261	23	−1	−1	NOUN
fuelectenerg-3309	261	24	0	0	NUM
fuelectenerg-3309	261	25	0	0	NUM
fuelectenerg-3309	261	26	0	0	NUM
fuelectenerg-3309	261	27	0	0	NUM
fuelectenerg-3309	261	28	1	1	NUM
fuelectenerg-3309	261	29	0	0	NUM
fuelectenerg-3309	261	30			NOUN
fuelectenerg-3309	262	1			NOUN
fuelectenerg-3309	262	2	.	.	PUNCT
fuelectenerg-3309	263	1	enumeration	enumeration	NOUN
fuelectenerg-3309	263	2	and	and	CCONJ
fuelectenerg-3309	263	3	coding	code	VERB
fuelectenerg-3309	263	4	permutations	permutation	NOUN
fuelectenerg-3309	263	5	and	and	CCONJ
fuelectenerg-3309	263	6	reversible	reversible	ADJ
fuelectenerg-3309	263	7	logical	logical	ADJ
fuelectenerg-3309	263	8	circuits	circuit	NOUN
fuelectenerg-3309	263	9	9	9	NUM
fuelectenerg-3309	263	10	we	we	PRON
fuelectenerg-3309	263	11	consider	consider	VERB
fuelectenerg-3309	263	12	now	now	ADV
fuelectenerg-3309	263	13	a	a	DET
fuelectenerg-3309	263	14	matrix	matrix	NOUN
fuelectenerg-3309	263	15	z−1	z−1	VERB
fuelectenerg-3309	263	16	as	as	ADP
fuelectenerg-3309	263	17	above	above	ADP
fuelectenerg-3309	263	18	corresponding	correspond	VERB
fuelectenerg-3309	263	19	to	to	ADP
fuelectenerg-3309	263	20	a	a	DET
fuelectenerg-3309	263	21	pair	pair	NOUN
fuelectenerg-3309	263	22	ρ	ρ	NOUN
fuelectenerg-3309	263	23	=	=	SYM
fuelectenerg-3309	263	24	(	(	PUNCT
fuelectenerg-3309	263	25	ρ1	ρ1	PROPN
fuelectenerg-3309	263	26	,	,	PUNCT
fuelectenerg-3309	263	27	...	...	PUNCT
fuelectenerg-3309	263	28	,	,	PUNCT
fuelectenerg-3309	263	29	ρm	ρm	X
fuelectenerg-3309	263	30	)	)	PUNCT
fuelectenerg-3309	263	31	∈	∈	PROPN
fuelectenerg-3309	263	32	p	p	X
fuelectenerg-3309	263	33	(	(	PUNCT
fuelectenerg-3309	263	34	m	m	NOUN
fuelectenerg-3309	263	35	)	)	PUNCT
fuelectenerg-3309	263	36	and	and	CCONJ
fuelectenerg-3309	263	37	s	s	NOUN
fuelectenerg-3309	263	38	=	=	SYM
fuelectenerg-3309	263	39	(	(	PUNCT
fuelectenerg-3309	263	40	s1	s1	PROPN
fuelectenerg-3309	263	41	,	,	PUNCT
fuelectenerg-3309	263	42	...	...	PUNCT
fuelectenerg-3309	263	43	,	,	PUNCT
fuelectenerg-3309	263	44	sm	sm	PROPN
fuelectenerg-3309	263	45	)	)	PUNCT
fuelectenerg-3309	263	46	∈	∈	PROPN
fuelectenerg-3309	263	47	s(m	s(m	PROPN
fuelectenerg-3309	263	48	)	)	PUNCT
fuelectenerg-3309	263	49	.	.	PUNCT
fuelectenerg-3309	264	1	we	we	PRON
fuelectenerg-3309	264	2	shall	shall	AUX
fuelectenerg-3309	264	3	use	use	VERB
fuelectenerg-3309	264	4	z−1	z−1	PROPN
fuelectenerg-3309	264	5	to	to	PART
fuelectenerg-3309	264	6	define	define	VERB
fuelectenerg-3309	264	7	a	a	DET
fuelectenerg-3309	264	8	new	new	ADJ
fuelectenerg-3309	264	9	shuffling	shuffling	NOUN
fuelectenerg-3309	264	10	method	method	NOUN
fuelectenerg-3309	264	11	.	.	PUNCT
fuelectenerg-3309	265	1	by	by	ADP
fuelectenerg-3309	265	2	elementary	elementary	ADJ
fuelectenerg-3309	265	3	calculations	calculation	NOUN
fuelectenerg-3309	265	4	,	,	PUNCT
fuelectenerg-3309	265	5	for	for	ADP
fuelectenerg-3309	265	6	any	any	DET
fuelectenerg-3309	265	7	real	real	ADJ
fuelectenerg-3309	265	8	row	row	NOUN
fuelectenerg-3309	265	9	vector	vector	NOUN
fuelectenerg-3309	265	10	e	e	NOUN
fuelectenerg-3309	265	11	=	=	PUNCT
fuelectenerg-3309	265	12	(	(	PUNCT
fuelectenerg-3309	265	13	e1	e1	PROPN
fuelectenerg-3309	265	14	,	,	PUNCT
fuelectenerg-3309	265	15	...	...	PUNCT
fuelectenerg-3309	265	16	,	,	PUNCT
fuelectenerg-3309	265	17	em	em	PRON
fuelectenerg-3309	265	18	)	)	PUNCT
fuelectenerg-3309	265	19	we	we	PRON
fuelectenerg-3309	265	20	obtain	obtain	VERB
fuelectenerg-3309	265	21	(	(	PUNCT
fuelectenerg-3309	265	22	ez−1	ez−1	NOUN
fuelectenerg-3309	265	23	)	)	PUNCT
fuelectenerg-3309	265	24	i	i	NOUN
fuelectenerg-3309	266	1	=	=	PUNCT
fuelectenerg-3309	266	2	eρi	eρi	NOUN
fuelectenerg-3309	267	1	−	−	NOUN
fuelectenerg-3309	267	2	(	(	PUNCT
fuelectenerg-3309	267	3	1−	1−	NUM
fuelectenerg-3309	267	4	δi	δi	NOUN
fuelectenerg-3309	267	5	,	,	PUNCT
fuelectenerg-3309	267	6	si	si	NOUN
fuelectenerg-3309	267	7	)	)	PUNCT
fuelectenerg-3309	267	8	eρsi	eρsi	NOUN
fuelectenerg-3309	267	9	,	,	PUNCT
fuelectenerg-3309	267	10	i	i	PRON
fuelectenerg-3309	267	11	=	=	NOUN
fuelectenerg-3309	267	12	1	1	NUM
fuelectenerg-3309	267	13	,	,	PUNCT
fuelectenerg-3309	267	14	...	...	PUNCT
fuelectenerg-3309	267	15	,	,	PUNCT
fuelectenerg-3309	267	16	m.	m.	NOUN
fuelectenerg-3309	267	17	(	(	PUNCT
fuelectenerg-3309	267	18	6	6	NUM
fuelectenerg-3309	267	19	)	)	PUNCT
fuelectenerg-3309	267	20	here	here	ADV
fuelectenerg-3309	267	21	,	,	PUNCT
fuelectenerg-3309	267	22	δi	δi	ADV
fuelectenerg-3309	267	23	,	,	PUNCT
fuelectenerg-3309	267	24	j	j	PROPN
fuelectenerg-3309	267	25	denotes	denote	VERB
fuelectenerg-3309	267	26	the	the	DET
fuelectenerg-3309	267	27	usual	usual	ADJ
fuelectenerg-3309	267	28	kronecker	kronecker	NOUN
fuelectenerg-3309	267	29	’s	’s	PART
fuelectenerg-3309	267	30	delta	delta	NOUN
fuelectenerg-3309	267	31	symbol	symbol	NOUN
fuelectenerg-3309	267	32	.	.	PUNCT
fuelectenerg-3309	268	1	inspired	inspire	VERB
fuelectenerg-3309	268	2	from	from	ADP
fuelectenerg-3309	268	3	(	(	PUNCT
fuelectenerg-3309	268	4	6	6	NUM
fuelectenerg-3309	268	5	)	)	PUNCT
fuelectenerg-3309	268	6	we	we	PRON
fuelectenerg-3309	268	7	have	have	AUX
fuelectenerg-3309	268	8	:	:	PUNCT
fuelectenerg-3309	268	9	theorem	theorem	VERB
fuelectenerg-3309	268	10	2	2	NUM
fuelectenerg-3309	268	11	let	let	VERB
fuelectenerg-3309	268	12	m	m	PRON
fuelectenerg-3309	268	13	,	,	PUNCT
fuelectenerg-3309	268	14	q	q	X
fuelectenerg-3309	268	15	≥	≥	NUM
fuelectenerg-3309	268	16	2	2	NUM
fuelectenerg-3309	268	17	be	be	AUX
fuelectenerg-3309	268	18	natural	natural	ADJ
fuelectenerg-3309	268	19	numbers	number	NOUN
fuelectenerg-3309	268	20	,	,	PUNCT
fuelectenerg-3309	268	21	ρ	ρ	PROPN
fuelectenerg-3309	268	22	=	=	SYM
fuelectenerg-3309	268	23	(	(	PUNCT
fuelectenerg-3309	268	24	ρ1	ρ1	PROPN
fuelectenerg-3309	268	25	,	,	PUNCT
fuelectenerg-3309	268	26	...	...	PUNCT
fuelectenerg-3309	268	27	,	,	PUNCT
fuelectenerg-3309	268	28	ρm	ρm	X
fuelectenerg-3309	268	29	)	)	PUNCT
fuelectenerg-3309	268	30	∈	∈	PROPN
fuelectenerg-3309	268	31	p	p	X
fuelectenerg-3309	268	32	(	(	PUNCT
fuelectenerg-3309	268	33	m	m	NOUN
fuelectenerg-3309	268	34	)	)	PUNCT
fuelectenerg-3309	268	35	and	and	CCONJ
fuelectenerg-3309	268	36	s	s	NOUN
fuelectenerg-3309	268	37	=	=	SYM
fuelectenerg-3309	268	38	(	(	PUNCT
fuelectenerg-3309	268	39	s1	s1	PROPN
fuelectenerg-3309	268	40	,	,	PUNCT
fuelectenerg-3309	268	41	...	...	PUNCT
fuelectenerg-3309	268	42	,	,	PUNCT
fuelectenerg-3309	268	43	sm	sm	PROPN
fuelectenerg-3309	268	44	)	)	PUNCT
fuelectenerg-3309	268	45	∈	∈	PROPN
fuelectenerg-3309	268	46	s(m	s(m	PROPN
fuelectenerg-3309	268	47	)	)	PUNCT
fuelectenerg-3309	268	48	.	.	PUNCT
fuelectenerg-3309	269	1	we	we	PRON
fuelectenerg-3309	269	2	define	define	VERB
fuelectenerg-3309	269	3	the	the	DET
fuelectenerg-3309	269	4	set	set	NOUN
fuelectenerg-3309	269	5	e(q	e(q	NOUN
fuelectenerg-3309	269	6	)	)	PUNCT
fuelectenerg-3309	269	7	m	m	PROPN
fuelectenerg-3309	269	8	=	=	PUNCT
fuelectenerg-3309	269	9	{	{	PUNCT
fuelectenerg-3309	269	10	en	en	X
fuelectenerg-3309	269	11	=	=	SYM
fuelectenerg-3309	269	12	(	(	PUNCT
fuelectenerg-3309	269	13	en,1	en,1	PROPN
fuelectenerg-3309	269	14	,	,	PUNCT
fuelectenerg-3309	269	15	...	...	PUNCT
fuelectenerg-3309	269	16	,	,	PUNCT
fuelectenerg-3309	269	17	en	en	X
fuelectenerg-3309	269	18	,	,	PUNCT
fuelectenerg-3309	269	19	m	m	NOUN
fuelectenerg-3309	269	20	)	)	PUNCT
fuelectenerg-3309	269	21	:	:	PUNCT
fuelectenerg-3309	270	1	n	n	PROPN
fuelectenerg-3309	270	2	=	=	SYM
fuelectenerg-3309	270	3	0	0	NUM
fuelectenerg-3309	270	4	,	,	PUNCT
fuelectenerg-3309	270	5	...	...	PUNCT
fuelectenerg-3309	270	6	,	,	PUNCT
fuelectenerg-3309	270	7	qm	qm	PROPN
fuelectenerg-3309	270	8	−	−	PROPN
fuelectenerg-3309	270	9	1	1	NUM
fuelectenerg-3309	270	10	}	}	PUNCT
fuelectenerg-3309	270	11	,	,	PUNCT
fuelectenerg-3309	270	12	where	where	SCONJ
fuelectenerg-3309	270	13	en	en	X
fuelectenerg-3309	270	14	is	be	AUX
fuelectenerg-3309	270	15	the	the	DET
fuelectenerg-3309	270	16	sequence	sequence	NOUN
fuelectenerg-3309	270	17	of	of	ADP
fuelectenerg-3309	270	18	digits	digit	NOUN
fuelectenerg-3309	270	19	of	of	ADP
fuelectenerg-3309	270	20	n	n	PRON
fuelectenerg-3309	270	21	∈	∈	PROPN
fuelectenerg-3309	270	22	{	{	PUNCT
fuelectenerg-3309	270	23	0	0	NUM
fuelectenerg-3309	270	24	,	,	PUNCT
fuelectenerg-3309	270	25	...	...	PUNCT
fuelectenerg-3309	270	26	,	,	PUNCT
fuelectenerg-3309	270	27	qm	qm	PROPN
fuelectenerg-3309	270	28	−	−	PROPN
fuelectenerg-3309	270	29	1	1	NUM
fuelectenerg-3309	270	30	}	}	PUNCT
fuelectenerg-3309	270	31	with	with	ADP
fuelectenerg-3309	270	32	respect	respect	NOUN
fuelectenerg-3309	270	33	to	to	ADP
fuelectenerg-3309	270	34	its	its	PRON
fuelectenerg-3309	270	35	q	q	ADJ
fuelectenerg-3309	270	36	-	-	PUNCT
fuelectenerg-3309	270	37	adic	adic	ADJ
fuelectenerg-3309	270	38	expansion	expansion	NOUN
fuelectenerg-3309	270	39	n	n	NOUN
fuelectenerg-3309	270	40	=	=	SYM
fuelectenerg-3309	270	41	m∑	m∑	CCONJ
fuelectenerg-3309	270	42	i=1	i=1	PROPN
fuelectenerg-3309	270	43	en	en	PROPN
fuelectenerg-3309	270	44	,	,	PUNCT
fuelectenerg-3309	270	45	iq	iq	PROPN
fuelectenerg-3309	270	46	i−1	i−1	PROPN
fuelectenerg-3309	270	47	.	.	PUNCT
fuelectenerg-3309	271	1	then	then	ADV
fuelectenerg-3309	271	2	the	the	DET
fuelectenerg-3309	271	3	map	map	NOUN
fuelectenerg-3309	271	4	tq	tq	ADP
fuelectenerg-3309	271	5	,	,	PUNCT
fuelectenerg-3309	271	6	ρ	ρ	PROPN
fuelectenerg-3309	271	7	,	,	PUNCT
fuelectenerg-3309	271	8	s	s	PART
fuelectenerg-3309	271	9	:	:	PUNCT
fuelectenerg-3309	271	10	e	e	NOUN
fuelectenerg-3309	271	11	(	(	PUNCT
fuelectenerg-3309	271	12	q	q	X
fuelectenerg-3309	271	13	)	)	PUNCT
fuelectenerg-3309	271	14	m	m	VERB
fuelectenerg-3309	271	15	→	→	SYM
fuelectenerg-3309	271	16	e(q	e(q	NOUN
fuelectenerg-3309	271	17	)	)	PUNCT
fuelectenerg-3309	271	18	m	m	VERB
fuelectenerg-3309	271	19	such	such	ADJ
fuelectenerg-3309	271	20	that	that	SCONJ
fuelectenerg-3309	271	21	for	for	ADP
fuelectenerg-3309	271	22	any	any	DET
fuelectenerg-3309	271	23	i	i	NOUN
fuelectenerg-3309	271	24	=	=	NOUN
fuelectenerg-3309	271	25	1	1	NUM
fuelectenerg-3309	271	26	,	,	PUNCT
fuelectenerg-3309	271	27	...	...	PUNCT
fuelectenerg-3309	271	28	,	,	PUNCT
fuelectenerg-3309	271	29	m	m	VERB
fuelectenerg-3309	271	30	tq	tq	ADP
fuelectenerg-3309	271	31	,	,	PUNCT
fuelectenerg-3309	271	32	ρ	ρ	PROPN
fuelectenerg-3309	271	33	,	,	PUNCT
fuelectenerg-3309	271	34	s	s	PART
fuelectenerg-3309	271	35	(	(	PUNCT
fuelectenerg-3309	271	36	en	en	X
fuelectenerg-3309	271	37	)	)	PUNCT
fuelectenerg-3309	271	38	i	i	PRON
fuelectenerg-3309	271	39	=	=	SYM
fuelectenerg-3309	271	40	mod	mod	PROPN
fuelectenerg-3309	271	41	(	(	PUNCT
fuelectenerg-3309	271	42	en	en	X
fuelectenerg-3309	271	43	,	,	PUNCT
fuelectenerg-3309	271	44	ρi	ρi	NOUN
fuelectenerg-3309	271	45	−	−	PROPN
fuelectenerg-3309	272	1	(	(	PUNCT
fuelectenerg-3309	272	2	1−	1−	NUM
fuelectenerg-3309	272	3	δi	δi	NOUN
fuelectenerg-3309	272	4	,	,	PUNCT
fuelectenerg-3309	272	5	si	si	NOUN
fuelectenerg-3309	272	6	)	)	PUNCT
fuelectenerg-3309	272	7	en	en	X
fuelectenerg-3309	272	8	,	,	PUNCT
fuelectenerg-3309	272	9	ρsi	ρsi	ADJ
fuelectenerg-3309	272	10	,	,	PUNCT
fuelectenerg-3309	272	11	q	q	PROPN
fuelectenerg-3309	272	12	)	)	PUNCT
fuelectenerg-3309	272	13	is	be	AUX
fuelectenerg-3309	272	14	a	a	DET
fuelectenerg-3309	272	15	bijection	bijection	NOUN
fuelectenerg-3309	272	16	.	.	PUNCT
fuelectenerg-3309	273	1	proof	proof	NOUN
fuelectenerg-3309	273	2	:	:	PUNCT
fuelectenerg-3309	273	3	for	for	ADP
fuelectenerg-3309	273	4	any	any	DET
fuelectenerg-3309	273	5	natural	natural	ADJ
fuelectenerg-3309	273	6	numbers	number	NOUN
fuelectenerg-3309	273	7	m	m	ADP
fuelectenerg-3309	273	8	,	,	PUNCT
fuelectenerg-3309	273	9	q	q	X
fuelectenerg-3309	273	10	≥	≥	NUM
fuelectenerg-3309	273	11	2	2	NUM
fuelectenerg-3309	273	12	we	we	PRON
fuelectenerg-3309	273	13	fix	fix	VERB
fuelectenerg-3309	273	14	a	a	DET
fuelectenerg-3309	273	15	pair	pair	NOUN
fuelectenerg-3309	273	16	(	(	PUNCT
fuelectenerg-3309	273	17	ρ	ρ	PROPN
fuelectenerg-3309	273	18	,	,	PUNCT
fuelectenerg-3309	273	19	s	s	PART
fuelectenerg-3309	273	20	)	)	PUNCT
fuelectenerg-3309	273	21	∈	∈	PROPN
fuelectenerg-3309	273	22	p	p	NOUN
fuelectenerg-3309	273	23	(	(	PUNCT
fuelectenerg-3309	273	24	m)×s(m	m)×s(m	NOUN
fuelectenerg-3309	273	25	)	)	PUNCT
fuelectenerg-3309	273	26	and	and	CCONJ
fuelectenerg-3309	273	27	we	we	PRON
fuelectenerg-3309	273	28	consider	consider	VERB
fuelectenerg-3309	273	29	the	the	DET
fuelectenerg-3309	273	30	above	above	ADJ
fuelectenerg-3309	273	31	operator	operator	NOUN
fuelectenerg-3309	273	32	tq	tq	ADP
fuelectenerg-3309	273	33	,	,	PUNCT
fuelectenerg-3309	273	34	ρ	ρ	PROPN
fuelectenerg-3309	273	35	,	,	PUNCT
fuelectenerg-3309	273	36	s.	s.	PROPN
fuelectenerg-3309	273	37	from	from	ADP
fuelectenerg-3309	273	38	now	now	ADV
fuelectenerg-3309	273	39	on	on	ADV
fuelectenerg-3309	273	40	we	we	PRON
fuelectenerg-3309	273	41	write	write	VERB
fuelectenerg-3309	273	42	t	t	PROPN
fuelectenerg-3309	273	43	=	=	SYM
fuelectenerg-3309	273	44	tq	tq	PROPN
fuelectenerg-3309	273	45	,	,	PUNCT
fuelectenerg-3309	273	46	ρ	ρ	PROPN
fuelectenerg-3309	273	47	,	,	PUNCT
fuelectenerg-3309	273	48	s	s	NOUN
fuelectenerg-3309	273	49	for	for	ADP
fuelectenerg-3309	273	50	simplicity	simplicity	NOUN
fuelectenerg-3309	273	51	.	.	PUNCT
fuelectenerg-3309	274	1	let	let	VERB
fuelectenerg-3309	274	2	t	t	PROPN
fuelectenerg-3309	274	3	(	(	PUNCT
fuelectenerg-3309	274	4	ek	ek	NOUN
fuelectenerg-3309	274	5	)	)	PUNCT
fuelectenerg-3309	274	6	and	and	CCONJ
fuelectenerg-3309	274	7	t	t	PROPN
fuelectenerg-3309	274	8	(	(	PUNCT
fuelectenerg-3309	274	9	en	en	X
fuelectenerg-3309	274	10	)	)	PUNCT
fuelectenerg-3309	274	11	be	be	VERB
fuelectenerg-3309	274	12	two	two	NUM
fuelectenerg-3309	274	13	sequences	sequence	NOUN
fuelectenerg-3309	274	14	for	for	ADP
fuelectenerg-3309	274	15	some	some	DET
fuelectenerg-3309	274	16	pair	pair	NOUN
fuelectenerg-3309	274	17	(	(	PUNCT
fuelectenerg-3309	274	18	k	k	NOUN
fuelectenerg-3309	274	19	,	,	PUNCT
fuelectenerg-3309	274	20	n	n	CCONJ
fuelectenerg-3309	274	21	)	)	PUNCT
fuelectenerg-3309	274	22	∈	∈	PROPN
fuelectenerg-3309	274	23	{	{	PUNCT
fuelectenerg-3309	274	24	0	0	NUM
fuelectenerg-3309	274	25	,	,	PUNCT
fuelectenerg-3309	274	26	...	...	PUNCT
fuelectenerg-3309	274	27	,	,	PUNCT
fuelectenerg-3309	274	28	qm−1}2	qm−1}2	PROPN
fuelectenerg-3309	274	29	.	.	PUNCT
fuelectenerg-3309	275	1	notice	notice	VERB
fuelectenerg-3309	275	2	that	that	SCONJ
fuelectenerg-3309	275	3	the	the	DET
fuelectenerg-3309	275	4	elements	element	NOUN
fuelectenerg-3309	275	5	of	of	ADP
fuelectenerg-3309	275	6	ek	ek	NOUN
fuelectenerg-3309	275	7	and	and	CCONJ
fuelectenerg-3309	275	8	en	en	ADP
fuelectenerg-3309	275	9	belong	belong	VERB
fuelectenerg-3309	275	10	in	in	ADP
fuelectenerg-3309	275	11	{	{	PUNCT
fuelectenerg-3309	275	12	0	0	NUM
fuelectenerg-3309	275	13	,	,	PUNCT
fuelectenerg-3309	275	14	...	...	PUNCT
fuelectenerg-3309	275	15	,	,	PUNCT
fuelectenerg-3309	275	16	q−1	q−1	PROPN
fuelectenerg-3309	275	17	}	}	PUNCT
fuelectenerg-3309	275	18	by	by	ADP
fuelectenerg-3309	275	19	definition	definition	NOUN
fuelectenerg-3309	275	20	.	.	PUNCT
fuelectenerg-3309	276	1	assume	assume	VERB
fuelectenerg-3309	276	2	that	that	SCONJ
fuelectenerg-3309	276	3	t	t	PROPN
fuelectenerg-3309	276	4	(	(	PUNCT
fuelectenerg-3309	276	5	ek	ek	NOUN
fuelectenerg-3309	276	6	)	)	PUNCT
fuelectenerg-3309	276	7	=	=	SYM
fuelectenerg-3309	276	8	t	t	PROPN
fuelectenerg-3309	276	9	(	(	PUNCT
fuelectenerg-3309	276	10	en	en	X
fuelectenerg-3309	276	11	)	)	PUNCT
fuelectenerg-3309	276	12	⇒	⇒	PROPN
fuelectenerg-3309	276	13	t	t	PROPN
fuelectenerg-3309	276	14	(	(	PUNCT
fuelectenerg-3309	276	15	ek)i	ek)i	PROPN
fuelectenerg-3309	276	16	=	=	SYM
fuelectenerg-3309	276	17	t	t	PROPN
fuelectenerg-3309	276	18	(	(	PUNCT
fuelectenerg-3309	276	19	en)i	en)i	PROPN
fuelectenerg-3309	276	20	,	,	PUNCT
fuelectenerg-3309	276	21	∀i	∀i	NOUN
fuelectenerg-3309	276	22	=	=	SYM
fuelectenerg-3309	276	23	1	1	NUM
fuelectenerg-3309	276	24	,	,	PUNCT
fuelectenerg-3309	276	25	...	...	PUNCT
fuelectenerg-3309	276	26	,	,	PUNCT
fuelectenerg-3309	276	27	m.	m.	NOUN
fuelectenerg-3309	276	28	(	(	PUNCT
fuelectenerg-3309	276	29	7	7	NUM
fuelectenerg-3309	276	30	)	)	PUNCT
fuelectenerg-3309	276	31	if	if	SCONJ
fuelectenerg-3309	276	32	i	i	PRON
fuelectenerg-3309	276	33	=	=	NOUN
fuelectenerg-3309	276	34	1	1	NUM
fuelectenerg-3309	276	35	in	in	ADP
fuelectenerg-3309	276	36	(	(	PUNCT
fuelectenerg-3309	276	37	7	7	NUM
fuelectenerg-3309	276	38	)	)	PUNCT
fuelectenerg-3309	276	39	,	,	PUNCT
fuelectenerg-3309	276	40	then	then	ADV
fuelectenerg-3309	276	41	by	by	ADP
fuelectenerg-3309	276	42	recalling	recall	VERB
fuelectenerg-3309	276	43	the	the	DET
fuelectenerg-3309	276	44	definition	definition	NOUN
fuelectenerg-3309	276	45	of	of	ADP
fuelectenerg-3309	276	46	s(m	s(m	PROPN
fuelectenerg-3309	276	47	)	)	PUNCT
fuelectenerg-3309	276	48	in	in	ADP
fuelectenerg-3309	276	49	(	(	PUNCT
fuelectenerg-3309	276	50	1	1	X
fuelectenerg-3309	276	51	)	)	PUNCT
fuelectenerg-3309	276	52	we	we	PRON
fuelectenerg-3309	276	53	have	have	AUX
fuelectenerg-3309	276	54	s1	s1	NOUN
fuelectenerg-3309	276	55	=	=	SYM
fuelectenerg-3309	276	56	1	1	NUM
fuelectenerg-3309	276	57	,	,	PUNCT
fuelectenerg-3309	276	58	so	so	SCONJ
fuelectenerg-3309	276	59	t	t	PROPN
fuelectenerg-3309	276	60	(	(	PUNCT
fuelectenerg-3309	276	61	ek)1	ek)1	PROPN
fuelectenerg-3309	276	62	=	=	SYM
fuelectenerg-3309	276	63	t	t	PROPN
fuelectenerg-3309	276	64	(	(	PUNCT
fuelectenerg-3309	276	65	en)1	en)1	PROPN
fuelectenerg-3309	276	66	⇒	⇒	NOUN
fuelectenerg-3309	276	67	mod	mod	NOUN
fuelectenerg-3309	276	68	(	(	PUNCT
fuelectenerg-3309	276	69	ek	ek	X
fuelectenerg-3309	276	70	,	,	PUNCT
fuelectenerg-3309	276	71	ρ1	ρ1	NOUN
fuelectenerg-3309	276	72	,	,	PUNCT
fuelectenerg-3309	276	73	q	q	NOUN
fuelectenerg-3309	276	74	)	)	PUNCT
fuelectenerg-3309	276	75	=	=	SYM
fuelectenerg-3309	276	76	mod	mod	NOUN
fuelectenerg-3309	276	77	(	(	PUNCT
fuelectenerg-3309	276	78	en	en	X
fuelectenerg-3309	276	79	,	,	PUNCT
fuelectenerg-3309	276	80	ρ1	ρ1	NOUN
fuelectenerg-3309	276	81	,	,	PUNCT
fuelectenerg-3309	276	82	q	q	PROPN
fuelectenerg-3309	276	83	)	)	PUNCT
fuelectenerg-3309	276	84	.	.	PUNCT
fuelectenerg-3309	277	1	248	248	NUM
fuelectenerg-3309	277	2	c.	c.	PROPN
fuelectenerg-3309	277	3	karanikas	karanikas	PROPN
fuelectenerg-3309	277	4	,	,	PUNCT
fuelectenerg-3309	277	5	n.	n.	PROPN
fuelectenerg-3309	277	6	atreas	atreas	PROPN
fuelectenerg-3309	277	7	enumeration	enumeration	PROPN
fuelectenerg-3309	277	8	and	and	CCONJ
fuelectenerg-3309	277	9	coding	code	VERB
fuelectenerg-3309	277	10	permutations	permutation	NOUN
fuelectenerg-3309	277	11	and	and	CCONJ
fuelectenerg-3309	277	12	reversible	reversible	ADJ
fuelectenerg-3309	277	13	logical	logical	ADJ
fuelectenerg-3309	277	14	circuits	circuit	NOUN
fuelectenerg-3309	277	15	249	249	NUM
fuelectenerg-3309	277	16	10	10	NUM
fuelectenerg-3309	277	17	n.	n.	PROPN
fuelectenerg-3309	277	18	atreas	atreas	PROPN
fuelectenerg-3309	277	19	and	and	CCONJ
fuelectenerg-3309	277	20	c.	c.	PROPN
fuelectenerg-3309	277	21	karanikas	karanikas	PROPN
fuelectenerg-3309	277	22	hence	hence	ADV
fuelectenerg-3309	277	23	ek	ek	PROPN
fuelectenerg-3309	277	24	,	,	PUNCT
fuelectenerg-3309	277	25	ρ1	ρ1	NOUN
fuelectenerg-3309	277	26	=	=	SYM
fuelectenerg-3309	277	27	en	en	X
fuelectenerg-3309	277	28	,	,	PUNCT
fuelectenerg-3309	277	29	ρ1	ρ1	NOUN
fuelectenerg-3309	277	30	.	.	PUNCT
fuelectenerg-3309	278	1	if	if	SCONJ
fuelectenerg-3309	278	2	i	i	PRON
fuelectenerg-3309	278	3	=	=	NOUN
fuelectenerg-3309	278	4	2	2	NUM
fuelectenerg-3309	278	5	,	,	PUNCT
fuelectenerg-3309	278	6	then	then	ADV
fuelectenerg-3309	278	7	s2	s2	VERB
fuelectenerg-3309	278	8	∈	∈	PROPN
fuelectenerg-3309	278	9	{	{	PUNCT
fuelectenerg-3309	278	10	0	0	NUM
fuelectenerg-3309	278	11	,	,	PUNCT
fuelectenerg-3309	278	12	1	1	NUM
fuelectenerg-3309	278	13	}	}	PUNCT
fuelectenerg-3309	278	14	.	.	PUNCT
fuelectenerg-3309	279	1	for	for	ADP
fuelectenerg-3309	279	2	s2	s2	NOUN
fuelectenerg-3309	279	3	=	=	PUNCT
fuelectenerg-3309	279	4	2	2	NUM
fuelectenerg-3309	279	5	we	we	PRON
fuelectenerg-3309	279	6	immediately	immediately	ADV
fuelectenerg-3309	279	7	obtain	obtain	VERB
fuelectenerg-3309	279	8	ek	ek	NOUN
fuelectenerg-3309	279	9	,	,	PUNCT
fuelectenerg-3309	279	10	ρ2	ρ2	NOUN
fuelectenerg-3309	279	11	=	=	SYM
fuelectenerg-3309	279	12	en	en	X
fuelectenerg-3309	279	13	,	,	PUNCT
fuelectenerg-3309	279	14	ρ2	ρ2	NOUN
fuelectenerg-3309	279	15	.	.	PUNCT
fuelectenerg-3309	280	1	for	for	ADP
fuelectenerg-3309	280	2	s2	s2	NOUN
fuelectenerg-3309	280	3	=	=	SYM
fuelectenerg-3309	280	4	1	1	NUM
fuelectenerg-3309	280	5	we	we	PRON
fuelectenerg-3309	280	6	have	have	VERB
fuelectenerg-3309	280	7	t	t	PROPN
fuelectenerg-3309	280	8	(	(	PUNCT
fuelectenerg-3309	280	9	ek)2	ek)2	PROPN
fuelectenerg-3309	280	10	=	=	SYM
fuelectenerg-3309	280	11	t	t	PROPN
fuelectenerg-3309	280	12	(	(	PUNCT
fuelectenerg-3309	280	13	en)2	en)2	VERB
fuelectenerg-3309	280	14	⇒	⇒	PROPN
fuelectenerg-3309	280	15	mod	mod	PROPN
fuelectenerg-3309	281	1	(	(	PUNCT
fuelectenerg-3309	281	2	ek	ek	X
fuelectenerg-3309	281	3	,	,	PUNCT
fuelectenerg-3309	281	4	ρ2	ρ2	NOUN
fuelectenerg-3309	281	5	−	−	PROPN
fuelectenerg-3309	281	6	ek	ek	PROPN
fuelectenerg-3309	281	7	,	,	PUNCT
fuelectenerg-3309	281	8	ρs2	ρs2	INTJ
fuelectenerg-3309	281	9	,	,	PUNCT
fuelectenerg-3309	281	10	q	q	NOUN
fuelectenerg-3309	281	11	)	)	PUNCT
fuelectenerg-3309	281	12	=	=	SYM
fuelectenerg-3309	281	13	mod	mod	X
fuelectenerg-3309	281	14	(	(	PUNCT
fuelectenerg-3309	281	15	en	en	X
fuelectenerg-3309	281	16	,	,	PUNCT
fuelectenerg-3309	281	17	ρ2	ρ2	NOUN
fuelectenerg-3309	281	18	−	−	PROPN
fuelectenerg-3309	281	19	en	en	X
fuelectenerg-3309	281	20	,	,	PUNCT
fuelectenerg-3309	281	21	ρs2	ρs2	INTJ
fuelectenerg-3309	281	22	,	,	PUNCT
fuelectenerg-3309	281	23	q	q	NOUN
fuelectenerg-3309	281	24	)	)	PUNCT
fuelectenerg-3309	281	25	⇒	⇒	NOUN
fuelectenerg-3309	281	26	mod	mod	PROPN
fuelectenerg-3309	281	27	(	(	PUNCT
fuelectenerg-3309	281	28	ek	ek	X
fuelectenerg-3309	281	29	,	,	PUNCT
fuelectenerg-3309	281	30	ρ2	ρ2	NOUN
fuelectenerg-3309	281	31	−	−	PROPN
fuelectenerg-3309	281	32	en	en	X
fuelectenerg-3309	281	33	,	,	PUNCT
fuelectenerg-3309	281	34	ρ1	ρ1	NOUN
fuelectenerg-3309	281	35	,	,	PUNCT
fuelectenerg-3309	281	36	q	q	NOUN
fuelectenerg-3309	281	37	)	)	PUNCT
fuelectenerg-3309	281	38	=	=	SYM
fuelectenerg-3309	281	39	mod	mod	X
fuelectenerg-3309	281	40	(	(	PUNCT
fuelectenerg-3309	281	41	en	en	X
fuelectenerg-3309	281	42	,	,	PUNCT
fuelectenerg-3309	281	43	ρ2	ρ2	NOUN
fuelectenerg-3309	281	44	−	−	PROPN
fuelectenerg-3309	281	45	en	en	X
fuelectenerg-3309	281	46	,	,	PUNCT
fuelectenerg-3309	281	47	ρ1	ρ1	NOUN
fuelectenerg-3309	281	48	,	,	PUNCT
fuelectenerg-3309	281	49	q	q	PROPN
fuelectenerg-3309	281	50	)	)	PUNCT
fuelectenerg-3309	281	51	,	,	PUNCT
fuelectenerg-3309	281	52	where	where	SCONJ
fuelectenerg-3309	281	53	the	the	DET
fuelectenerg-3309	281	54	last	last	ADJ
fuelectenerg-3309	281	55	equality	equality	NOUN
fuelectenerg-3309	281	56	was	be	AUX
fuelectenerg-3309	281	57	derived	derive	VERB
fuelectenerg-3309	281	58	from	from	ADP
fuelectenerg-3309	281	59	the	the	DET
fuelectenerg-3309	281	60	fact	fact	NOUN
fuelectenerg-3309	281	61	that	that	SCONJ
fuelectenerg-3309	281	62	ek	ek	PROPN
fuelectenerg-3309	281	63	,	,	PUNCT
fuelectenerg-3309	281	64	ρ1	ρ1	NOUN
fuelectenerg-3309	281	65	=	=	SYM
fuelectenerg-3309	281	66	en	en	X
fuelectenerg-3309	281	67	,	,	PUNCT
fuelectenerg-3309	281	68	ρ1	ρ1	NOUN
fuelectenerg-3309	281	69	as	as	SCONJ
fuelectenerg-3309	281	70	we	we	PRON
fuelectenerg-3309	281	71	showed	show	VERB
fuelectenerg-3309	281	72	above	above	ADV
fuelectenerg-3309	281	73	.	.	PUNCT
fuelectenerg-3309	282	1	hence	hence	ADV
fuelectenerg-3309	282	2	,	,	PUNCT
fuelectenerg-3309	282	3	either	either	CCONJ
fuelectenerg-3309	282	4	ek	ek	PROPN
fuelectenerg-3309	282	5	,	,	PUNCT
fuelectenerg-3309	282	6	ρ2	ρ2	NOUN
fuelectenerg-3309	282	7	−	−	PROPN
fuelectenerg-3309	282	8	en	en	X
fuelectenerg-3309	282	9	,	,	PUNCT
fuelectenerg-3309	282	10	ρ1	ρ1	NOUN
fuelectenerg-3309	282	11	=	=	SYM
fuelectenerg-3309	282	12	en	en	X
fuelectenerg-3309	282	13	,	,	PUNCT
fuelectenerg-3309	282	14	ρ2	ρ2	NOUN
fuelectenerg-3309	282	15	−	−	PROPN
fuelectenerg-3309	282	16	en	en	X
fuelectenerg-3309	282	17	,	,	PUNCT
fuelectenerg-3309	282	18	ρ1	ρ1	NOUN
fuelectenerg-3309	282	19	⇒	⇒	PROPN
fuelectenerg-3309	282	20	ek	ek	PROPN
fuelectenerg-3309	282	21	,	,	PUNCT
fuelectenerg-3309	282	22	ρ2	ρ2	PROPN
fuelectenerg-3309	282	23	=	=	SYM
fuelectenerg-3309	282	24	en	en	X
fuelectenerg-3309	282	25	,	,	PUNCT
fuelectenerg-3309	282	26	ρ2	ρ2	NOUN
fuelectenerg-3309	282	27	or	or	CCONJ
fuelectenerg-3309	282	28	q	q	NOUN
fuelectenerg-3309	282	29	−	−	PROPN
fuelectenerg-3309	282	30	(	(	PUNCT
fuelectenerg-3309	282	31	ek	ek	X
fuelectenerg-3309	282	32	,	,	PUNCT
fuelectenerg-3309	282	33	ρ2	ρ2	NOUN
fuelectenerg-3309	282	34	−	−	PROPN
fuelectenerg-3309	282	35	en	en	X
fuelectenerg-3309	282	36	,	,	PUNCT
fuelectenerg-3309	282	37	ρ1	ρ1	NOUN
fuelectenerg-3309	282	38	)	)	PUNCT
fuelectenerg-3309	282	39	=	=	PUNCT
fuelectenerg-3309	283	1	q	q	NOUN
fuelectenerg-3309	284	1	−	−	PROPN
fuelectenerg-3309	284	2	(	(	PUNCT
fuelectenerg-3309	284	3	en	en	X
fuelectenerg-3309	284	4	,	,	PUNCT
fuelectenerg-3309	284	5	ρ2	ρ2	NOUN
fuelectenerg-3309	284	6	−	−	PROPN
fuelectenerg-3309	284	7	en	en	X
fuelectenerg-3309	284	8	,	,	PUNCT
fuelectenerg-3309	284	9	ρ1	ρ1	NOUN
fuelectenerg-3309	284	10	)	)	PUNCT
fuelectenerg-3309	284	11	⇒	⇒	PROPN
fuelectenerg-3309	284	12	ek	ek	PROPN
fuelectenerg-3309	284	13	,	,	PUNCT
fuelectenerg-3309	284	14	ρ2	ρ2	PROPN
fuelectenerg-3309	284	15	=	=	SYM
fuelectenerg-3309	284	16	en	en	X
fuelectenerg-3309	284	17	,	,	PUNCT
fuelectenerg-3309	284	18	ρ2	ρ2	NOUN
fuelectenerg-3309	284	19	.	.	PUNCT
fuelectenerg-3309	285	1	therefore	therefore	ADV
fuelectenerg-3309	285	2	,	,	PUNCT
fuelectenerg-3309	285	3	in	in	ADP
fuelectenerg-3309	285	4	any	any	DET
fuelectenerg-3309	285	5	case	case	NOUN
fuelectenerg-3309	285	6	we	we	PRON
fuelectenerg-3309	285	7	obtain	obtain	VERB
fuelectenerg-3309	285	8	ek	ek	NOUN
fuelectenerg-3309	285	9	,	,	PUNCT
fuelectenerg-3309	285	10	ρ2	ρ2	NOUN
fuelectenerg-3309	285	11	=	=	SYM
fuelectenerg-3309	285	12	en	en	X
fuelectenerg-3309	285	13	,	,	PUNCT
fuelectenerg-3309	285	14	ρ2	ρ2	NOUN
fuelectenerg-3309	285	15	.	.	PUNCT
fuelectenerg-3309	286	1	we	we	PRON
fuelectenerg-3309	286	2	proceed	proceed	VERB
fuelectenerg-3309	286	3	in	in	ADP
fuelectenerg-3309	286	4	the	the	DET
fuelectenerg-3309	286	5	same	same	ADJ
fuelectenerg-3309	286	6	manner	manner	NOUN
fuelectenerg-3309	286	7	for	for	ADP
fuelectenerg-3309	286	8	the	the	DET
fuelectenerg-3309	286	9	remaining	remain	VERB
fuelectenerg-3309	286	10	values	value	NOUN
fuelectenerg-3309	286	11	i	i	X
fuelectenerg-3309	286	12	=	=	NOUN
fuelectenerg-3309	286	13	3	3	NUM
fuelectenerg-3309	286	14	,	,	PUNCT
fuelectenerg-3309	286	15	...	...	PUNCT
fuelectenerg-3309	286	16	,	,	PUNCT
fuelectenerg-3309	286	17	m	m	AUX
fuelectenerg-3309	286	18	obtaining	obtain	VERB
fuelectenerg-3309	286	19	ek	ek	NOUN
fuelectenerg-3309	286	20	,	,	PUNCT
fuelectenerg-3309	286	21	ρi	ρi	NOUN
fuelectenerg-3309	286	22	=	=	SYM
fuelectenerg-3309	286	23	en	en	X
fuelectenerg-3309	286	24	,	,	PUNCT
fuelectenerg-3309	286	25	ρi	ρi	NOUN
fuelectenerg-3309	286	26	,	,	PUNCT
fuelectenerg-3309	286	27	∀i	∀i	NOUN
fuelectenerg-3309	286	28	=	=	SYM
fuelectenerg-3309	286	29	1	1	NUM
fuelectenerg-3309	286	30	,	,	PUNCT
fuelectenerg-3309	286	31	...	...	PUNCT
fuelectenerg-3309	286	32	,	,	PUNCT
fuelectenerg-3309	286	33	m.	m.	NOUN
fuelectenerg-3309	286	34	since	since	SCONJ
fuelectenerg-3309	286	35	ρ	ρ	PROPN
fuelectenerg-3309	286	36	is	be	AUX
fuelectenerg-3309	286	37	a	a	DET
fuelectenerg-3309	286	38	permutation	permutation	NOUN
fuelectenerg-3309	286	39	,	,	PUNCT
fuelectenerg-3309	286	40	necessarily	necessarily	ADV
fuelectenerg-3309	286	41	ek	ek	VERB
fuelectenerg-3309	286	42	,	,	PUNCT
fuelectenerg-3309	286	43	i	i	PROPN
fuelectenerg-3309	286	44	=	=	SYM
fuelectenerg-3309	286	45	en	en	X
fuelectenerg-3309	286	46	,	,	PUNCT
fuelectenerg-3309	286	47	i	i	PRON
fuelectenerg-3309	286	48	,	,	PUNCT
fuelectenerg-3309	286	49	∀i	∀i	X
fuelectenerg-3309	286	50	=	=	SYM
fuelectenerg-3309	286	51	1	1	NUM
fuelectenerg-3309	286	52	,	,	PUNCT
fuelectenerg-3309	286	53	...	...	PUNCT
fuelectenerg-3309	286	54	,	,	PUNCT
fuelectenerg-3309	286	55	m	m	VERB
fuelectenerg-3309	286	56	and	and	CCONJ
fuelectenerg-3309	286	57	the	the	DET
fuelectenerg-3309	286	58	proof	proof	NOUN
fuelectenerg-3309	286	59	is	be	AUX
fuelectenerg-3309	286	60	complete	complete	ADJ
fuelectenerg-3309	286	61	.	.	PUNCT
fuelectenerg-3309	287	1	it	it	PRON
fuelectenerg-3309	287	2	is	be	AUX
fuelectenerg-3309	287	3	clear	clear	ADJ
fuelectenerg-3309	287	4	that	that	SCONJ
fuelectenerg-3309	287	5	the	the	DET
fuelectenerg-3309	287	6	above	above	ADJ
fuelectenerg-3309	287	7	operator	operator	NOUN
fuelectenerg-3309	287	8	tq	tq	ADP
fuelectenerg-3309	287	9	,	,	PUNCT
fuelectenerg-3309	287	10	ρ	ρ	PROPN
fuelectenerg-3309	287	11	,	,	PUNCT
fuelectenerg-3309	287	12	s	s	X
fuelectenerg-3309	287	13	provides	provide	VERB
fuelectenerg-3309	287	14	a	a	DET
fuelectenerg-3309	287	15	code	code	NOUN
fuelectenerg-3309	287	16	for	for	ADP
fuelectenerg-3309	287	17	shuffling	shuffle	VERB
fuelectenerg-3309	287	18	the	the	DET
fuelectenerg-3309	287	19	elements	element	NOUN
fuelectenerg-3309	287	20	of	of	ADP
fuelectenerg-3309	287	21	the	the	DET
fuelectenerg-3309	287	22	set	set	NOUN
fuelectenerg-3309	287	23	{	{	PUNCT
fuelectenerg-3309	287	24	0	0	NUM
fuelectenerg-3309	287	25	,	,	PUNCT
fuelectenerg-3309	287	26	...	...	PUNCT
fuelectenerg-3309	287	27	,	,	PUNCT
fuelectenerg-3309	287	28	qm	qm	PROPN
fuelectenerg-3309	287	29	−	−	PROPN
fuelectenerg-3309	287	30	1	1	NUM
fuelectenerg-3309	287	31	}	}	PUNCT
fuelectenerg-3309	287	32	.	.	PUNCT
fuelectenerg-3309	288	1	example	example	NOUN
fuelectenerg-3309	288	2	6	6	NUM
fuelectenerg-3309	288	3	let	let	VERB
fuelectenerg-3309	288	4	q	q	NOUN
fuelectenerg-3309	289	1	=	=	SYM
fuelectenerg-3309	289	2	3	3	NUM
fuelectenerg-3309	289	3	,	,	PUNCT
fuelectenerg-3309	289	4	ρ	ρ	NOUN
fuelectenerg-3309	289	5	=	=	SYM
fuelectenerg-3309	289	6	(	(	PUNCT
fuelectenerg-3309	289	7	2	2	NUM
fuelectenerg-3309	289	8	,	,	PUNCT
fuelectenerg-3309	289	9	1	1	NUM
fuelectenerg-3309	289	10	)	)	PUNCT
fuelectenerg-3309	289	11	,	,	PUNCT
fuelectenerg-3309	290	1	s	s	X
fuelectenerg-3309	290	2	=	=	PUNCT
fuelectenerg-3309	290	3	(	(	PUNCT
fuelectenerg-3309	290	4	1	1	NUM
fuelectenerg-3309	290	5	,	,	PUNCT
fuelectenerg-3309	290	6	2	2	NUM
fuelectenerg-3309	290	7	)	)	PUNCT
fuelectenerg-3309	290	8	and	and	CCONJ
fuelectenerg-3309	290	9	e	e	X
fuelectenerg-3309	290	10	(	(	PUNCT
fuelectenerg-3309	290	11	3	3	X
fuelectenerg-3309	290	12	)	)	SYM
fuelectenerg-3309	290	13	2	2	NUM
fuelectenerg-3309	290	14	=	=	SYM
fuelectenerg-3309	290	15	{	{	PUNCT
fuelectenerg-3309	290	16	(	(	PUNCT
fuelectenerg-3309	290	17	0	0	NUM
fuelectenerg-3309	290	18	,	,	PUNCT
fuelectenerg-3309	290	19	0	0	NUM
fuelectenerg-3309	290	20	)	)	PUNCT
fuelectenerg-3309	290	21	,	,	PUNCT
fuelectenerg-3309	290	22	(	(	PUNCT
fuelectenerg-3309	290	23	0	0	NUM
fuelectenerg-3309	290	24	,	,	PUNCT
fuelectenerg-3309	290	25	1	1	NUM
fuelectenerg-3309	290	26	)	)	PUNCT
fuelectenerg-3309	290	27	,	,	PUNCT
fuelectenerg-3309	290	28	(	(	PUNCT
fuelectenerg-3309	290	29	0	0	NUM
fuelectenerg-3309	290	30	,	,	PUNCT
fuelectenerg-3309	290	31	2	2	NUM
fuelectenerg-3309	290	32	)	)	PUNCT
fuelectenerg-3309	290	33	,	,	PUNCT
fuelectenerg-3309	290	34	(	(	PUNCT
fuelectenerg-3309	290	35	1	1	NUM
fuelectenerg-3309	290	36	,	,	PUNCT
fuelectenerg-3309	290	37	0	0	NUM
fuelectenerg-3309	290	38	)	)	PUNCT
fuelectenerg-3309	290	39	,	,	PUNCT
fuelectenerg-3309	290	40	(	(	PUNCT
fuelectenerg-3309	290	41	1	1	NUM
fuelectenerg-3309	290	42	,	,	PUNCT
fuelectenerg-3309	290	43	1	1	NUM
fuelectenerg-3309	290	44	)	)	PUNCT
fuelectenerg-3309	290	45	,	,	PUNCT
fuelectenerg-3309	290	46	(	(	PUNCT
fuelectenerg-3309	290	47	1	1	NUM
fuelectenerg-3309	290	48	,	,	PUNCT
fuelectenerg-3309	290	49	2	2	NUM
fuelectenerg-3309	290	50	)	)	PUNCT
fuelectenerg-3309	290	51	,	,	PUNCT
fuelectenerg-3309	290	52	(	(	PUNCT
fuelectenerg-3309	290	53	2	2	NUM
fuelectenerg-3309	290	54	,	,	PUNCT
fuelectenerg-3309	290	55	0	0	NUM
fuelectenerg-3309	290	56	)	)	PUNCT
fuelectenerg-3309	290	57	,	,	PUNCT
fuelectenerg-3309	290	58	(	(	PUNCT
fuelectenerg-3309	290	59	2	2	NUM
fuelectenerg-3309	290	60	,	,	PUNCT
fuelectenerg-3309	290	61	1	1	NUM
fuelectenerg-3309	290	62	)	)	PUNCT
fuelectenerg-3309	290	63	,	,	PUNCT
fuelectenerg-3309	290	64	(	(	PUNCT
fuelectenerg-3309	290	65	2	2	NUM
fuelectenerg-3309	290	66	,	,	PUNCT
fuelectenerg-3309	290	67	2	2	NUM
fuelectenerg-3309	290	68	)	)	PUNCT
fuelectenerg-3309	290	69	}	}	PUNCT
fuelectenerg-3309	290	70	.	.	PUNCT
fuelectenerg-3309	291	1	then	then	ADV
fuelectenerg-3309	291	2	by	by	ADP
fuelectenerg-3309	291	3	the	the	DET
fuelectenerg-3309	291	4	above	above	ADJ
fuelectenerg-3309	291	5	definition	definition	NOUN
fuelectenerg-3309	291	6	of	of	ADP
fuelectenerg-3309	291	7	tq	tq	PRON
fuelectenerg-3309	291	8	,	,	PUNCT
fuelectenerg-3309	291	9	ρ	ρ	PROPN
fuelectenerg-3309	291	10	,	,	PUNCT
fuelectenerg-3309	291	11	s	s	PART
fuelectenerg-3309	291	12	we	we	PRON
fuelectenerg-3309	291	13	obtain	obtain	VERB
fuelectenerg-3309	291	14	(	(	PUNCT
fuelectenerg-3309	291	15	0	0	NUM
fuelectenerg-3309	291	16	,	,	PUNCT
fuelectenerg-3309	291	17	0	0	NUM
fuelectenerg-3309	291	18	)	)	PUNCT
fuelectenerg-3309	291	19	→	→	SYM
fuelectenerg-3309	291	20	(	(	PUNCT
fuelectenerg-3309	291	21	0	0	NUM
fuelectenerg-3309	291	22	,	,	PUNCT
fuelectenerg-3309	291	23	0	0	NUM
fuelectenerg-3309	291	24	)	)	PUNCT
fuelectenerg-3309	291	25	,	,	PUNCT
fuelectenerg-3309	291	26	(	(	PUNCT
fuelectenerg-3309	291	27	0	0	NUM
fuelectenerg-3309	291	28	,	,	PUNCT
fuelectenerg-3309	291	29	1	1	NUM
fuelectenerg-3309	291	30	)	)	PUNCT
fuelectenerg-3309	291	31	→	→	X
fuelectenerg-3309	291	32	(	(	PUNCT
fuelectenerg-3309	291	33	1	1	NUM
fuelectenerg-3309	291	34	,	,	PUNCT
fuelectenerg-3309	291	35	0	0	NUM
fuelectenerg-3309	291	36	)	)	PUNCT
fuelectenerg-3309	291	37	,	,	PUNCT
fuelectenerg-3309	291	38	(	(	PUNCT
fuelectenerg-3309	291	39	0	0	NUM
fuelectenerg-3309	291	40	,	,	PUNCT
fuelectenerg-3309	291	41	2	2	NUM
fuelectenerg-3309	291	42	)	)	PUNCT
fuelectenerg-3309	291	43	→	→	X
fuelectenerg-3309	291	44	(	(	PUNCT
fuelectenerg-3309	291	45	2	2	NUM
fuelectenerg-3309	291	46	,	,	PUNCT
fuelectenerg-3309	291	47	0	0	NUM
fuelectenerg-3309	291	48	)	)	PUNCT
fuelectenerg-3309	291	49	,	,	PUNCT
fuelectenerg-3309	291	50	(	(	PUNCT
fuelectenerg-3309	291	51	1	1	NUM
fuelectenerg-3309	291	52	,	,	PUNCT
fuelectenerg-3309	291	53	0	0	NUM
fuelectenerg-3309	291	54	)	)	PUNCT
fuelectenerg-3309	291	55	→	→	SYM
fuelectenerg-3309	291	56	(	(	PUNCT
fuelectenerg-3309	291	57	0	0	NUM
fuelectenerg-3309	291	58	,	,	PUNCT
fuelectenerg-3309	291	59	1	1	NUM
fuelectenerg-3309	291	60	)	)	PUNCT
fuelectenerg-3309	291	61	,	,	PUNCT
fuelectenerg-3309	291	62	(	(	PUNCT
fuelectenerg-3309	291	63	1	1	NUM
fuelectenerg-3309	291	64	,	,	PUNCT
fuelectenerg-3309	291	65	1	1	NUM
fuelectenerg-3309	291	66	)	)	PUNCT
fuelectenerg-3309	291	67	→	→	X
fuelectenerg-3309	291	68	(	(	PUNCT
fuelectenerg-3309	291	69	1	1	NUM
fuelectenerg-3309	291	70	,	,	PUNCT
fuelectenerg-3309	291	71	1	1	NUM
fuelectenerg-3309	291	72	)	)	PUNCT
fuelectenerg-3309	291	73	,	,	PUNCT
fuelectenerg-3309	291	74	(	(	PUNCT
fuelectenerg-3309	291	75	1	1	NUM
fuelectenerg-3309	291	76	,	,	PUNCT
fuelectenerg-3309	291	77	2	2	NUM
fuelectenerg-3309	291	78	)	)	PUNCT
fuelectenerg-3309	291	79	→	→	X
fuelectenerg-3309	291	80	(	(	PUNCT
fuelectenerg-3309	291	81	2	2	NUM
fuelectenerg-3309	291	82	,	,	PUNCT
fuelectenerg-3309	291	83	1	1	NUM
fuelectenerg-3309	291	84	)	)	PUNCT
fuelectenerg-3309	291	85	,	,	PUNCT
fuelectenerg-3309	291	86	(	(	PUNCT
fuelectenerg-3309	291	87	2	2	NUM
fuelectenerg-3309	291	88	,	,	PUNCT
fuelectenerg-3309	291	89	0	0	NUM
fuelectenerg-3309	291	90	)	)	PUNCT
fuelectenerg-3309	291	91	→	→	SYM
fuelectenerg-3309	291	92	(	(	PUNCT
fuelectenerg-3309	291	93	0	0	NUM
fuelectenerg-3309	291	94	,	,	PUNCT
fuelectenerg-3309	291	95	2	2	NUM
fuelectenerg-3309	291	96	)	)	PUNCT
fuelectenerg-3309	291	97	,	,	PUNCT
fuelectenerg-3309	291	98	(	(	PUNCT
fuelectenerg-3309	291	99	2	2	NUM
fuelectenerg-3309	291	100	,	,	PUNCT
fuelectenerg-3309	291	101	1	1	NUM
fuelectenerg-3309	291	102	)	)	PUNCT
fuelectenerg-3309	291	103	→	→	X
fuelectenerg-3309	291	104	(	(	PUNCT
fuelectenerg-3309	291	105	1	1	NUM
fuelectenerg-3309	291	106	,	,	PUNCT
fuelectenerg-3309	291	107	2	2	NUM
fuelectenerg-3309	291	108	)	)	PUNCT
fuelectenerg-3309	291	109	and	and	CCONJ
fuelectenerg-3309	291	110	(	(	PUNCT
fuelectenerg-3309	291	111	2	2	NUM
fuelectenerg-3309	291	112	,	,	PUNCT
fuelectenerg-3309	291	113	2	2	NUM
fuelectenerg-3309	291	114	)	)	PUNCT
fuelectenerg-3309	291	115	→	→	X
fuelectenerg-3309	291	116	(	(	PUNCT
fuelectenerg-3309	291	117	2	2	NUM
fuelectenerg-3309	291	118	,	,	PUNCT
fuelectenerg-3309	291	119	2	2	NUM
fuelectenerg-3309	291	120	)	)	PUNCT
fuelectenerg-3309	291	121	or	or	CCONJ
fuelectenerg-3309	291	122	tq	tq	ADP
fuelectenerg-3309	291	123	,	,	PUNCT
fuelectenerg-3309	291	124	ρ	ρ	PROPN
fuelectenerg-3309	291	125	,	,	PUNCT
fuelectenerg-3309	291	126	s	s	PART
fuelectenerg-3309	291	127	:	:	PUNCT
fuelectenerg-3309	291	128	{	{	PUNCT
fuelectenerg-3309	291	129	0	0	NUM
fuelectenerg-3309	291	130	,	,	PUNCT
fuelectenerg-3309	291	131	1	1	NUM
fuelectenerg-3309	291	132	,	,	PUNCT
fuelectenerg-3309	291	133	2	2	NUM
fuelectenerg-3309	291	134	,	,	PUNCT
fuelectenerg-3309	291	135	3	3	NUM
fuelectenerg-3309	291	136	,	,	PUNCT
fuelectenerg-3309	291	137	4	4	NUM
fuelectenerg-3309	291	138	,	,	PUNCT
fuelectenerg-3309	291	139	5	5	NUM
fuelectenerg-3309	291	140	,	,	PUNCT
fuelectenerg-3309	291	141	6	6	NUM
fuelectenerg-3309	291	142	,	,	PUNCT
fuelectenerg-3309	291	143	7	7	NUM
fuelectenerg-3309	291	144	,	,	PUNCT
fuelectenerg-3309	291	145	8	8	NUM
fuelectenerg-3309	291	146	}	}	PUNCT
fuelectenerg-3309	291	147	→	→	SYM
fuelectenerg-3309	291	148	{	{	PUNCT
fuelectenerg-3309	291	149	0	0	NUM
fuelectenerg-3309	291	150	,	,	PUNCT
fuelectenerg-3309	291	151	3	3	NUM
fuelectenerg-3309	291	152	,	,	PUNCT
fuelectenerg-3309	291	153	6	6	NUM
fuelectenerg-3309	291	154	,	,	PUNCT
fuelectenerg-3309	291	155	1	1	NUM
fuelectenerg-3309	291	156	,	,	PUNCT
fuelectenerg-3309	291	157	4	4	NUM
fuelectenerg-3309	291	158	,	,	PUNCT
fuelectenerg-3309	291	159	7	7	NUM
fuelectenerg-3309	291	160	,	,	PUNCT
fuelectenerg-3309	291	161	2	2	NUM
fuelectenerg-3309	291	162	,	,	PUNCT
fuelectenerg-3309	291	163	5	5	NUM
fuelectenerg-3309	291	164	,	,	PUNCT
fuelectenerg-3309	291	165	8	8	NUM
fuelectenerg-3309	291	166	}	}	PUNCT
fuelectenerg-3309	291	167	.	.	PUNCT
fuelectenerg-3309	292	1	250	250	NUM
fuelectenerg-3309	292	2	c.	c.	PROPN
fuelectenerg-3309	292	3	karanikas	karanikas	PROPN
fuelectenerg-3309	292	4	,	,	PUNCT
fuelectenerg-3309	292	5	n.	n.	PROPN
fuelectenerg-3309	292	6	atreas	atreas	PROPN
fuelectenerg-3309	292	7	enumeration	enumeration	PROPN
fuelectenerg-3309	292	8	and	and	CCONJ
fuelectenerg-3309	292	9	coding	code	VERB
fuelectenerg-3309	292	10	permutations	permutation	NOUN
fuelectenerg-3309	292	11	and	and	CCONJ
fuelectenerg-3309	292	12	reversible	reversible	ADJ
fuelectenerg-3309	292	13	logical	logical	ADJ
fuelectenerg-3309	292	14	circuits	circuit	NOUN
fuelectenerg-3309	292	15	251	251	NUM
fuelectenerg-3309	292	16	10	10	NUM
fuelectenerg-3309	292	17	n.	n.	PROPN
fuelectenerg-3309	292	18	atreas	atreas	PROPN
fuelectenerg-3309	292	19	and	and	CCONJ
fuelectenerg-3309	292	20	c.	c.	PROPN
fuelectenerg-3309	292	21	karanikas	karanikas	PROPN
fuelectenerg-3309	292	22	hence	hence	ADV
fuelectenerg-3309	292	23	ek	ek	PROPN
fuelectenerg-3309	292	24	,	,	PUNCT
fuelectenerg-3309	292	25	ρ1	ρ1	NOUN
fuelectenerg-3309	292	26	=	=	SYM
fuelectenerg-3309	292	27	en	en	X
fuelectenerg-3309	292	28	,	,	PUNCT
fuelectenerg-3309	292	29	ρ1	ρ1	NOUN
fuelectenerg-3309	292	30	.	.	PUNCT
fuelectenerg-3309	293	1	if	if	SCONJ
fuelectenerg-3309	293	2	i	i	PRON
fuelectenerg-3309	293	3	=	=	NOUN
fuelectenerg-3309	293	4	2	2	NUM
fuelectenerg-3309	293	5	,	,	PUNCT
fuelectenerg-3309	293	6	then	then	ADV
fuelectenerg-3309	293	7	s2	s2	VERB
fuelectenerg-3309	293	8	∈	∈	PROPN
fuelectenerg-3309	293	9	{	{	PUNCT
fuelectenerg-3309	293	10	0	0	NUM
fuelectenerg-3309	293	11	,	,	PUNCT
fuelectenerg-3309	293	12	1	1	NUM
fuelectenerg-3309	293	13	}	}	PUNCT
fuelectenerg-3309	293	14	.	.	PUNCT
fuelectenerg-3309	294	1	for	for	ADP
fuelectenerg-3309	294	2	s2	s2	NOUN
fuelectenerg-3309	294	3	=	=	PUNCT
fuelectenerg-3309	294	4	2	2	NUM
fuelectenerg-3309	294	5	we	we	PRON
fuelectenerg-3309	294	6	immediately	immediately	ADV
fuelectenerg-3309	294	7	obtain	obtain	VERB
fuelectenerg-3309	294	8	ek	ek	NOUN
fuelectenerg-3309	294	9	,	,	PUNCT
fuelectenerg-3309	294	10	ρ2	ρ2	NOUN
fuelectenerg-3309	294	11	=	=	SYM
fuelectenerg-3309	294	12	en	en	X
fuelectenerg-3309	294	13	,	,	PUNCT
fuelectenerg-3309	294	14	ρ2	ρ2	NOUN
fuelectenerg-3309	294	15	.	.	PUNCT
fuelectenerg-3309	295	1	for	for	ADP
fuelectenerg-3309	295	2	s2	s2	NOUN
fuelectenerg-3309	295	3	=	=	SYM
fuelectenerg-3309	295	4	1	1	NUM
fuelectenerg-3309	295	5	we	we	PRON
fuelectenerg-3309	295	6	have	have	VERB
fuelectenerg-3309	295	7	t	t	PROPN
fuelectenerg-3309	295	8	(	(	PUNCT
fuelectenerg-3309	295	9	ek)2	ek)2	PROPN
fuelectenerg-3309	295	10	=	=	SYM
fuelectenerg-3309	295	11	t	t	PROPN
fuelectenerg-3309	295	12	(	(	PUNCT
fuelectenerg-3309	295	13	en)2	en)2	VERB
fuelectenerg-3309	295	14	⇒	⇒	PROPN
fuelectenerg-3309	295	15	mod	mod	PROPN
fuelectenerg-3309	296	1	(	(	PUNCT
fuelectenerg-3309	296	2	ek	ek	X
fuelectenerg-3309	296	3	,	,	PUNCT
fuelectenerg-3309	296	4	ρ2	ρ2	NOUN
fuelectenerg-3309	296	5	−	−	PROPN
fuelectenerg-3309	296	6	ek	ek	PROPN
fuelectenerg-3309	296	7	,	,	PUNCT
fuelectenerg-3309	296	8	ρs2	ρs2	INTJ
fuelectenerg-3309	296	9	,	,	PUNCT
fuelectenerg-3309	296	10	q	q	NOUN
fuelectenerg-3309	296	11	)	)	PUNCT
fuelectenerg-3309	296	12	=	=	SYM
fuelectenerg-3309	296	13	mod	mod	X
fuelectenerg-3309	296	14	(	(	PUNCT
fuelectenerg-3309	296	15	en	en	X
fuelectenerg-3309	296	16	,	,	PUNCT
fuelectenerg-3309	296	17	ρ2	ρ2	NOUN
fuelectenerg-3309	296	18	−	−	PROPN
fuelectenerg-3309	296	19	en	en	X
fuelectenerg-3309	296	20	,	,	PUNCT
fuelectenerg-3309	296	21	ρs2	ρs2	INTJ
fuelectenerg-3309	296	22	,	,	PUNCT
fuelectenerg-3309	296	23	q	q	NOUN
fuelectenerg-3309	296	24	)	)	PUNCT
fuelectenerg-3309	296	25	⇒	⇒	NOUN
fuelectenerg-3309	296	26	mod	mod	PROPN
fuelectenerg-3309	296	27	(	(	PUNCT
fuelectenerg-3309	296	28	ek	ek	X
fuelectenerg-3309	296	29	,	,	PUNCT
fuelectenerg-3309	296	30	ρ2	ρ2	NOUN
fuelectenerg-3309	296	31	−	−	PROPN
fuelectenerg-3309	296	32	en	en	X
fuelectenerg-3309	296	33	,	,	PUNCT
fuelectenerg-3309	296	34	ρ1	ρ1	NOUN
fuelectenerg-3309	296	35	,	,	PUNCT
fuelectenerg-3309	296	36	q	q	NOUN
fuelectenerg-3309	296	37	)	)	PUNCT
fuelectenerg-3309	296	38	=	=	SYM
fuelectenerg-3309	296	39	mod	mod	X
fuelectenerg-3309	296	40	(	(	PUNCT
fuelectenerg-3309	296	41	en	en	X
fuelectenerg-3309	296	42	,	,	PUNCT
fuelectenerg-3309	296	43	ρ2	ρ2	NOUN
fuelectenerg-3309	296	44	−	−	PROPN
fuelectenerg-3309	296	45	en	en	X
fuelectenerg-3309	296	46	,	,	PUNCT
fuelectenerg-3309	296	47	ρ1	ρ1	NOUN
fuelectenerg-3309	296	48	,	,	PUNCT
fuelectenerg-3309	296	49	q	q	PROPN
fuelectenerg-3309	296	50	)	)	PUNCT
fuelectenerg-3309	296	51	,	,	PUNCT
fuelectenerg-3309	296	52	where	where	SCONJ
fuelectenerg-3309	296	53	the	the	DET
fuelectenerg-3309	296	54	last	last	ADJ
fuelectenerg-3309	296	55	equality	equality	NOUN
fuelectenerg-3309	296	56	was	be	AUX
fuelectenerg-3309	296	57	derived	derive	VERB
fuelectenerg-3309	296	58	from	from	ADP
fuelectenerg-3309	296	59	the	the	DET
fuelectenerg-3309	296	60	fact	fact	NOUN
fuelectenerg-3309	296	61	that	that	SCONJ
fuelectenerg-3309	296	62	ek	ek	PROPN
fuelectenerg-3309	296	63	,	,	PUNCT
fuelectenerg-3309	296	64	ρ1	ρ1	NOUN
fuelectenerg-3309	296	65	=	=	SYM
fuelectenerg-3309	296	66	en	en	X
fuelectenerg-3309	296	67	,	,	PUNCT
fuelectenerg-3309	296	68	ρ1	ρ1	NOUN
fuelectenerg-3309	296	69	as	as	SCONJ
fuelectenerg-3309	296	70	we	we	PRON
fuelectenerg-3309	296	71	showed	show	VERB
fuelectenerg-3309	296	72	above	above	ADV
fuelectenerg-3309	296	73	.	.	PUNCT
fuelectenerg-3309	297	1	hence	hence	ADV
fuelectenerg-3309	297	2	,	,	PUNCT
fuelectenerg-3309	297	3	either	either	CCONJ
fuelectenerg-3309	297	4	ek	ek	PROPN
fuelectenerg-3309	297	5	,	,	PUNCT
fuelectenerg-3309	297	6	ρ2	ρ2	NOUN
fuelectenerg-3309	297	7	−	−	PROPN
fuelectenerg-3309	297	8	en	en	X
fuelectenerg-3309	297	9	,	,	PUNCT
fuelectenerg-3309	297	10	ρ1	ρ1	NOUN
fuelectenerg-3309	297	11	=	=	SYM
fuelectenerg-3309	297	12	en	en	X
fuelectenerg-3309	297	13	,	,	PUNCT
fuelectenerg-3309	297	14	ρ2	ρ2	NOUN
fuelectenerg-3309	297	15	−	−	PROPN
fuelectenerg-3309	297	16	en	en	X
fuelectenerg-3309	297	17	,	,	PUNCT
fuelectenerg-3309	297	18	ρ1	ρ1	NOUN
fuelectenerg-3309	297	19	⇒	⇒	PROPN
fuelectenerg-3309	297	20	ek	ek	PROPN
fuelectenerg-3309	297	21	,	,	PUNCT
fuelectenerg-3309	297	22	ρ2	ρ2	PROPN
fuelectenerg-3309	297	23	=	=	SYM
fuelectenerg-3309	297	24	en	en	X
fuelectenerg-3309	297	25	,	,	PUNCT
fuelectenerg-3309	297	26	ρ2	ρ2	NOUN
fuelectenerg-3309	297	27	or	or	CCONJ
fuelectenerg-3309	297	28	q	q	NOUN
fuelectenerg-3309	297	29	−	−	PROPN
fuelectenerg-3309	297	30	(	(	PUNCT
fuelectenerg-3309	297	31	ek	ek	X
fuelectenerg-3309	297	32	,	,	PUNCT
fuelectenerg-3309	297	33	ρ2	ρ2	NOUN
fuelectenerg-3309	297	34	−	−	PROPN
fuelectenerg-3309	297	35	en	en	X
fuelectenerg-3309	297	36	,	,	PUNCT
fuelectenerg-3309	297	37	ρ1	ρ1	NOUN
fuelectenerg-3309	297	38	)	)	PUNCT
fuelectenerg-3309	297	39	=	=	PUNCT
fuelectenerg-3309	298	1	q	q	NOUN
fuelectenerg-3309	299	1	−	−	PROPN
fuelectenerg-3309	299	2	(	(	PUNCT
fuelectenerg-3309	299	3	en	en	X
fuelectenerg-3309	299	4	,	,	PUNCT
fuelectenerg-3309	299	5	ρ2	ρ2	NOUN
fuelectenerg-3309	299	6	−	−	PROPN
fuelectenerg-3309	299	7	en	en	X
fuelectenerg-3309	299	8	,	,	PUNCT
fuelectenerg-3309	299	9	ρ1	ρ1	NOUN
fuelectenerg-3309	299	10	)	)	PUNCT
fuelectenerg-3309	299	11	⇒	⇒	PROPN
fuelectenerg-3309	299	12	ek	ek	PROPN
fuelectenerg-3309	299	13	,	,	PUNCT
fuelectenerg-3309	299	14	ρ2	ρ2	PROPN
fuelectenerg-3309	299	15	=	=	SYM
fuelectenerg-3309	299	16	en	en	X
fuelectenerg-3309	299	17	,	,	PUNCT
fuelectenerg-3309	299	18	ρ2	ρ2	NOUN
fuelectenerg-3309	299	19	.	.	PUNCT
fuelectenerg-3309	300	1	therefore	therefore	ADV
fuelectenerg-3309	300	2	,	,	PUNCT
fuelectenerg-3309	300	3	in	in	ADP
fuelectenerg-3309	300	4	any	any	DET
fuelectenerg-3309	300	5	case	case	NOUN
fuelectenerg-3309	300	6	we	we	PRON
fuelectenerg-3309	300	7	obtain	obtain	VERB
fuelectenerg-3309	300	8	ek	ek	NOUN
fuelectenerg-3309	300	9	,	,	PUNCT
fuelectenerg-3309	300	10	ρ2	ρ2	NOUN
fuelectenerg-3309	300	11	=	=	SYM
fuelectenerg-3309	300	12	en	en	X
fuelectenerg-3309	300	13	,	,	PUNCT
fuelectenerg-3309	300	14	ρ2	ρ2	NOUN
fuelectenerg-3309	300	15	.	.	PUNCT
fuelectenerg-3309	301	1	we	we	PRON
fuelectenerg-3309	301	2	proceed	proceed	VERB
fuelectenerg-3309	301	3	in	in	ADP
fuelectenerg-3309	301	4	the	the	DET
fuelectenerg-3309	301	5	same	same	ADJ
fuelectenerg-3309	301	6	manner	manner	NOUN
fuelectenerg-3309	301	7	for	for	ADP
fuelectenerg-3309	301	8	the	the	DET
fuelectenerg-3309	301	9	remaining	remain	VERB
fuelectenerg-3309	301	10	values	value	NOUN
fuelectenerg-3309	301	11	i	i	X
fuelectenerg-3309	301	12	=	=	NOUN
fuelectenerg-3309	301	13	3	3	NUM
fuelectenerg-3309	301	14	,	,	PUNCT
fuelectenerg-3309	301	15	...	...	PUNCT
fuelectenerg-3309	301	16	,	,	PUNCT
fuelectenerg-3309	301	17	m	m	AUX
fuelectenerg-3309	301	18	obtaining	obtain	VERB
fuelectenerg-3309	301	19	ek	ek	NOUN
fuelectenerg-3309	301	20	,	,	PUNCT
fuelectenerg-3309	301	21	ρi	ρi	NOUN
fuelectenerg-3309	301	22	=	=	SYM
fuelectenerg-3309	301	23	en	en	X
fuelectenerg-3309	301	24	,	,	PUNCT
fuelectenerg-3309	301	25	ρi	ρi	NOUN
fuelectenerg-3309	301	26	,	,	PUNCT
fuelectenerg-3309	301	27	∀i	∀i	NOUN
fuelectenerg-3309	301	28	=	=	SYM
fuelectenerg-3309	301	29	1	1	NUM
fuelectenerg-3309	301	30	,	,	PUNCT
fuelectenerg-3309	301	31	...	...	PUNCT
fuelectenerg-3309	301	32	,	,	PUNCT
fuelectenerg-3309	301	33	m.	m.	NOUN
fuelectenerg-3309	301	34	since	since	SCONJ
fuelectenerg-3309	301	35	ρ	ρ	PROPN
fuelectenerg-3309	301	36	is	be	AUX
fuelectenerg-3309	301	37	a	a	DET
fuelectenerg-3309	301	38	permutation	permutation	NOUN
fuelectenerg-3309	301	39	,	,	PUNCT
fuelectenerg-3309	301	40	necessarily	necessarily	ADV
fuelectenerg-3309	301	41	ek	ek	VERB
fuelectenerg-3309	301	42	,	,	PUNCT
fuelectenerg-3309	301	43	i	i	PROPN
fuelectenerg-3309	301	44	=	=	SYM
fuelectenerg-3309	301	45	en	en	X
fuelectenerg-3309	301	46	,	,	PUNCT
fuelectenerg-3309	301	47	i	i	PRON
fuelectenerg-3309	301	48	,	,	PUNCT
fuelectenerg-3309	301	49	∀i	∀i	X
fuelectenerg-3309	301	50	=	=	SYM
fuelectenerg-3309	301	51	1	1	NUM
fuelectenerg-3309	301	52	,	,	PUNCT
fuelectenerg-3309	301	53	...	...	PUNCT
fuelectenerg-3309	301	54	,	,	PUNCT
fuelectenerg-3309	301	55	m	m	VERB
fuelectenerg-3309	301	56	and	and	CCONJ
fuelectenerg-3309	301	57	the	the	DET
fuelectenerg-3309	301	58	proof	proof	NOUN
fuelectenerg-3309	301	59	is	be	AUX
fuelectenerg-3309	301	60	complete	complete	ADJ
fuelectenerg-3309	301	61	.	.	PUNCT
fuelectenerg-3309	302	1	it	it	PRON
fuelectenerg-3309	302	2	is	be	AUX
fuelectenerg-3309	302	3	clear	clear	ADJ
fuelectenerg-3309	302	4	that	that	SCONJ
fuelectenerg-3309	302	5	the	the	DET
fuelectenerg-3309	302	6	above	above	ADJ
fuelectenerg-3309	302	7	operator	operator	NOUN
fuelectenerg-3309	302	8	tq	tq	ADP
fuelectenerg-3309	302	9	,	,	PUNCT
fuelectenerg-3309	302	10	ρ	ρ	PROPN
fuelectenerg-3309	302	11	,	,	PUNCT
fuelectenerg-3309	302	12	s	s	X
fuelectenerg-3309	302	13	provides	provide	VERB
fuelectenerg-3309	302	14	a	a	DET
fuelectenerg-3309	302	15	code	code	NOUN
fuelectenerg-3309	302	16	for	for	ADP
fuelectenerg-3309	302	17	shuffling	shuffle	VERB
fuelectenerg-3309	302	18	the	the	DET
fuelectenerg-3309	302	19	elements	element	NOUN
fuelectenerg-3309	302	20	of	of	ADP
fuelectenerg-3309	302	21	the	the	DET
fuelectenerg-3309	302	22	set	set	NOUN
fuelectenerg-3309	302	23	{	{	PUNCT
fuelectenerg-3309	302	24	0	0	NUM
fuelectenerg-3309	302	25	,	,	PUNCT
fuelectenerg-3309	302	26	...	...	PUNCT
fuelectenerg-3309	302	27	,	,	PUNCT
fuelectenerg-3309	302	28	qm	qm	PROPN
fuelectenerg-3309	302	29	−	−	PROPN
fuelectenerg-3309	302	30	1	1	NUM
fuelectenerg-3309	302	31	}	}	PUNCT
fuelectenerg-3309	302	32	.	.	PUNCT
fuelectenerg-3309	303	1	example	example	NOUN
fuelectenerg-3309	303	2	6	6	NUM
fuelectenerg-3309	303	3	let	let	VERB
fuelectenerg-3309	303	4	q	q	NOUN
fuelectenerg-3309	304	1	=	=	SYM
fuelectenerg-3309	304	2	3	3	NUM
fuelectenerg-3309	304	3	,	,	PUNCT
fuelectenerg-3309	304	4	ρ	ρ	NOUN
fuelectenerg-3309	304	5	=	=	SYM
fuelectenerg-3309	304	6	(	(	PUNCT
fuelectenerg-3309	304	7	2	2	NUM
fuelectenerg-3309	304	8	,	,	PUNCT
fuelectenerg-3309	304	9	1	1	NUM
fuelectenerg-3309	304	10	)	)	PUNCT
fuelectenerg-3309	304	11	,	,	PUNCT
fuelectenerg-3309	305	1	s	s	X
fuelectenerg-3309	305	2	=	=	PUNCT
fuelectenerg-3309	305	3	(	(	PUNCT
fuelectenerg-3309	305	4	1	1	NUM
fuelectenerg-3309	305	5	,	,	PUNCT
fuelectenerg-3309	305	6	2	2	NUM
fuelectenerg-3309	305	7	)	)	PUNCT
fuelectenerg-3309	305	8	and	and	CCONJ
fuelectenerg-3309	305	9	e	e	X
fuelectenerg-3309	305	10	(	(	PUNCT
fuelectenerg-3309	305	11	3	3	X
fuelectenerg-3309	305	12	)	)	SYM
fuelectenerg-3309	305	13	2	2	NUM
fuelectenerg-3309	305	14	=	=	SYM
fuelectenerg-3309	305	15	{	{	PUNCT
fuelectenerg-3309	305	16	(	(	PUNCT
fuelectenerg-3309	305	17	0	0	NUM
fuelectenerg-3309	305	18	,	,	PUNCT
fuelectenerg-3309	305	19	0	0	NUM
fuelectenerg-3309	305	20	)	)	PUNCT
fuelectenerg-3309	305	21	,	,	PUNCT
fuelectenerg-3309	305	22	(	(	PUNCT
fuelectenerg-3309	305	23	0	0	NUM
fuelectenerg-3309	305	24	,	,	PUNCT
fuelectenerg-3309	305	25	1	1	NUM
fuelectenerg-3309	305	26	)	)	PUNCT
fuelectenerg-3309	305	27	,	,	PUNCT
fuelectenerg-3309	305	28	(	(	PUNCT
fuelectenerg-3309	305	29	0	0	NUM
fuelectenerg-3309	305	30	,	,	PUNCT
fuelectenerg-3309	305	31	2	2	NUM
fuelectenerg-3309	305	32	)	)	PUNCT
fuelectenerg-3309	305	33	,	,	PUNCT
fuelectenerg-3309	305	34	(	(	PUNCT
fuelectenerg-3309	305	35	1	1	NUM
fuelectenerg-3309	305	36	,	,	PUNCT
fuelectenerg-3309	305	37	0	0	NUM
fuelectenerg-3309	305	38	)	)	PUNCT
fuelectenerg-3309	305	39	,	,	PUNCT
fuelectenerg-3309	305	40	(	(	PUNCT
fuelectenerg-3309	305	41	1	1	NUM
fuelectenerg-3309	305	42	,	,	PUNCT
fuelectenerg-3309	305	43	1	1	NUM
fuelectenerg-3309	305	44	)	)	PUNCT
fuelectenerg-3309	305	45	,	,	PUNCT
fuelectenerg-3309	305	46	(	(	PUNCT
fuelectenerg-3309	305	47	1	1	NUM
fuelectenerg-3309	305	48	,	,	PUNCT
fuelectenerg-3309	305	49	2	2	NUM
fuelectenerg-3309	305	50	)	)	PUNCT
fuelectenerg-3309	305	51	,	,	PUNCT
fuelectenerg-3309	305	52	(	(	PUNCT
fuelectenerg-3309	305	53	2	2	NUM
fuelectenerg-3309	305	54	,	,	PUNCT
fuelectenerg-3309	305	55	0	0	NUM
fuelectenerg-3309	305	56	)	)	PUNCT
fuelectenerg-3309	305	57	,	,	PUNCT
fuelectenerg-3309	305	58	(	(	PUNCT
fuelectenerg-3309	305	59	2	2	NUM
fuelectenerg-3309	305	60	,	,	PUNCT
fuelectenerg-3309	305	61	1	1	NUM
fuelectenerg-3309	305	62	)	)	PUNCT
fuelectenerg-3309	305	63	,	,	PUNCT
fuelectenerg-3309	305	64	(	(	PUNCT
fuelectenerg-3309	305	65	2	2	NUM
fuelectenerg-3309	305	66	,	,	PUNCT
fuelectenerg-3309	305	67	2	2	NUM
fuelectenerg-3309	305	68	)	)	PUNCT
fuelectenerg-3309	305	69	}	}	PUNCT
fuelectenerg-3309	305	70	.	.	PUNCT
fuelectenerg-3309	306	1	then	then	ADV
fuelectenerg-3309	306	2	by	by	ADP
fuelectenerg-3309	306	3	the	the	DET
fuelectenerg-3309	306	4	above	above	ADJ
fuelectenerg-3309	306	5	definition	definition	NOUN
fuelectenerg-3309	306	6	of	of	ADP
fuelectenerg-3309	306	7	tq	tq	PRON
fuelectenerg-3309	306	8	,	,	PUNCT
fuelectenerg-3309	306	9	ρ	ρ	PROPN
fuelectenerg-3309	306	10	,	,	PUNCT
fuelectenerg-3309	306	11	s	s	PART
fuelectenerg-3309	306	12	we	we	PRON
fuelectenerg-3309	306	13	obtain	obtain	VERB
fuelectenerg-3309	306	14	(	(	PUNCT
fuelectenerg-3309	306	15	0	0	NUM
fuelectenerg-3309	306	16	,	,	PUNCT
fuelectenerg-3309	306	17	0	0	NUM
fuelectenerg-3309	306	18	)	)	PUNCT
fuelectenerg-3309	306	19	→	→	SYM
fuelectenerg-3309	306	20	(	(	PUNCT
fuelectenerg-3309	306	21	0	0	NUM
fuelectenerg-3309	306	22	,	,	PUNCT
fuelectenerg-3309	306	23	0	0	NUM
fuelectenerg-3309	306	24	)	)	PUNCT
fuelectenerg-3309	306	25	,	,	PUNCT
fuelectenerg-3309	306	26	(	(	PUNCT
fuelectenerg-3309	306	27	0	0	NUM
fuelectenerg-3309	306	28	,	,	PUNCT
fuelectenerg-3309	306	29	1	1	NUM
fuelectenerg-3309	306	30	)	)	PUNCT
fuelectenerg-3309	306	31	→	→	X
fuelectenerg-3309	306	32	(	(	PUNCT
fuelectenerg-3309	306	33	1	1	NUM
fuelectenerg-3309	306	34	,	,	PUNCT
fuelectenerg-3309	306	35	0	0	NUM
fuelectenerg-3309	306	36	)	)	PUNCT
fuelectenerg-3309	306	37	,	,	PUNCT
fuelectenerg-3309	306	38	(	(	PUNCT
fuelectenerg-3309	306	39	0	0	NUM
fuelectenerg-3309	306	40	,	,	PUNCT
fuelectenerg-3309	306	41	2	2	NUM
fuelectenerg-3309	306	42	)	)	PUNCT
fuelectenerg-3309	306	43	→	→	X
fuelectenerg-3309	306	44	(	(	PUNCT
fuelectenerg-3309	306	45	2	2	NUM
fuelectenerg-3309	306	46	,	,	PUNCT
fuelectenerg-3309	306	47	0	0	NUM
fuelectenerg-3309	306	48	)	)	PUNCT
fuelectenerg-3309	306	49	,	,	PUNCT
fuelectenerg-3309	306	50	(	(	PUNCT
fuelectenerg-3309	306	51	1	1	NUM
fuelectenerg-3309	306	52	,	,	PUNCT
fuelectenerg-3309	306	53	0	0	NUM
fuelectenerg-3309	306	54	)	)	PUNCT
fuelectenerg-3309	306	55	→	→	SYM
fuelectenerg-3309	306	56	(	(	PUNCT
fuelectenerg-3309	306	57	0	0	NUM
fuelectenerg-3309	306	58	,	,	PUNCT
fuelectenerg-3309	306	59	1	1	NUM
fuelectenerg-3309	306	60	)	)	PUNCT
fuelectenerg-3309	306	61	,	,	PUNCT
fuelectenerg-3309	306	62	(	(	PUNCT
fuelectenerg-3309	306	63	1	1	NUM
fuelectenerg-3309	306	64	,	,	PUNCT
fuelectenerg-3309	306	65	1	1	NUM
fuelectenerg-3309	306	66	)	)	PUNCT
fuelectenerg-3309	306	67	→	→	X
fuelectenerg-3309	306	68	(	(	PUNCT
fuelectenerg-3309	306	69	1	1	NUM
fuelectenerg-3309	306	70	,	,	PUNCT
fuelectenerg-3309	306	71	1	1	NUM
fuelectenerg-3309	306	72	)	)	PUNCT
fuelectenerg-3309	306	73	,	,	PUNCT
fuelectenerg-3309	306	74	(	(	PUNCT
fuelectenerg-3309	306	75	1	1	NUM
fuelectenerg-3309	306	76	,	,	PUNCT
fuelectenerg-3309	306	77	2	2	NUM
fuelectenerg-3309	306	78	)	)	PUNCT
fuelectenerg-3309	306	79	→	→	X
fuelectenerg-3309	306	80	(	(	PUNCT
fuelectenerg-3309	306	81	2	2	NUM
fuelectenerg-3309	306	82	,	,	PUNCT
fuelectenerg-3309	306	83	1	1	NUM
fuelectenerg-3309	306	84	)	)	PUNCT
fuelectenerg-3309	306	85	,	,	PUNCT
fuelectenerg-3309	306	86	(	(	PUNCT
fuelectenerg-3309	306	87	2	2	NUM
fuelectenerg-3309	306	88	,	,	PUNCT
fuelectenerg-3309	306	89	0	0	NUM
fuelectenerg-3309	306	90	)	)	PUNCT
fuelectenerg-3309	306	91	→	→	SYM
fuelectenerg-3309	306	92	(	(	PUNCT
fuelectenerg-3309	306	93	0	0	NUM
fuelectenerg-3309	306	94	,	,	PUNCT
fuelectenerg-3309	306	95	2	2	NUM
fuelectenerg-3309	306	96	)	)	PUNCT
fuelectenerg-3309	306	97	,	,	PUNCT
fuelectenerg-3309	306	98	(	(	PUNCT
fuelectenerg-3309	306	99	2	2	NUM
fuelectenerg-3309	306	100	,	,	PUNCT
fuelectenerg-3309	306	101	1	1	NUM
fuelectenerg-3309	306	102	)	)	PUNCT
fuelectenerg-3309	306	103	→	→	X
fuelectenerg-3309	306	104	(	(	PUNCT
fuelectenerg-3309	306	105	1	1	NUM
fuelectenerg-3309	306	106	,	,	PUNCT
fuelectenerg-3309	306	107	2	2	NUM
fuelectenerg-3309	306	108	)	)	PUNCT
fuelectenerg-3309	306	109	and	and	CCONJ
fuelectenerg-3309	306	110	(	(	PUNCT
fuelectenerg-3309	306	111	2	2	NUM
fuelectenerg-3309	306	112	,	,	PUNCT
fuelectenerg-3309	306	113	2	2	NUM
fuelectenerg-3309	306	114	)	)	PUNCT
fuelectenerg-3309	306	115	→	→	X
fuelectenerg-3309	306	116	(	(	PUNCT
fuelectenerg-3309	306	117	2	2	NUM
fuelectenerg-3309	306	118	,	,	PUNCT
fuelectenerg-3309	306	119	2	2	NUM
fuelectenerg-3309	306	120	)	)	PUNCT
fuelectenerg-3309	306	121	or	or	CCONJ
fuelectenerg-3309	306	122	tq	tq	ADP
fuelectenerg-3309	306	123	,	,	PUNCT
fuelectenerg-3309	306	124	ρ	ρ	PROPN
fuelectenerg-3309	306	125	,	,	PUNCT
fuelectenerg-3309	306	126	s	s	PART
fuelectenerg-3309	306	127	:	:	PUNCT
fuelectenerg-3309	306	128	{	{	PUNCT
fuelectenerg-3309	306	129	0	0	NUM
fuelectenerg-3309	306	130	,	,	PUNCT
fuelectenerg-3309	306	131	1	1	NUM
fuelectenerg-3309	306	132	,	,	PUNCT
fuelectenerg-3309	306	133	2	2	NUM
fuelectenerg-3309	306	134	,	,	PUNCT
fuelectenerg-3309	306	135	3	3	NUM
fuelectenerg-3309	306	136	,	,	PUNCT
fuelectenerg-3309	306	137	4	4	NUM
fuelectenerg-3309	306	138	,	,	PUNCT
fuelectenerg-3309	306	139	5	5	NUM
fuelectenerg-3309	306	140	,	,	PUNCT
fuelectenerg-3309	306	141	6	6	NUM
fuelectenerg-3309	306	142	,	,	PUNCT
fuelectenerg-3309	306	143	7	7	NUM
fuelectenerg-3309	306	144	,	,	PUNCT
fuelectenerg-3309	306	145	8	8	NUM
fuelectenerg-3309	306	146	}	}	PUNCT
fuelectenerg-3309	306	147	→	→	SYM
fuelectenerg-3309	306	148	{	{	PUNCT
fuelectenerg-3309	306	149	0	0	NUM
fuelectenerg-3309	306	150	,	,	PUNCT
fuelectenerg-3309	306	151	3	3	NUM
fuelectenerg-3309	306	152	,	,	PUNCT
fuelectenerg-3309	306	153	6	6	NUM
fuelectenerg-3309	306	154	,	,	PUNCT
fuelectenerg-3309	306	155	1	1	NUM
fuelectenerg-3309	306	156	,	,	PUNCT
fuelectenerg-3309	306	157	4	4	NUM
fuelectenerg-3309	306	158	,	,	PUNCT
fuelectenerg-3309	306	159	7	7	NUM
fuelectenerg-3309	306	160	,	,	PUNCT
fuelectenerg-3309	306	161	2	2	NUM
fuelectenerg-3309	306	162	,	,	PUNCT
fuelectenerg-3309	306	163	5	5	NUM
fuelectenerg-3309	306	164	,	,	PUNCT
fuelectenerg-3309	306	165	8	8	NUM
fuelectenerg-3309	306	166	}	}	PUNCT
fuelectenerg-3309	306	167	.	.	PUNCT
fuelectenerg-3309	307	1	enumeration	enumeration	NOUN
fuelectenerg-3309	307	2	and	and	CCONJ
fuelectenerg-3309	307	3	coding	code	VERB
fuelectenerg-3309	307	4	permutations	permutation	NOUN
fuelectenerg-3309	307	5	and	and	CCONJ
fuelectenerg-3309	307	6	reversible	reversible	ADJ
fuelectenerg-3309	307	7	logical	logical	ADJ
fuelectenerg-3309	307	8	circuits	circuit	NOUN
fuelectenerg-3309	307	9	11	11	NUM
fuelectenerg-3309	307	10	4	4	NUM
fuelectenerg-3309	307	11	on	on	ADP
fuelectenerg-3309	307	12	reversible	reversible	ADJ
fuelectenerg-3309	307	13	gates	gate	NOUN
fuelectenerg-3309	307	14	in	in	ADP
fuelectenerg-3309	307	15	this	this	DET
fuelectenerg-3309	307	16	section	section	NOUN
fuelectenerg-3309	307	17	we	we	PRON
fuelectenerg-3309	307	18	see	see	VERB
fuelectenerg-3309	307	19	that	that	SCONJ
fuelectenerg-3309	307	20	several	several	ADJ
fuelectenerg-3309	307	21	of	of	ADP
fuelectenerg-3309	307	22	the	the	DET
fuelectenerg-3309	307	23	well	well	ADV
fuelectenerg-3309	307	24	known	know	VERB
fuelectenerg-3309	307	25	reversible	reversible	ADJ
fuelectenerg-3309	307	26	gates	gate	NOUN
fuelectenerg-3309	307	27	can	can	AUX
fuelectenerg-3309	307	28	be	be	AUX
fuelectenerg-3309	307	29	obtained	obtain	VERB
fuelectenerg-3309	307	30	by	by	ADP
fuelectenerg-3309	307	31	the	the	DET
fuelectenerg-3309	307	32	bijection	bijection	NOUN
fuelectenerg-3309	307	33	maps	map	NOUN
fuelectenerg-3309	307	34	of	of	ADP
fuelectenerg-3309	307	35	theorem	theorem	NOUN
fuelectenerg-3309	307	36	2	2	NUM
fuelectenerg-3309	307	37	.	.	PUNCT
fuelectenerg-3309	308	1	first	first	ADV
fuelectenerg-3309	308	2	,	,	PUNCT
fuelectenerg-3309	308	3	we	we	PRON
fuelectenerg-3309	308	4	modify	modify	VERB
fuelectenerg-3309	308	5	theorem	theorem	NOUN
fuelectenerg-3309	308	6	2	2	NUM
fuelectenerg-3309	308	7	as	as	SCONJ
fuelectenerg-3309	308	8	follows	follow	VERB
fuelectenerg-3309	308	9	:	:	PUNCT
fuelectenerg-3309	308	10	theorem	theorem	NOUN
fuelectenerg-3309	308	11	3	3	NUM
fuelectenerg-3309	308	12	for	for	ADP
fuelectenerg-3309	308	13	any	any	DET
fuelectenerg-3309	308	14	natural	natural	ADJ
fuelectenerg-3309	308	15	number	number	NOUN
fuelectenerg-3309	308	16	m	m	NOUN
fuelectenerg-3309	308	17	,	,	PUNCT
fuelectenerg-3309	308	18	let	let	VERB
fuelectenerg-3309	308	19	(	(	PUNCT
fuelectenerg-3309	308	20	ρ	ρ	PROPN
fuelectenerg-3309	308	21	,	,	PUNCT
fuelectenerg-3309	308	22	s	s	PART
fuelectenerg-3309	308	23	)	)	PUNCT
fuelectenerg-3309	308	24	∈	∈	PROPN
fuelectenerg-3309	308	25	p	p	NOUN
fuelectenerg-3309	308	26	(	(	PUNCT
fuelectenerg-3309	308	27	m)×	m)×	X
fuelectenerg-3309	308	28	s(m	s(m	PROPN
fuelectenerg-3309	308	29	)	)	PUNCT
fuelectenerg-3309	308	30	be	be	VERB
fuelectenerg-3309	308	31	as	as	ADP
fuelectenerg-3309	308	32	in	in	ADP
fuelectenerg-3309	308	33	theorem	theorem	NOUN
fuelectenerg-3309	308	34	2	2	NUM
fuelectenerg-3309	308	35	and	and	CCONJ
fuelectenerg-3309	308	36	em	em	PRON
fuelectenerg-3309	308	37	=	=	PUNCT
fuelectenerg-3309	308	38	{	{	PUNCT
fuelectenerg-3309	308	39	en	en	X
fuelectenerg-3309	308	40	:	:	PUNCT
fuelectenerg-3309	308	41	=	=	SYM
fuelectenerg-3309	308	42	(	(	PUNCT
fuelectenerg-3309	308	43	en,1	en,1	PROPN
fuelectenerg-3309	308	44	,	,	PUNCT
fuelectenerg-3309	308	45	...	...	PUNCT
fuelectenerg-3309	308	46	,	,	PUNCT
fuelectenerg-3309	308	47	en	en	X
fuelectenerg-3309	308	48	,	,	PUNCT
fuelectenerg-3309	308	49	m	m	NOUN
fuelectenerg-3309	308	50	)	)	PUNCT
fuelectenerg-3309	308	51	:	:	PUNCT
fuelectenerg-3309	309	1	n	n	X
fuelectenerg-3309	309	2	=	=	SYM
fuelectenerg-3309	309	3	{	{	PUNCT
fuelectenerg-3309	309	4	0	0	NUM
fuelectenerg-3309	309	5	,	,	PUNCT
fuelectenerg-3309	309	6	...	...	PUNCT
fuelectenerg-3309	309	7	,	,	PUNCT
fuelectenerg-3309	309	8	2	2	NUM
fuelectenerg-3309	309	9	m	m	NOUN
fuelectenerg-3309	309	10	−	−	NOUN
fuelectenerg-3309	309	11	1	1	NUM
fuelectenerg-3309	309	12	}	}	PUNCT
fuelectenerg-3309	309	13	}	}	PUNCT
fuelectenerg-3309	309	14	be	be	AUX
fuelectenerg-3309	309	15	the	the	DET
fuelectenerg-3309	309	16	set	set	NOUN
fuelectenerg-3309	309	17	of	of	ADP
fuelectenerg-3309	309	18	all	all	DET
fuelectenerg-3309	309	19	m	m	NOUN
fuelectenerg-3309	309	20	-	-	PUNCT
fuelectenerg-3309	309	21	bit	bit	NOUN
fuelectenerg-3309	309	22	arrays	array	VERB
fuelectenerg-3309	309	23	.	.	PUNCT
fuelectenerg-3309	310	1	then	then	ADV
fuelectenerg-3309	310	2	:	:	PUNCT
fuelectenerg-3309	310	3	(	(	PUNCT
fuelectenerg-3309	310	4	i	i	NOUN
fuelectenerg-3309	310	5	)	)	PUNCT
fuelectenerg-3309	310	6	the	the	DET
fuelectenerg-3309	310	7	map	map	NOUN
fuelectenerg-3309	310	8	tρ	tρ	VERB
fuelectenerg-3309	310	9	,	,	PUNCT
fuelectenerg-3309	310	10	σ	σ	PROPN
fuelectenerg-3309	310	11	:	:	PUNCT
fuelectenerg-3309	310	12	em	em	PRON
fuelectenerg-3309	310	13	→	→	PUNCT
fuelectenerg-3309	310	14	em	em	PRON
fuelectenerg-3309	310	15	such	such	ADJ
fuelectenerg-3309	310	16	that	that	PRON
fuelectenerg-3309	310	17	for	for	ADP
fuelectenerg-3309	310	18	any	any	DET
fuelectenerg-3309	310	19	j	j	NOUN
fuelectenerg-3309	310	20	=	=	SYM
fuelectenerg-3309	310	21	1	1	NUM
fuelectenerg-3309	310	22	,	,	PUNCT
fuelectenerg-3309	310	23	...	...	PUNCT
fuelectenerg-3309	310	24	,	,	PUNCT
fuelectenerg-3309	310	25	m	m	AUX
fuelectenerg-3309	310	26	we	we	PRON
fuelectenerg-3309	310	27	have	have	VERB
fuelectenerg-3309	310	28	tρ	tρ	PROPN
fuelectenerg-3309	310	29	,	,	PUNCT
fuelectenerg-3309	310	30	s(en)j	s(en)j	PROPN
fuelectenerg-3309	310	31	=	=	SYM
fuelectenerg-3309	310	32	∣∣en	∣∣en	PROPN
fuelectenerg-3309	310	33	,	,	PUNCT
fuelectenerg-3309	310	34	ρj	ρj	PRON
fuelectenerg-3309	310	35	−	−	PROPN
fuelectenerg-3309	310	36	(	(	PUNCT
fuelectenerg-3309	310	37	1−	1−	NUM
fuelectenerg-3309	310	38	δj	δj	NOUN
fuelectenerg-3309	310	39	,	,	PUNCT
fuelectenerg-3309	310	40	s(j))en	s(j))en	NOUN
fuelectenerg-3309	310	41	,	,	PUNCT
fuelectenerg-3309	310	42	ρs(j	ρs(j	NUM
fuelectenerg-3309	310	43	)	)	PUNCT
fuelectenerg-3309	310	44	∣∣	∣∣	NUM
fuelectenerg-3309	310	45	is	be	AUX
fuelectenerg-3309	310	46	a	a	DET
fuelectenerg-3309	310	47	bijection	bijection	NOUN
fuelectenerg-3309	310	48	.	.	PUNCT
fuelectenerg-3309	311	1	(	(	PUNCT
fuelectenerg-3309	311	2	ii	ii	NOUN
fuelectenerg-3309	311	3	)	)	PUNCT
fuelectenerg-3309	311	4	for	for	ADP
fuelectenerg-3309	311	5	any	any	DET
fuelectenerg-3309	311	6	permutation	permutation	NOUN
fuelectenerg-3309	311	7	τ	τ	X
fuelectenerg-3309	311	8	∈	∈	PROPN
fuelectenerg-3309	312	1	p	p	X
fuelectenerg-3309	312	2	(	(	PUNCT
fuelectenerg-3309	312	3	m	m	NOUN
fuelectenerg-3309	312	4	)	)	PUNCT
fuelectenerg-3309	312	5	we	we	PRON
fuelectenerg-3309	312	6	denote	denote	VERB
fuelectenerg-3309	312	7	by	by	ADP
fuelectenerg-3309	312	8	lτ	lτ	X
fuelectenerg-3309	312	9	(	(	PUNCT
fuelectenerg-3309	312	10	en	en	X
fuelectenerg-3309	312	11	)	)	PUNCT
fuelectenerg-3309	312	12	=	=	SYM
fuelectenerg-3309	312	13	(	(	PUNCT
fuelectenerg-3309	312	14	en	en	X
fuelectenerg-3309	312	15	,	,	PUNCT
fuelectenerg-3309	312	16	τ(1	τ(1	PROPN
fuelectenerg-3309	312	17	)	)	PUNCT
fuelectenerg-3309	312	18	,	,	PUNCT
fuelectenerg-3309	312	19	...	...	PUNCT
fuelectenerg-3309	312	20	,	,	PUNCT
fuelectenerg-3309	312	21	en	en	X
fuelectenerg-3309	312	22	,	,	PUNCT
fuelectenerg-3309	312	23	τ(m	τ(m	PROPN
fuelectenerg-3309	312	24	)	)	PUNCT
fuelectenerg-3309	312	25	)	)	PUNCT
fuelectenerg-3309	312	26	the	the	DET
fuelectenerg-3309	312	27	element	element	NOUN
fuelectenerg-3309	312	28	of	of	ADP
fuelectenerg-3309	312	29	em	em	PRON
fuelectenerg-3309	312	30	obtained	obtain	VERB
fuelectenerg-3309	312	31	from	from	ADP
fuelectenerg-3309	312	32	shuffling	shuffle	VERB
fuelectenerg-3309	312	33	en	en	ADV
fuelectenerg-3309	312	34	by	by	ADP
fuelectenerg-3309	312	35	the	the	DET
fuelectenerg-3309	312	36	permutation	permutation	NOUN
fuelectenerg-3309	312	37	τ	τ	X
fuelectenerg-3309	312	38	.	.	PUNCT
fuelectenerg-3309	313	1	then	then	ADV
fuelectenerg-3309	313	2	lτtρ	lτtρ	PROPN
fuelectenerg-3309	313	3	,	,	PUNCT
fuelectenerg-3309	313	4	σ	σ	PROPN
fuelectenerg-3309	313	5	:	:	PUNCT
fuelectenerg-3309	313	6	em	em	PRON
fuelectenerg-3309	313	7	→	→	PUNCT
fuelectenerg-3309	313	8	em	em	PRON
fuelectenerg-3309	313	9	is	be	AUX
fuelectenerg-3309	313	10	a	a	DET
fuelectenerg-3309	313	11	bijection	bijection	NOUN
fuelectenerg-3309	313	12	too	too	ADV
fuelectenerg-3309	313	13	.	.	PUNCT
fuelectenerg-3309	314	1	proof	proof	NOUN
fuelectenerg-3309	314	2	:	:	PUNCT
fuelectenerg-3309	314	3	(	(	PUNCT
fuelectenerg-3309	314	4	i	i	NOUN
fuelectenerg-3309	314	5	)	)	PUNCT
fuelectenerg-3309	314	6	.	.	PUNCT
fuelectenerg-3309	315	1	it	it	PRON
fuelectenerg-3309	315	2	is	be	AUX
fuelectenerg-3309	315	3	a	a	DET
fuelectenerg-3309	315	4	direct	direct	ADJ
fuelectenerg-3309	315	5	consequence	consequence	NOUN
fuelectenerg-3309	315	6	of	of	ADP
fuelectenerg-3309	315	7	theorem	theorem	NOUN
fuelectenerg-3309	315	8	2	2	NUM
fuelectenerg-3309	315	9	for	for	ADP
fuelectenerg-3309	315	10	q	q	NOUN
fuelectenerg-3309	315	11	=	=	SYM
fuelectenerg-3309	315	12	2	2	NUM
fuelectenerg-3309	315	13	.	.	PUNCT
fuelectenerg-3309	315	14	(	(	PUNCT
fuelectenerg-3309	315	15	ii	ii	NOUN
fuelectenerg-3309	315	16	)	)	PUNCT
fuelectenerg-3309	315	17	it	it	PRON
fuelectenerg-3309	315	18	is	be	AUX
fuelectenerg-3309	315	19	immediate	immediate	ADJ
fuelectenerg-3309	315	20	.	.	PUNCT
fuelectenerg-3309	316	1	example	example	NOUN
fuelectenerg-3309	316	2	7	7	NUM
fuelectenerg-3309	316	3	the	the	DET
fuelectenerg-3309	316	4	feynman	feynman	PROPN
fuelectenerg-3309	316	5	gate	gate	PROPN
fuelectenerg-3309	316	6	.	.	PUNCT
fuelectenerg-3309	317	1	it	it	PRON
fuelectenerg-3309	317	2	is	be	AUX
fuelectenerg-3309	317	3	a	a	DET
fuelectenerg-3309	317	4	2	2	NUM
fuelectenerg-3309	317	5	-	-	PUNCT
fuelectenerg-3309	317	6	bit	bit	NOUN
fuelectenerg-3309	317	7	reversible	reversible	ADJ
fuelectenerg-3309	317	8	map	map	NOUN
fuelectenerg-3309	317	9	such	such	ADJ
fuelectenerg-3309	317	10	that	that	SCONJ
fuelectenerg-3309	317	11	(	(	PUNCT
fuelectenerg-3309	317	12	0	0	NUM
fuelectenerg-3309	317	13	,	,	PUNCT
fuelectenerg-3309	317	14	0	0	NUM
fuelectenerg-3309	317	15	)	)	PUNCT
fuelectenerg-3309	317	16	→	→	SYM
fuelectenerg-3309	317	17	(	(	PUNCT
fuelectenerg-3309	317	18	0	0	NUM
fuelectenerg-3309	317	19	,	,	PUNCT
fuelectenerg-3309	317	20	0	0	NUM
fuelectenerg-3309	317	21	)	)	PUNCT
fuelectenerg-3309	317	22	,	,	PUNCT
fuelectenerg-3309	317	23	(	(	PUNCT
fuelectenerg-3309	317	24	0	0	NUM
fuelectenerg-3309	317	25	,	,	PUNCT
fuelectenerg-3309	317	26	1	1	NUM
fuelectenerg-3309	317	27	)	)	PUNCT
fuelectenerg-3309	317	28	→	→	SYM
fuelectenerg-3309	317	29	(	(	PUNCT
fuelectenerg-3309	317	30	0	0	NUM
fuelectenerg-3309	317	31	,	,	PUNCT
fuelectenerg-3309	317	32	1	1	NUM
fuelectenerg-3309	317	33	)	)	PUNCT
fuelectenerg-3309	317	34	,	,	PUNCT
fuelectenerg-3309	317	35	(	(	PUNCT
fuelectenerg-3309	317	36	1	1	NUM
fuelectenerg-3309	317	37	,	,	PUNCT
fuelectenerg-3309	317	38	0	0	NUM
fuelectenerg-3309	317	39	)	)	PUNCT
fuelectenerg-3309	317	40	→	→	SYM
fuelectenerg-3309	317	41	(	(	PUNCT
fuelectenerg-3309	317	42	1	1	NUM
fuelectenerg-3309	317	43	,	,	PUNCT
fuelectenerg-3309	317	44	1	1	NUM
fuelectenerg-3309	317	45	)	)	PUNCT
fuelectenerg-3309	317	46	and	and	CCONJ
fuelectenerg-3309	317	47	(	(	PUNCT
fuelectenerg-3309	317	48	1	1	NUM
fuelectenerg-3309	317	49	,	,	PUNCT
fuelectenerg-3309	317	50	1	1	NUM
fuelectenerg-3309	317	51	)	)	PUNCT
fuelectenerg-3309	317	52	→	→	X
fuelectenerg-3309	317	53	(	(	PUNCT
fuelectenerg-3309	317	54	1	1	NUM
fuelectenerg-3309	317	55	,	,	PUNCT
fuelectenerg-3309	317	56	0	0	NUM
fuelectenerg-3309	317	57	)	)	PUNCT
fuelectenerg-3309	317	58	.	.	PUNCT
fuelectenerg-3309	318	1	according	accord	VERB
fuelectenerg-3309	318	2	to	to	ADP
fuelectenerg-3309	318	3	theorem	theorem	NOUN
fuelectenerg-3309	318	4	3	3	NUM
fuelectenerg-3309	318	5	,	,	PUNCT
fuelectenerg-3309	318	6	this	this	DET
fuelectenerg-3309	318	7	gate	gate	NOUN
fuelectenerg-3309	318	8	corresponds	correspond	VERB
fuelectenerg-3309	318	9	to	to	ADP
fuelectenerg-3309	318	10	the	the	DET
fuelectenerg-3309	318	11	map	map	NOUN
fuelectenerg-3309	318	12	tρ	tρ	PROPN
fuelectenerg-3309	318	13	,	,	PUNCT
fuelectenerg-3309	318	14	σ	σ	PROPN
fuelectenerg-3309	318	15	,	,	PUNCT
fuelectenerg-3309	318	16	where	where	SCONJ
fuelectenerg-3309	318	17	ρ	ρ	NOUN
fuelectenerg-3309	318	18	=	=	SYM
fuelectenerg-3309	318	19	(	(	PUNCT
fuelectenerg-3309	318	20	1	1	NUM
fuelectenerg-3309	318	21	,	,	PUNCT
fuelectenerg-3309	318	22	2	2	NUM
fuelectenerg-3309	318	23	)	)	PUNCT
fuelectenerg-3309	318	24	and	and	CCONJ
fuelectenerg-3309	318	25	σ	σ	NUM
fuelectenerg-3309	318	26	=	=	SYM
fuelectenerg-3309	318	27	(	(	PUNCT
fuelectenerg-3309	318	28	1	1	NUM
fuelectenerg-3309	318	29	,	,	PUNCT
fuelectenerg-3309	318	30	1	1	NUM
fuelectenerg-3309	318	31	)	)	PUNCT
fuelectenerg-3309	318	32	.	.	PUNCT
fuelectenerg-3309	319	1	250	250	NUM
fuelectenerg-3309	319	2	c.	c.	PROPN
fuelectenerg-3309	319	3	karanikas	karanikas	PROPN
fuelectenerg-3309	319	4	,	,	PUNCT
fuelectenerg-3309	319	5	n.	n.	PROPN
fuelectenerg-3309	319	6	atreas	atreas	PROPN
fuelectenerg-3309	319	7	enumeration	enumeration	PROPN
fuelectenerg-3309	319	8	and	and	CCONJ
fuelectenerg-3309	319	9	coding	code	VERB
fuelectenerg-3309	319	10	permutations	permutation	NOUN
fuelectenerg-3309	319	11	and	and	CCONJ
fuelectenerg-3309	319	12	reversible	reversible	ADJ
fuelectenerg-3309	319	13	logical	logical	ADJ
fuelectenerg-3309	319	14	circuits	circuit	NOUN
fuelectenerg-3309	319	15	251	251	NUM
fuelectenerg-3309	319	16	12	12	NUM
fuelectenerg-3309	319	17	n.	n.	NOUN
fuelectenerg-3309	319	18	atreas	atreas	PROPN
fuelectenerg-3309	319	19	and	and	CCONJ
fuelectenerg-3309	319	20	c.	c.	PROPN
fuelectenerg-3309	319	21	karanikas	karanikas	PROPN
fuelectenerg-3309	319	22	in	in	ADP
fuelectenerg-3309	319	23	a	a	DET
fuelectenerg-3309	319	24	different	different	ADJ
fuelectenerg-3309	319	25	notation	notation	NOUN
fuelectenerg-3309	319	26	this	this	DET
fuelectenerg-3309	319	27	gate	gate	NOUN
fuelectenerg-3309	319	28	can	can	AUX
fuelectenerg-3309	319	29	be	be	AUX
fuelectenerg-3309	319	30	uniquely	uniquely	ADV
fuelectenerg-3309	319	31	described	describe	VERB
fuelectenerg-3309	319	32	by	by	ADP
fuelectenerg-3309	319	33	a	a	DET
fuelectenerg-3309	319	34	matrix	matrix	NOUN
fuelectenerg-3309	319	35	in	in	ADP
fuelectenerg-3309	319	36	the	the	DET
fuelectenerg-3309	319	37	class	class	NOUN
fuelectenerg-3309	319	38	z2	z2	NOUN
fuelectenerg-3309	319	39	associated	associate	VERB
fuelectenerg-3309	319	40	with	with	ADP
fuelectenerg-3309	319	41	the	the	DET
fuelectenerg-3309	319	42	above	above	ADJ
fuelectenerg-3309	319	43	pair	pair	NOUN
fuelectenerg-3309	319	44	(	(	PUNCT
fuelectenerg-3309	319	45	ρ	ρ	PROPN
fuelectenerg-3309	319	46	,	,	PUNCT
fuelectenerg-3309	319	47	s	s	PART
fuelectenerg-3309	319	48	)	)	PUNCT
fuelectenerg-3309	319	49	∈	∈	PROPN
fuelectenerg-3309	319	50	p	p	NOUN
fuelectenerg-3309	319	51	(	(	PUNCT
fuelectenerg-3309	319	52	2)×	2)×	NUM
fuelectenerg-3309	319	53	s(2	s(2	NOUN
fuelectenerg-3309	319	54	)	)	PUNCT
fuelectenerg-3309	319	55	(	(	PUNCT
fuelectenerg-3309	319	56	see	see	VERB
fuelectenerg-3309	319	57	definition	definition	NOUN
fuelectenerg-3309	319	58	1	1	NUM
fuelectenerg-3309	319	59	or	or	CCONJ
fuelectenerg-3309	319	60	example	example	NOUN
fuelectenerg-3309	319	61	4	4	NUM
fuelectenerg-3309	319	62	)	)	PUNCT
fuelectenerg-3309	319	63	zρ	zρ	NOUN
fuelectenerg-3309	319	64	,	,	PUNCT
fuelectenerg-3309	319	65	s	s	PART
fuelectenerg-3309	319	66	=	=	PUNCT
fuelectenerg-3309	319	67	(	(	PUNCT
fuelectenerg-3309	319	68	1	1	NUM
fuelectenerg-3309	319	69	1	1	NUM
fuelectenerg-3309	319	70	0	0	NUM
fuelectenerg-3309	319	71	1	1	NUM
fuelectenerg-3309	319	72	)	)	PUNCT
fuelectenerg-3309	319	73	.	.	PUNCT
fuelectenerg-3309	320	1	also	also	ADV
fuelectenerg-3309	320	2	,	,	PUNCT
fuelectenerg-3309	320	3	in	in	ADP
fuelectenerg-3309	320	4	a	a	DET
fuelectenerg-3309	320	5	different	different	ADJ
fuelectenerg-3309	320	6	notation	notation	NOUN
fuelectenerg-3309	320	7	this	this	DET
fuelectenerg-3309	320	8	gate	gate	NOUN
fuelectenerg-3309	320	9	can	can	AUX
fuelectenerg-3309	320	10	be	be	AUX
fuelectenerg-3309	320	11	described	describe	VERB
fuelectenerg-3309	320	12	by	by	ADP
fuelectenerg-3309	320	13	the	the	DET
fuelectenerg-3309	320	14	following	follow	VERB
fuelectenerg-3309	320	15	4×	4×	NOUN
fuelectenerg-3309	320	16	4	4	NUM
fuelectenerg-3309	320	17	matrix	matrix	NOUN
fuelectenerg-3309	320	18	(	(	PUNCT
fuelectenerg-3309	320	19	by	by	ADP
fuelectenerg-3309	320	20	concatenating	concatenate	VERB
fuelectenerg-3309	320	21	the	the	DET
fuelectenerg-3309	320	22	corresponding	corresponding	ADJ
fuelectenerg-3309	320	23	inputs	input	NOUN
fuelectenerg-3309	320	24	and	and	CCONJ
fuelectenerg-3309	320	25	outputs	output	NOUN
fuelectenerg-3309	320	26	)	)	PUNCT
fuelectenerg-3309	320	27			NOUN
fuelectenerg-3309	320	28			NOUN
fuelectenerg-3309	320	29	0	0	NUM
fuelectenerg-3309	320	30	0	0	NUM
fuelectenerg-3309	320	31	0	0	NUM
fuelectenerg-3309	320	32	0	0	NUM
fuelectenerg-3309	320	33	0	0	NUM
fuelectenerg-3309	320	34	1	1	NUM
fuelectenerg-3309	320	35	0	0	NUM
fuelectenerg-3309	320	36	1	1	NUM
fuelectenerg-3309	320	37	1	1	NUM
fuelectenerg-3309	320	38	0	0	NUM
fuelectenerg-3309	320	39	1	1	NUM
fuelectenerg-3309	320	40	1	1	NUM
fuelectenerg-3309	320	41	1	1	NUM
fuelectenerg-3309	320	42	1	1	NUM
fuelectenerg-3309	320	43	1	1	NUM
fuelectenerg-3309	320	44	0	0	NUM
fuelectenerg-3309	320	45			PROPN
fuelectenerg-3309	320	46			PROPN
fuelectenerg-3309	320	47	.	.	PUNCT
fuelectenerg-3309	321	1	example	example	NOUN
fuelectenerg-3309	321	2	8	8	NUM
fuelectenerg-3309	321	3	the	the	DET
fuelectenerg-3309	321	4	double	double	ADJ
fuelectenerg-3309	321	5	feynman	feynman	PROPN
fuelectenerg-3309	321	6	gate	gate	NOUN
fuelectenerg-3309	321	7	.	.	PUNCT
fuelectenerg-3309	322	1	it	it	PRON
fuelectenerg-3309	322	2	is	be	AUX
fuelectenerg-3309	322	3	a	a	DET
fuelectenerg-3309	322	4	reversible	reversible	ADJ
fuelectenerg-3309	322	5	map	map	NOUN
fuelectenerg-3309	322	6	on	on	ADP
fuelectenerg-3309	322	7	the	the	DET
fuelectenerg-3309	322	8	3	3	NUM
fuelectenerg-3309	322	9	bit	bit	NOUN
fuelectenerg-3309	322	10	binary	binary	NOUN
fuelectenerg-3309	322	11	arrays	array	NOUN
fuelectenerg-3309	322	12	so	so	SCONJ
fuelectenerg-3309	322	13	that	that	SCONJ
fuelectenerg-3309	322	14	(	(	PUNCT
fuelectenerg-3309	322	15	0	0	NUM
fuelectenerg-3309	322	16	,	,	PUNCT
fuelectenerg-3309	322	17	0	0	NUM
fuelectenerg-3309	322	18	,	,	PUNCT
fuelectenerg-3309	322	19	0	0	NUM
fuelectenerg-3309	322	20	)	)	PUNCT
fuelectenerg-3309	322	21	→	→	SYM
fuelectenerg-3309	322	22	(	(	PUNCT
fuelectenerg-3309	322	23	0	0	NUM
fuelectenerg-3309	322	24	,	,	PUNCT
fuelectenerg-3309	322	25	0	0	NUM
fuelectenerg-3309	322	26	,	,	PUNCT
fuelectenerg-3309	322	27	0	0	NUM
fuelectenerg-3309	322	28	)	)	PUNCT
fuelectenerg-3309	322	29	,	,	PUNCT
fuelectenerg-3309	322	30	(	(	PUNCT
fuelectenerg-3309	322	31	1	1	NUM
fuelectenerg-3309	322	32	,	,	PUNCT
fuelectenerg-3309	322	33	0	0	NUM
fuelectenerg-3309	322	34	,	,	PUNCT
fuelectenerg-3309	322	35	0	0	NUM
fuelectenerg-3309	322	36	)	)	PUNCT
fuelectenerg-3309	322	37	→	→	SYM
fuelectenerg-3309	322	38	(	(	PUNCT
fuelectenerg-3309	322	39	1	1	NUM
fuelectenerg-3309	322	40	,	,	PUNCT
fuelectenerg-3309	322	41	1	1	NUM
fuelectenerg-3309	322	42	,	,	PUNCT
fuelectenerg-3309	322	43	1	1	NUM
fuelectenerg-3309	322	44	)	)	PUNCT
fuelectenerg-3309	322	45	,	,	PUNCT
fuelectenerg-3309	322	46	(	(	PUNCT
fuelectenerg-3309	322	47	0	0	NUM
fuelectenerg-3309	322	48	,	,	PUNCT
fuelectenerg-3309	322	49	1	1	NUM
fuelectenerg-3309	322	50	,	,	PUNCT
fuelectenerg-3309	322	51	0	0	NUM
fuelectenerg-3309	322	52	)	)	PUNCT
fuelectenerg-3309	322	53	→	→	SYM
fuelectenerg-3309	322	54	(	(	PUNCT
fuelectenerg-3309	322	55	0	0	NUM
fuelectenerg-3309	322	56	,	,	PUNCT
fuelectenerg-3309	322	57	1	1	NUM
fuelectenerg-3309	322	58	,	,	PUNCT
fuelectenerg-3309	322	59	0	0	NUM
fuelectenerg-3309	322	60	)	)	PUNCT
fuelectenerg-3309	322	61	,	,	PUNCT
fuelectenerg-3309	322	62	(	(	PUNCT
fuelectenerg-3309	322	63	1	1	NUM
fuelectenerg-3309	322	64	,	,	PUNCT
fuelectenerg-3309	322	65	1	1	NUM
fuelectenerg-3309	322	66	,	,	PUNCT
fuelectenerg-3309	322	67	0	0	NUM
fuelectenerg-3309	322	68	)	)	PUNCT
fuelectenerg-3309	322	69	→	→	SYM
fuelectenerg-3309	322	70	(	(	PUNCT
fuelectenerg-3309	322	71	1	1	NUM
fuelectenerg-3309	322	72	,	,	PUNCT
fuelectenerg-3309	322	73	0	0	NUM
fuelectenerg-3309	322	74	,	,	PUNCT
fuelectenerg-3309	322	75	1	1	NUM
fuelectenerg-3309	322	76	)	)	PUNCT
fuelectenerg-3309	322	77	,	,	PUNCT
fuelectenerg-3309	322	78	(	(	PUNCT
fuelectenerg-3309	322	79	0	0	NUM
fuelectenerg-3309	322	80	,	,	PUNCT
fuelectenerg-3309	322	81	0	0	NUM
fuelectenerg-3309	322	82	,	,	PUNCT
fuelectenerg-3309	322	83	1	1	NUM
fuelectenerg-3309	322	84	)	)	PUNCT
fuelectenerg-3309	322	85	→	→	X
fuelectenerg-3309	322	86	(	(	PUNCT
fuelectenerg-3309	322	87	0	0	NUM
fuelectenerg-3309	322	88	,	,	PUNCT
fuelectenerg-3309	322	89	0	0	NUM
fuelectenerg-3309	322	90	,	,	PUNCT
fuelectenerg-3309	322	91	1	1	NUM
fuelectenerg-3309	322	92	)	)	PUNCT
fuelectenerg-3309	322	93	,	,	PUNCT
fuelectenerg-3309	322	94	(	(	PUNCT
fuelectenerg-3309	322	95	1	1	NUM
fuelectenerg-3309	322	96	,	,	PUNCT
fuelectenerg-3309	322	97	0	0	NUM
fuelectenerg-3309	322	98	,	,	PUNCT
fuelectenerg-3309	322	99	1	1	NUM
fuelectenerg-3309	322	100	)	)	PUNCT
fuelectenerg-3309	322	101	→	→	X
fuelectenerg-3309	322	102	(	(	PUNCT
fuelectenerg-3309	322	103	1	1	NUM
fuelectenerg-3309	322	104	,	,	PUNCT
fuelectenerg-3309	322	105	1	1	NUM
fuelectenerg-3309	322	106	,	,	PUNCT
fuelectenerg-3309	322	107	0	0	NUM
fuelectenerg-3309	322	108	)	)	PUNCT
fuelectenerg-3309	322	109	,	,	PUNCT
fuelectenerg-3309	322	110	(	(	PUNCT
fuelectenerg-3309	322	111	0	0	NUM
fuelectenerg-3309	322	112	,	,	PUNCT
fuelectenerg-3309	322	113	1	1	NUM
fuelectenerg-3309	322	114	,	,	PUNCT
fuelectenerg-3309	322	115	1	1	NUM
fuelectenerg-3309	322	116	)	)	PUNCT
fuelectenerg-3309	322	117	→	→	SYM
fuelectenerg-3309	322	118	(	(	PUNCT
fuelectenerg-3309	322	119	0	0	NUM
fuelectenerg-3309	322	120	,	,	PUNCT
fuelectenerg-3309	322	121	1	1	NUM
fuelectenerg-3309	322	122	,	,	PUNCT
fuelectenerg-3309	322	123	1	1	NUM
fuelectenerg-3309	322	124	)	)	PUNCT
fuelectenerg-3309	322	125	and	and	CCONJ
fuelectenerg-3309	322	126	(	(	PUNCT
fuelectenerg-3309	322	127	1	1	NUM
fuelectenerg-3309	322	128	,	,	PUNCT
fuelectenerg-3309	322	129	1	1	NUM
fuelectenerg-3309	322	130	,	,	PUNCT
fuelectenerg-3309	322	131	1	1	NUM
fuelectenerg-3309	322	132	)	)	PUNCT
fuelectenerg-3309	322	133	→	→	X
fuelectenerg-3309	322	134	(	(	PUNCT
fuelectenerg-3309	322	135	1	1	NUM
fuelectenerg-3309	322	136	,	,	PUNCT
fuelectenerg-3309	322	137	0	0	NUM
fuelectenerg-3309	322	138	,	,	PUNCT
fuelectenerg-3309	322	139	0	0	NUM
fuelectenerg-3309	322	140	)	)	PUNCT
fuelectenerg-3309	322	141	.	.	PUNCT
fuelectenerg-3309	323	1	according	accord	VERB
fuelectenerg-3309	323	2	to	to	ADP
fuelectenerg-3309	323	3	theorem	theorem	NOUN
fuelectenerg-3309	323	4	3	3	NUM
fuelectenerg-3309	323	5	,	,	PUNCT
fuelectenerg-3309	323	6	this	this	DET
fuelectenerg-3309	323	7	gate	gate	NOUN
fuelectenerg-3309	323	8	corresponds	correspond	VERB
fuelectenerg-3309	323	9	to	to	ADP
fuelectenerg-3309	323	10	the	the	DET
fuelectenerg-3309	323	11	map	map	NOUN
fuelectenerg-3309	323	12	tρ	tρ	PROPN
fuelectenerg-3309	323	13	,	,	PUNCT
fuelectenerg-3309	323	14	σ	σ	PROPN
fuelectenerg-3309	323	15	,	,	PUNCT
fuelectenerg-3309	323	16	where	where	SCONJ
fuelectenerg-3309	323	17	ρ	ρ	NOUN
fuelectenerg-3309	323	18	=	=	SYM
fuelectenerg-3309	323	19	(	(	PUNCT
fuelectenerg-3309	323	20	1	1	NUM
fuelectenerg-3309	323	21	,	,	PUNCT
fuelectenerg-3309	323	22	2	2	NUM
fuelectenerg-3309	323	23	,	,	PUNCT
fuelectenerg-3309	323	24	3	3	NUM
fuelectenerg-3309	323	25	)	)	PUNCT
fuelectenerg-3309	323	26	and	and	CCONJ
fuelectenerg-3309	323	27	σ	σ	NUM
fuelectenerg-3309	323	28	=	=	SYM
fuelectenerg-3309	323	29	(	(	PUNCT
fuelectenerg-3309	323	30	1	1	NUM
fuelectenerg-3309	323	31	,	,	PUNCT
fuelectenerg-3309	323	32	1	1	NUM
fuelectenerg-3309	323	33	,	,	PUNCT
fuelectenerg-3309	323	34	1	1	NUM
fuelectenerg-3309	323	35	)	)	PUNCT
fuelectenerg-3309	323	36	.	.	PUNCT
fuelectenerg-3309	324	1	in	in	ADP
fuelectenerg-3309	324	2	a	a	DET
fuelectenerg-3309	324	3	different	different	ADJ
fuelectenerg-3309	324	4	notation	notation	NOUN
fuelectenerg-3309	324	5	,	,	PUNCT
fuelectenerg-3309	324	6	this	this	DET
fuelectenerg-3309	324	7	gate	gate	NOUN
fuelectenerg-3309	324	8	can	can	AUX
fuelectenerg-3309	324	9	be	be	AUX
fuelectenerg-3309	324	10	uniquely	uniquely	ADV
fuelectenerg-3309	324	11	described	describe	VERB
fuelectenerg-3309	324	12	by	by	ADP
fuelectenerg-3309	324	13	a	a	DET
fuelectenerg-3309	324	14	matrix	matrix	NOUN
fuelectenerg-3309	324	15	in	in	ADP
fuelectenerg-3309	324	16	the	the	DET
fuelectenerg-3309	324	17	class	class	NOUN
fuelectenerg-3309	324	18	z3	z3	PROPN
fuelectenerg-3309	324	19	associated	associate	VERB
fuelectenerg-3309	324	20	with	with	ADP
fuelectenerg-3309	324	21	the	the	DET
fuelectenerg-3309	324	22	above	above	ADJ
fuelectenerg-3309	324	23	pair	pair	NOUN
fuelectenerg-3309	324	24	(	(	PUNCT
fuelectenerg-3309	324	25	ρ	ρ	PROPN
fuelectenerg-3309	324	26	,	,	PUNCT
fuelectenerg-3309	324	27	s	s	PART
fuelectenerg-3309	324	28	)	)	PUNCT
fuelectenerg-3309	324	29	∈	∈	PROPN
fuelectenerg-3309	324	30	p	p	NOUN
fuelectenerg-3309	324	31	(	(	PUNCT
fuelectenerg-3309	324	32	3	3	NUM
fuelectenerg-3309	324	33	)	)	PUNCT
fuelectenerg-3309	324	34	×	×	NOUN
fuelectenerg-3309	324	35	s(3	s(3	PROPN
fuelectenerg-3309	324	36	)	)	PUNCT
fuelectenerg-3309	324	37	(	(	PUNCT
fuelectenerg-3309	324	38	see	see	VERB
fuelectenerg-3309	324	39	the	the	DET
fuelectenerg-3309	324	40	above	above	ADJ
fuelectenerg-3309	324	41	definition	definition	NOUN
fuelectenerg-3309	324	42	1	1	NUM
fuelectenerg-3309	324	43	or	or	CCONJ
fuelectenerg-3309	324	44	example	example	NOUN
fuelectenerg-3309	324	45	4	4	NUM
fuelectenerg-3309	324	46	)	)	PUNCT
fuelectenerg-3309	324	47	zρ	zρ	NOUN
fuelectenerg-3309	324	48	,	,	PUNCT
fuelectenerg-3309	324	49	s	s	PART
fuelectenerg-3309	324	50	=	=	NOUN
fuelectenerg-3309	324	51			NOUN
fuelectenerg-3309	324	52			NOUN
fuelectenerg-3309	324	53	1	1	NUM
fuelectenerg-3309	324	54	1	1	NUM
fuelectenerg-3309	324	55	1	1	NUM
fuelectenerg-3309	324	56	0	0	NUM
fuelectenerg-3309	324	57	1	1	NUM
fuelectenerg-3309	324	58	0	0	NUM
fuelectenerg-3309	324	59	0	0	NUM
fuelectenerg-3309	324	60	0	0	NUM
fuelectenerg-3309	324	61	1	1	NUM
fuelectenerg-3309	324	62			NOUN
fuelectenerg-3309	324	63			PUNCT
fuelectenerg-3309	324	64	.	.	PUNCT
fuelectenerg-3309	325	1	also	also	ADV
fuelectenerg-3309	325	2	,	,	PUNCT
fuelectenerg-3309	325	3	in	in	ADP
fuelectenerg-3309	325	4	a	a	DET
fuelectenerg-3309	325	5	different	different	ADJ
fuelectenerg-3309	325	6	notation	notation	NOUN
fuelectenerg-3309	325	7	this	this	DET
fuelectenerg-3309	325	8	gate	gate	NOUN
fuelectenerg-3309	325	9	can	can	AUX
fuelectenerg-3309	325	10	be	be	AUX
fuelectenerg-3309	325	11	described	describe	VERB
fuelectenerg-3309	325	12	by	by	ADP
fuelectenerg-3309	325	13	the	the	DET
fuelectenerg-3309	325	14	following	follow	VERB
fuelectenerg-3309	325	15	8×	8×	NUM
fuelectenerg-3309	325	16	6	6	NUM
fuelectenerg-3309	325	17	matrix	matrix	NOUN
fuelectenerg-3309	325	18	(	(	PUNCT
fuelectenerg-3309	325	19	by	by	ADP
fuelectenerg-3309	325	20	concatenating	concatenate	VERB
fuelectenerg-3309	325	21	the	the	DET
fuelectenerg-3309	325	22	corresponding	corresponding	ADJ
fuelectenerg-3309	325	23	inputs	input	NOUN
fuelectenerg-3309	325	24	and	and	CCONJ
fuelectenerg-3309	325	25	outputs	output	NOUN
fuelectenerg-3309	325	26	)	)	PUNCT
fuelectenerg-3309	325	27			PROPN
fuelectenerg-3309	325	28			PROPN
fuelectenerg-3309	325	29	0	0	NUM
fuelectenerg-3309	325	30	0	0	NUM
fuelectenerg-3309	325	31	0	0	NUM
fuelectenerg-3309	325	32	0	0	NUM
fuelectenerg-3309	325	33	0	0	NUM
fuelectenerg-3309	325	34	0	0	NUM
fuelectenerg-3309	325	35	0	0	NUM
fuelectenerg-3309	325	36	0	0	NUM
fuelectenerg-3309	326	1	1	1	NUM
fuelectenerg-3309	326	2	0	0	NUM
fuelectenerg-3309	326	3	0	0	NUM
fuelectenerg-3309	326	4	1	1	NUM
fuelectenerg-3309	326	5	0	0	NUM
fuelectenerg-3309	326	6	1	1	NUM
fuelectenerg-3309	326	7	0	0	NUM
fuelectenerg-3309	326	8	0	0	NUM
fuelectenerg-3309	326	9	1	1	NUM
fuelectenerg-3309	326	10	0	0	NUM
fuelectenerg-3309	326	11	0	0	NUM
fuelectenerg-3309	326	12	1	1	NUM
fuelectenerg-3309	326	13	1	1	NUM
fuelectenerg-3309	326	14	0	0	NUM
fuelectenerg-3309	326	15	1	1	NUM
fuelectenerg-3309	326	16	1	1	NUM
fuelectenerg-3309	326	17	1	1	NUM
fuelectenerg-3309	326	18	0	0	NUM
fuelectenerg-3309	326	19	0	0	NUM
fuelectenerg-3309	326	20	1	1	NUM
fuelectenerg-3309	326	21	1	1	NUM
fuelectenerg-3309	326	22	1	1	NUM
fuelectenerg-3309	326	23	1	1	NUM
fuelectenerg-3309	326	24	0	0	NUM
fuelectenerg-3309	326	25	1	1	NUM
fuelectenerg-3309	326	26	1	1	NUM
fuelectenerg-3309	326	27	1	1	NUM
fuelectenerg-3309	326	28	0	0	NUM
fuelectenerg-3309	326	29	1	1	NUM
fuelectenerg-3309	326	30	1	1	NUM
fuelectenerg-3309	326	31	0	0	NUM
fuelectenerg-3309	326	32	1	1	NUM
fuelectenerg-3309	326	33	0	0	NUM
fuelectenerg-3309	326	34	1	1	NUM
fuelectenerg-3309	326	35	1	1	NUM
fuelectenerg-3309	326	36	1	1	NUM
fuelectenerg-3309	326	37	1	1	NUM
fuelectenerg-3309	326	38	1	1	NUM
fuelectenerg-3309	326	39	0	0	NUM
fuelectenerg-3309	326	40	0	0	NUM
fuelectenerg-3309	326	41			PUNCT
fuelectenerg-3309	327	1			NOUN
fuelectenerg-3309	327	2	.	.	PUNCT
fuelectenerg-3309	328	1	252	252	NUM
fuelectenerg-3309	328	2	c.	c.	PROPN
fuelectenerg-3309	328	3	karanikas	karanikas	PROPN
fuelectenerg-3309	328	4	,	,	PUNCT
fuelectenerg-3309	328	5	n.	n.	PROPN
fuelectenerg-3309	328	6	atreas	atreas	PROPN
fuelectenerg-3309	328	7	enumeration	enumeration	PROPN
fuelectenerg-3309	328	8	and	and	CCONJ
fuelectenerg-3309	328	9	coding	code	VERB
fuelectenerg-3309	328	10	permutations	permutation	NOUN
fuelectenerg-3309	328	11	and	and	CCONJ
fuelectenerg-3309	328	12	reversible	reversible	ADJ
fuelectenerg-3309	328	13	logical	logical	ADJ
fuelectenerg-3309	328	14	circuits	circuit	NOUN
fuelectenerg-3309	328	15	253	253	NUM
fuelectenerg-3309	328	16	12	12	NUM
fuelectenerg-3309	328	17	n.	n.	NOUN
fuelectenerg-3309	328	18	atreas	atreas	PROPN
fuelectenerg-3309	328	19	and	and	CCONJ
fuelectenerg-3309	328	20	c.	c.	PROPN
fuelectenerg-3309	328	21	karanikas	karanikas	PROPN
fuelectenerg-3309	328	22	in	in	ADP
fuelectenerg-3309	328	23	a	a	DET
fuelectenerg-3309	328	24	different	different	ADJ
fuelectenerg-3309	328	25	notation	notation	NOUN
fuelectenerg-3309	328	26	this	this	DET
fuelectenerg-3309	328	27	gate	gate	NOUN
fuelectenerg-3309	328	28	can	can	AUX
fuelectenerg-3309	328	29	be	be	AUX
fuelectenerg-3309	328	30	uniquely	uniquely	ADV
fuelectenerg-3309	328	31	described	describe	VERB
fuelectenerg-3309	328	32	by	by	ADP
fuelectenerg-3309	328	33	a	a	DET
fuelectenerg-3309	328	34	matrix	matrix	NOUN
fuelectenerg-3309	328	35	in	in	ADP
fuelectenerg-3309	328	36	the	the	DET
fuelectenerg-3309	328	37	class	class	NOUN
fuelectenerg-3309	328	38	z2	z2	NOUN
fuelectenerg-3309	328	39	associated	associate	VERB
fuelectenerg-3309	328	40	with	with	ADP
fuelectenerg-3309	328	41	the	the	DET
fuelectenerg-3309	328	42	above	above	ADJ
fuelectenerg-3309	328	43	pair	pair	NOUN
fuelectenerg-3309	328	44	(	(	PUNCT
fuelectenerg-3309	328	45	ρ	ρ	PROPN
fuelectenerg-3309	328	46	,	,	PUNCT
fuelectenerg-3309	328	47	s	s	PART
fuelectenerg-3309	328	48	)	)	PUNCT
fuelectenerg-3309	328	49	∈	∈	PROPN
fuelectenerg-3309	328	50	p	p	NOUN
fuelectenerg-3309	328	51	(	(	PUNCT
fuelectenerg-3309	328	52	2)×	2)×	NUM
fuelectenerg-3309	328	53	s(2	s(2	NOUN
fuelectenerg-3309	328	54	)	)	PUNCT
fuelectenerg-3309	328	55	(	(	PUNCT
fuelectenerg-3309	328	56	see	see	VERB
fuelectenerg-3309	328	57	definition	definition	NOUN
fuelectenerg-3309	328	58	1	1	NUM
fuelectenerg-3309	328	59	or	or	CCONJ
fuelectenerg-3309	328	60	example	example	NOUN
fuelectenerg-3309	328	61	4	4	NUM
fuelectenerg-3309	328	62	)	)	PUNCT
fuelectenerg-3309	328	63	zρ	zρ	NOUN
fuelectenerg-3309	328	64	,	,	PUNCT
fuelectenerg-3309	328	65	s	s	PART
fuelectenerg-3309	328	66	=	=	PUNCT
fuelectenerg-3309	328	67	(	(	PUNCT
fuelectenerg-3309	328	68	1	1	NUM
fuelectenerg-3309	328	69	1	1	NUM
fuelectenerg-3309	328	70	0	0	NUM
fuelectenerg-3309	328	71	1	1	NUM
fuelectenerg-3309	328	72	)	)	PUNCT
fuelectenerg-3309	328	73	.	.	PUNCT
fuelectenerg-3309	329	1	also	also	ADV
fuelectenerg-3309	329	2	,	,	PUNCT
fuelectenerg-3309	329	3	in	in	ADP
fuelectenerg-3309	329	4	a	a	DET
fuelectenerg-3309	329	5	different	different	ADJ
fuelectenerg-3309	329	6	notation	notation	NOUN
fuelectenerg-3309	329	7	this	this	DET
fuelectenerg-3309	329	8	gate	gate	NOUN
fuelectenerg-3309	329	9	can	can	AUX
fuelectenerg-3309	329	10	be	be	AUX
fuelectenerg-3309	329	11	described	describe	VERB
fuelectenerg-3309	329	12	by	by	ADP
fuelectenerg-3309	329	13	the	the	DET
fuelectenerg-3309	329	14	following	follow	VERB
fuelectenerg-3309	329	15	4×	4×	NOUN
fuelectenerg-3309	329	16	4	4	NUM
fuelectenerg-3309	329	17	matrix	matrix	NOUN
fuelectenerg-3309	329	18	(	(	PUNCT
fuelectenerg-3309	329	19	by	by	ADP
fuelectenerg-3309	329	20	concatenating	concatenate	VERB
fuelectenerg-3309	329	21	the	the	DET
fuelectenerg-3309	329	22	corresponding	corresponding	ADJ
fuelectenerg-3309	329	23	inputs	input	NOUN
fuelectenerg-3309	329	24	and	and	CCONJ
fuelectenerg-3309	329	25	outputs	output	NOUN
fuelectenerg-3309	329	26	)	)	PUNCT
fuelectenerg-3309	329	27			NOUN
fuelectenerg-3309	329	28			NOUN
fuelectenerg-3309	329	29	0	0	NUM
fuelectenerg-3309	329	30	0	0	NUM
fuelectenerg-3309	329	31	0	0	NUM
fuelectenerg-3309	329	32	0	0	NUM
fuelectenerg-3309	329	33	0	0	NUM
fuelectenerg-3309	329	34	1	1	NUM
fuelectenerg-3309	329	35	0	0	NUM
fuelectenerg-3309	329	36	1	1	NUM
fuelectenerg-3309	329	37	1	1	NUM
fuelectenerg-3309	329	38	0	0	NUM
fuelectenerg-3309	329	39	1	1	NUM
fuelectenerg-3309	329	40	1	1	NUM
fuelectenerg-3309	329	41	1	1	NUM
fuelectenerg-3309	329	42	1	1	NUM
fuelectenerg-3309	329	43	1	1	NUM
fuelectenerg-3309	329	44	0	0	NUM
fuelectenerg-3309	329	45			PROPN
fuelectenerg-3309	329	46			PROPN
fuelectenerg-3309	329	47	.	.	PUNCT
fuelectenerg-3309	330	1	example	example	NOUN
fuelectenerg-3309	330	2	8	8	NUM
fuelectenerg-3309	330	3	the	the	DET
fuelectenerg-3309	330	4	double	double	ADJ
fuelectenerg-3309	330	5	feynman	feynman	PROPN
fuelectenerg-3309	330	6	gate	gate	NOUN
fuelectenerg-3309	330	7	.	.	PUNCT
fuelectenerg-3309	331	1	it	it	PRON
fuelectenerg-3309	331	2	is	be	AUX
fuelectenerg-3309	331	3	a	a	DET
fuelectenerg-3309	331	4	reversible	reversible	ADJ
fuelectenerg-3309	331	5	map	map	NOUN
fuelectenerg-3309	331	6	on	on	ADP
fuelectenerg-3309	331	7	the	the	DET
fuelectenerg-3309	331	8	3	3	NUM
fuelectenerg-3309	331	9	bit	bit	NOUN
fuelectenerg-3309	331	10	binary	binary	NOUN
fuelectenerg-3309	331	11	arrays	array	NOUN
fuelectenerg-3309	331	12	so	so	SCONJ
fuelectenerg-3309	331	13	that	that	SCONJ
fuelectenerg-3309	331	14	(	(	PUNCT
fuelectenerg-3309	331	15	0	0	NUM
fuelectenerg-3309	331	16	,	,	PUNCT
fuelectenerg-3309	331	17	0	0	NUM
fuelectenerg-3309	331	18	,	,	PUNCT
fuelectenerg-3309	331	19	0	0	NUM
fuelectenerg-3309	331	20	)	)	PUNCT
fuelectenerg-3309	331	21	→	→	SYM
fuelectenerg-3309	331	22	(	(	PUNCT
fuelectenerg-3309	331	23	0	0	NUM
fuelectenerg-3309	331	24	,	,	PUNCT
fuelectenerg-3309	331	25	0	0	NUM
fuelectenerg-3309	331	26	,	,	PUNCT
fuelectenerg-3309	331	27	0	0	NUM
fuelectenerg-3309	331	28	)	)	PUNCT
fuelectenerg-3309	331	29	,	,	PUNCT
fuelectenerg-3309	331	30	(	(	PUNCT
fuelectenerg-3309	331	31	1	1	NUM
fuelectenerg-3309	331	32	,	,	PUNCT
fuelectenerg-3309	331	33	0	0	NUM
fuelectenerg-3309	331	34	,	,	PUNCT
fuelectenerg-3309	331	35	0	0	NUM
fuelectenerg-3309	331	36	)	)	PUNCT
fuelectenerg-3309	331	37	→	→	SYM
fuelectenerg-3309	331	38	(	(	PUNCT
fuelectenerg-3309	331	39	1	1	NUM
fuelectenerg-3309	331	40	,	,	PUNCT
fuelectenerg-3309	331	41	1	1	NUM
fuelectenerg-3309	331	42	,	,	PUNCT
fuelectenerg-3309	331	43	1	1	NUM
fuelectenerg-3309	331	44	)	)	PUNCT
fuelectenerg-3309	331	45	,	,	PUNCT
fuelectenerg-3309	331	46	(	(	PUNCT
fuelectenerg-3309	331	47	0	0	NUM
fuelectenerg-3309	331	48	,	,	PUNCT
fuelectenerg-3309	331	49	1	1	NUM
fuelectenerg-3309	331	50	,	,	PUNCT
fuelectenerg-3309	331	51	0	0	NUM
fuelectenerg-3309	331	52	)	)	PUNCT
fuelectenerg-3309	331	53	→	→	SYM
fuelectenerg-3309	331	54	(	(	PUNCT
fuelectenerg-3309	331	55	0	0	NUM
fuelectenerg-3309	331	56	,	,	PUNCT
fuelectenerg-3309	331	57	1	1	NUM
fuelectenerg-3309	331	58	,	,	PUNCT
fuelectenerg-3309	331	59	0	0	NUM
fuelectenerg-3309	331	60	)	)	PUNCT
fuelectenerg-3309	331	61	,	,	PUNCT
fuelectenerg-3309	331	62	(	(	PUNCT
fuelectenerg-3309	331	63	1	1	NUM
fuelectenerg-3309	331	64	,	,	PUNCT
fuelectenerg-3309	331	65	1	1	NUM
fuelectenerg-3309	331	66	,	,	PUNCT
fuelectenerg-3309	331	67	0	0	NUM
fuelectenerg-3309	331	68	)	)	PUNCT
fuelectenerg-3309	331	69	→	→	SYM
fuelectenerg-3309	331	70	(	(	PUNCT
fuelectenerg-3309	331	71	1	1	NUM
fuelectenerg-3309	331	72	,	,	PUNCT
fuelectenerg-3309	331	73	0	0	NUM
fuelectenerg-3309	331	74	,	,	PUNCT
fuelectenerg-3309	331	75	1	1	NUM
fuelectenerg-3309	331	76	)	)	PUNCT
fuelectenerg-3309	331	77	,	,	PUNCT
fuelectenerg-3309	331	78	(	(	PUNCT
fuelectenerg-3309	331	79	0	0	NUM
fuelectenerg-3309	331	80	,	,	PUNCT
fuelectenerg-3309	331	81	0	0	NUM
fuelectenerg-3309	331	82	,	,	PUNCT
fuelectenerg-3309	331	83	1	1	NUM
fuelectenerg-3309	331	84	)	)	PUNCT
fuelectenerg-3309	331	85	→	→	X
fuelectenerg-3309	331	86	(	(	PUNCT
fuelectenerg-3309	331	87	0	0	NUM
fuelectenerg-3309	331	88	,	,	PUNCT
fuelectenerg-3309	331	89	0	0	NUM
fuelectenerg-3309	331	90	,	,	PUNCT
fuelectenerg-3309	331	91	1	1	NUM
fuelectenerg-3309	331	92	)	)	PUNCT
fuelectenerg-3309	331	93	,	,	PUNCT
fuelectenerg-3309	331	94	(	(	PUNCT
fuelectenerg-3309	331	95	1	1	NUM
fuelectenerg-3309	331	96	,	,	PUNCT
fuelectenerg-3309	331	97	0	0	NUM
fuelectenerg-3309	331	98	,	,	PUNCT
fuelectenerg-3309	331	99	1	1	NUM
fuelectenerg-3309	331	100	)	)	PUNCT
fuelectenerg-3309	331	101	→	→	X
fuelectenerg-3309	331	102	(	(	PUNCT
fuelectenerg-3309	331	103	1	1	NUM
fuelectenerg-3309	331	104	,	,	PUNCT
fuelectenerg-3309	331	105	1	1	NUM
fuelectenerg-3309	331	106	,	,	PUNCT
fuelectenerg-3309	331	107	0	0	NUM
fuelectenerg-3309	331	108	)	)	PUNCT
fuelectenerg-3309	331	109	,	,	PUNCT
fuelectenerg-3309	331	110	(	(	PUNCT
fuelectenerg-3309	331	111	0	0	NUM
fuelectenerg-3309	331	112	,	,	PUNCT
fuelectenerg-3309	331	113	1	1	NUM
fuelectenerg-3309	331	114	,	,	PUNCT
fuelectenerg-3309	331	115	1	1	NUM
fuelectenerg-3309	331	116	)	)	PUNCT
fuelectenerg-3309	331	117	→	→	SYM
fuelectenerg-3309	331	118	(	(	PUNCT
fuelectenerg-3309	331	119	0	0	NUM
fuelectenerg-3309	331	120	,	,	PUNCT
fuelectenerg-3309	331	121	1	1	NUM
fuelectenerg-3309	331	122	,	,	PUNCT
fuelectenerg-3309	331	123	1	1	NUM
fuelectenerg-3309	331	124	)	)	PUNCT
fuelectenerg-3309	331	125	and	and	CCONJ
fuelectenerg-3309	331	126	(	(	PUNCT
fuelectenerg-3309	331	127	1	1	NUM
fuelectenerg-3309	331	128	,	,	PUNCT
fuelectenerg-3309	331	129	1	1	NUM
fuelectenerg-3309	331	130	,	,	PUNCT
fuelectenerg-3309	331	131	1	1	NUM
fuelectenerg-3309	331	132	)	)	PUNCT
fuelectenerg-3309	331	133	→	→	X
fuelectenerg-3309	331	134	(	(	PUNCT
fuelectenerg-3309	331	135	1	1	NUM
fuelectenerg-3309	331	136	,	,	PUNCT
fuelectenerg-3309	331	137	0	0	NUM
fuelectenerg-3309	331	138	,	,	PUNCT
fuelectenerg-3309	331	139	0	0	NUM
fuelectenerg-3309	331	140	)	)	PUNCT
fuelectenerg-3309	331	141	.	.	PUNCT
fuelectenerg-3309	332	1	according	accord	VERB
fuelectenerg-3309	332	2	to	to	ADP
fuelectenerg-3309	332	3	theorem	theorem	NOUN
fuelectenerg-3309	332	4	3	3	NUM
fuelectenerg-3309	332	5	,	,	PUNCT
fuelectenerg-3309	332	6	this	this	DET
fuelectenerg-3309	332	7	gate	gate	NOUN
fuelectenerg-3309	332	8	corresponds	correspond	VERB
fuelectenerg-3309	332	9	to	to	ADP
fuelectenerg-3309	332	10	the	the	DET
fuelectenerg-3309	332	11	map	map	NOUN
fuelectenerg-3309	332	12	tρ	tρ	PROPN
fuelectenerg-3309	332	13	,	,	PUNCT
fuelectenerg-3309	332	14	σ	σ	PROPN
fuelectenerg-3309	332	15	,	,	PUNCT
fuelectenerg-3309	332	16	where	where	SCONJ
fuelectenerg-3309	332	17	ρ	ρ	NOUN
fuelectenerg-3309	332	18	=	=	SYM
fuelectenerg-3309	332	19	(	(	PUNCT
fuelectenerg-3309	332	20	1	1	NUM
fuelectenerg-3309	332	21	,	,	PUNCT
fuelectenerg-3309	332	22	2	2	NUM
fuelectenerg-3309	332	23	,	,	PUNCT
fuelectenerg-3309	332	24	3	3	NUM
fuelectenerg-3309	332	25	)	)	PUNCT
fuelectenerg-3309	332	26	and	and	CCONJ
fuelectenerg-3309	332	27	σ	σ	NUM
fuelectenerg-3309	332	28	=	=	SYM
fuelectenerg-3309	332	29	(	(	PUNCT
fuelectenerg-3309	332	30	1	1	NUM
fuelectenerg-3309	332	31	,	,	PUNCT
fuelectenerg-3309	332	32	1	1	NUM
fuelectenerg-3309	332	33	,	,	PUNCT
fuelectenerg-3309	332	34	1	1	NUM
fuelectenerg-3309	332	35	)	)	PUNCT
fuelectenerg-3309	332	36	.	.	PUNCT
fuelectenerg-3309	333	1	in	in	ADP
fuelectenerg-3309	333	2	a	a	DET
fuelectenerg-3309	333	3	different	different	ADJ
fuelectenerg-3309	333	4	notation	notation	NOUN
fuelectenerg-3309	333	5	,	,	PUNCT
fuelectenerg-3309	333	6	this	this	DET
fuelectenerg-3309	333	7	gate	gate	NOUN
fuelectenerg-3309	333	8	can	can	AUX
fuelectenerg-3309	333	9	be	be	AUX
fuelectenerg-3309	333	10	uniquely	uniquely	ADV
fuelectenerg-3309	333	11	described	describe	VERB
fuelectenerg-3309	333	12	by	by	ADP
fuelectenerg-3309	333	13	a	a	DET
fuelectenerg-3309	333	14	matrix	matrix	NOUN
fuelectenerg-3309	333	15	in	in	ADP
fuelectenerg-3309	333	16	the	the	DET
fuelectenerg-3309	333	17	class	class	NOUN
fuelectenerg-3309	333	18	z3	z3	PROPN
fuelectenerg-3309	333	19	associated	associate	VERB
fuelectenerg-3309	333	20	with	with	ADP
fuelectenerg-3309	333	21	the	the	DET
fuelectenerg-3309	333	22	above	above	ADJ
fuelectenerg-3309	333	23	pair	pair	NOUN
fuelectenerg-3309	333	24	(	(	PUNCT
fuelectenerg-3309	333	25	ρ	ρ	PROPN
fuelectenerg-3309	333	26	,	,	PUNCT
fuelectenerg-3309	333	27	s	s	PART
fuelectenerg-3309	333	28	)	)	PUNCT
fuelectenerg-3309	333	29	∈	∈	PROPN
fuelectenerg-3309	333	30	p	p	NOUN
fuelectenerg-3309	333	31	(	(	PUNCT
fuelectenerg-3309	333	32	3	3	NUM
fuelectenerg-3309	333	33	)	)	PUNCT
fuelectenerg-3309	333	34	×	×	NOUN
fuelectenerg-3309	333	35	s(3	s(3	PROPN
fuelectenerg-3309	333	36	)	)	PUNCT
fuelectenerg-3309	333	37	(	(	PUNCT
fuelectenerg-3309	333	38	see	see	VERB
fuelectenerg-3309	333	39	the	the	DET
fuelectenerg-3309	333	40	above	above	ADJ
fuelectenerg-3309	333	41	definition	definition	NOUN
fuelectenerg-3309	333	42	1	1	NUM
fuelectenerg-3309	333	43	or	or	CCONJ
fuelectenerg-3309	333	44	example	example	NOUN
fuelectenerg-3309	333	45	4	4	NUM
fuelectenerg-3309	333	46	)	)	PUNCT
fuelectenerg-3309	333	47	zρ	zρ	NOUN
fuelectenerg-3309	333	48	,	,	PUNCT
fuelectenerg-3309	333	49	s	s	PART
fuelectenerg-3309	333	50	=	=	NOUN
fuelectenerg-3309	333	51			NOUN
fuelectenerg-3309	333	52			NOUN
fuelectenerg-3309	333	53	1	1	NUM
fuelectenerg-3309	333	54	1	1	NUM
fuelectenerg-3309	333	55	1	1	NUM
fuelectenerg-3309	333	56	0	0	NUM
fuelectenerg-3309	333	57	1	1	NUM
fuelectenerg-3309	333	58	0	0	NUM
fuelectenerg-3309	333	59	0	0	NUM
fuelectenerg-3309	333	60	0	0	NUM
fuelectenerg-3309	333	61	1	1	NUM
fuelectenerg-3309	333	62			NOUN
fuelectenerg-3309	333	63			PUNCT
fuelectenerg-3309	333	64	.	.	PUNCT
fuelectenerg-3309	334	1	also	also	ADV
fuelectenerg-3309	334	2	,	,	PUNCT
fuelectenerg-3309	334	3	in	in	ADP
fuelectenerg-3309	334	4	a	a	DET
fuelectenerg-3309	334	5	different	different	ADJ
fuelectenerg-3309	334	6	notation	notation	NOUN
fuelectenerg-3309	334	7	this	this	DET
fuelectenerg-3309	334	8	gate	gate	NOUN
fuelectenerg-3309	334	9	can	can	AUX
fuelectenerg-3309	334	10	be	be	AUX
fuelectenerg-3309	334	11	described	describe	VERB
fuelectenerg-3309	334	12	by	by	ADP
fuelectenerg-3309	334	13	the	the	DET
fuelectenerg-3309	334	14	following	follow	VERB
fuelectenerg-3309	334	15	8×	8×	NUM
fuelectenerg-3309	334	16	6	6	NUM
fuelectenerg-3309	334	17	matrix	matrix	NOUN
fuelectenerg-3309	334	18	(	(	PUNCT
fuelectenerg-3309	334	19	by	by	ADP
fuelectenerg-3309	334	20	concatenating	concatenate	VERB
fuelectenerg-3309	334	21	the	the	DET
fuelectenerg-3309	334	22	corresponding	corresponding	ADJ
fuelectenerg-3309	334	23	inputs	input	NOUN
fuelectenerg-3309	334	24	and	and	CCONJ
fuelectenerg-3309	334	25	outputs	output	NOUN
fuelectenerg-3309	334	26	)	)	PUNCT
fuelectenerg-3309	334	27			PROPN
fuelectenerg-3309	334	28			PROPN
fuelectenerg-3309	334	29	0	0	NUM
fuelectenerg-3309	334	30	0	0	NUM
fuelectenerg-3309	334	31	0	0	NUM
fuelectenerg-3309	334	32	0	0	NUM
fuelectenerg-3309	334	33	0	0	NUM
fuelectenerg-3309	334	34	0	0	NUM
fuelectenerg-3309	334	35	0	0	NUM
fuelectenerg-3309	334	36	0	0	NUM
fuelectenerg-3309	335	1	1	1	NUM
fuelectenerg-3309	335	2	0	0	NUM
fuelectenerg-3309	335	3	0	0	NUM
fuelectenerg-3309	335	4	1	1	NUM
fuelectenerg-3309	335	5	0	0	NUM
fuelectenerg-3309	335	6	1	1	NUM
fuelectenerg-3309	335	7	0	0	NUM
fuelectenerg-3309	335	8	0	0	NUM
fuelectenerg-3309	335	9	1	1	NUM
fuelectenerg-3309	335	10	0	0	NUM
fuelectenerg-3309	335	11	0	0	NUM
fuelectenerg-3309	335	12	1	1	NUM
fuelectenerg-3309	335	13	1	1	NUM
fuelectenerg-3309	335	14	0	0	NUM
fuelectenerg-3309	335	15	1	1	NUM
fuelectenerg-3309	335	16	1	1	NUM
fuelectenerg-3309	335	17	1	1	NUM
fuelectenerg-3309	335	18	0	0	NUM
fuelectenerg-3309	335	19	0	0	NUM
fuelectenerg-3309	335	20	1	1	NUM
fuelectenerg-3309	335	21	1	1	NUM
fuelectenerg-3309	335	22	1	1	NUM
fuelectenerg-3309	335	23	1	1	NUM
fuelectenerg-3309	335	24	0	0	NUM
fuelectenerg-3309	335	25	1	1	NUM
fuelectenerg-3309	335	26	1	1	NUM
fuelectenerg-3309	335	27	1	1	NUM
fuelectenerg-3309	335	28	0	0	NUM
fuelectenerg-3309	335	29	1	1	NUM
fuelectenerg-3309	335	30	1	1	NUM
fuelectenerg-3309	335	31	0	0	NUM
fuelectenerg-3309	335	32	1	1	NUM
fuelectenerg-3309	335	33	0	0	NUM
fuelectenerg-3309	335	34	1	1	NUM
fuelectenerg-3309	335	35	1	1	NUM
fuelectenerg-3309	335	36	1	1	NUM
fuelectenerg-3309	335	37	1	1	NUM
fuelectenerg-3309	335	38	1	1	NUM
fuelectenerg-3309	335	39	0	0	NUM
fuelectenerg-3309	335	40	0	0	NUM
fuelectenerg-3309	335	41			PUNCT
fuelectenerg-3309	336	1			PROPN
fuelectenerg-3309	336	2	.	.	PUNCT
fuelectenerg-3309	337	1	enumeration	enumeration	NOUN
fuelectenerg-3309	337	2	and	and	CCONJ
fuelectenerg-3309	337	3	coding	code	VERB
fuelectenerg-3309	337	4	permutations	permutation	NOUN
fuelectenerg-3309	337	5	and	and	CCONJ
fuelectenerg-3309	337	6	reversible	reversible	ADJ
fuelectenerg-3309	337	7	logical	logical	ADJ
fuelectenerg-3309	337	8	circuits	circuit	NOUN
fuelectenerg-3309	337	9	13	13	NUM
fuelectenerg-3309	337	10	fig	fig	NOUN
fuelectenerg-3309	337	11	.	.	PUNCT
fuelectenerg-3309	338	1	1	1	NUM
fuelectenerg-3309	338	2	:	:	PUNCT
fuelectenerg-3309	338	3	the	the	DET
fuelectenerg-3309	338	4	set	set	NOUN
fuelectenerg-3309	338	5	of	of	ADP
fuelectenerg-3309	338	6	points	point	NOUN
fuelectenerg-3309	338	7	{	{	PUNCT
fuelectenerg-3309	338	8	(	(	PUNCT
fuelectenerg-3309	338	9	n	n	X
fuelectenerg-3309	338	10	,	,	PUNCT
fuelectenerg-3309	338	11	t2,ρ	t2,ρ	PROPN
fuelectenerg-3309	338	12	,	,	PUNCT
fuelectenerg-3309	338	13	s(n	s(n	PROPN
fuelectenerg-3309	338	14	)	)	PUNCT
fuelectenerg-3309	338	15	)	)	PUNCT
fuelectenerg-3309	338	16	:	:	PUNCT
fuelectenerg-3309	339	1	n	n	CCONJ
fuelectenerg-3309	339	2	∈	∈	PROPN
fuelectenerg-3309	339	3	i8	i8	NOUN
fuelectenerg-3309	339	4	}	}	PUNCT
fuelectenerg-3309	339	5	for	for	ADP
fuelectenerg-3309	339	6	the	the	DET
fuelectenerg-3309	339	7	selection	selection	NOUN
fuelectenerg-3309	339	8	of	of	ADP
fuelectenerg-3309	339	9	the	the	DET
fuelectenerg-3309	339	10	pair	pair	NOUN
fuelectenerg-3309	339	11	(	(	PUNCT
fuelectenerg-3309	339	12	ρ	ρ	PROPN
fuelectenerg-3309	339	13	,	,	PUNCT
fuelectenerg-3309	339	14	s	s	PART
fuelectenerg-3309	339	15	)	)	PUNCT
fuelectenerg-3309	339	16	as	as	ADP
fuelectenerg-3309	339	17	in	in	ADP
fuelectenerg-3309	339	18	example	example	NOUN
fuelectenerg-3309	339	19	9	9	NUM
fuelectenerg-3309	339	20	.	.	X
fuelectenerg-3309	339	21	recall	recall	VERB
fuelectenerg-3309	339	22	that	that	SCONJ
fuelectenerg-3309	339	23	the	the	DET
fuelectenerg-3309	339	24	map	map	NOUN
fuelectenerg-3309	339	25	t2,ρ	t2,ρ	PROPN
fuelectenerg-3309	339	26	,	,	PUNCT
fuelectenerg-3309	339	27	s	s	PART
fuelectenerg-3309	339	28	is	be	AUX
fuelectenerg-3309	339	29	a	a	DET
fuelectenerg-3309	339	30	bijection	bijection	NOUN
fuelectenerg-3309	339	31	on	on	ADP
fuelectenerg-3309	339	32	the	the	DET
fuelectenerg-3309	339	33	set	set	ADJ
fuelectenerg-3309	339	34	i8	i8	NOUN
fuelectenerg-3309	339	35	providing	provide	VERB
fuelectenerg-3309	339	36	a	a	DET
fuelectenerg-3309	339	37	shuffling	shuffling	NOUN
fuelectenerg-3309	339	38	method	method	NOUN
fuelectenerg-3309	339	39	for	for	ADP
fuelectenerg-3309	339	40	i8	i8	NOUN
fuelectenerg-3309	339	41	.	.	PUNCT
fuelectenerg-3309	340	1	we	we	PRON
fuelectenerg-3309	340	2	mention	mention	VERB
fuelectenerg-3309	340	3	here	here	ADV
fuelectenerg-3309	340	4	that	that	SCONJ
fuelectenerg-3309	340	5	the	the	DET
fuelectenerg-3309	340	6	2	2	NUM
fuelectenerg-3309	340	7	-	-	PUNCT
fuelectenerg-3309	340	8	bit	bit	NOUN
fuelectenerg-3309	340	9	swap	swap	NOUN
fuelectenerg-3309	340	10	gate	gate	NOUN
fuelectenerg-3309	340	11	can	can	AUX
fuelectenerg-3309	340	12	be	be	AUX
fuelectenerg-3309	340	13	also	also	ADV
fuelectenerg-3309	340	14	implemented	implement	VERB
fuelectenerg-3309	340	15	by	by	ADP
fuelectenerg-3309	340	16	the	the	DET
fuelectenerg-3309	340	17	map	map	NOUN
fuelectenerg-3309	340	18	tρ	tρ	ADP
fuelectenerg-3309	340	19	,	,	PUNCT
fuelectenerg-3309	340	20	s	s	PART
fuelectenerg-3309	340	21	by	by	ADP
fuelectenerg-3309	340	22	selecting	select	VERB
fuelectenerg-3309	340	23	ρ	ρ	NOUN
fuelectenerg-3309	340	24	=	=	SYM
fuelectenerg-3309	340	25	(	(	PUNCT
fuelectenerg-3309	340	26	2	2	NUM
fuelectenerg-3309	340	27	,	,	PUNCT
fuelectenerg-3309	340	28	1	1	NUM
fuelectenerg-3309	340	29	)	)	PUNCT
fuelectenerg-3309	340	30	and	and	CCONJ
fuelectenerg-3309	340	31	s	s	VERB
fuelectenerg-3309	340	32	=	=	X
fuelectenerg-3309	340	33	(	(	PUNCT
fuelectenerg-3309	340	34	1	1	NUM
fuelectenerg-3309	340	35	,	,	PUNCT
fuelectenerg-3309	340	36	2	2	NUM
fuelectenerg-3309	340	37	)	)	PUNCT
fuelectenerg-3309	340	38	.	.	PUNCT
fuelectenerg-3309	341	1	however	however	ADV
fuelectenerg-3309	341	2	,	,	PUNCT
fuelectenerg-3309	341	3	the	the	DET
fuelectenerg-3309	341	4	3	3	NUM
fuelectenerg-3309	341	5	-	-	PUNCT
fuelectenerg-3309	341	6	bit	bit	NOUN
fuelectenerg-3309	341	7	toffoli	toffoli	NOUN
fuelectenerg-3309	341	8	and	and	CCONJ
fuelectenerg-3309	341	9	fredkin	fredkin	NOUN
fuelectenerg-3309	341	10	gates	gate	NOUN
fuelectenerg-3309	341	11	can	can	AUX
fuelectenerg-3309	341	12	not	not	PART
fuelectenerg-3309	341	13	be	be	AUX
fuelectenerg-3309	341	14	implemented	implement	VERB
fuelectenerg-3309	341	15	via	via	ADP
fuelectenerg-3309	341	16	tρ	tρ	PROPN
fuelectenerg-3309	341	17	,	,	PUNCT
fuelectenerg-3309	341	18	s.	s.	PROPN
fuelectenerg-3309	341	19	5	5	NUM
fuelectenerg-3309	341	20	coding	code	VERB
fuelectenerg-3309	341	21	pseudorandom	pseudorandom	NOUN
fuelectenerg-3309	341	22	permutations	permutation	NOUN
fuelectenerg-3309	341	23	we	we	PRON
fuelectenerg-3309	341	24	apply	apply	VERB
fuelectenerg-3309	341	25	theorem	theorem	VERB
fuelectenerg-3309	341	26	2	2	NUM
fuelectenerg-3309	341	27	to	to	PART
fuelectenerg-3309	341	28	give	give	VERB
fuelectenerg-3309	341	29	by	by	ADP
fuelectenerg-3309	341	30	an	an	DET
fuelectenerg-3309	341	31	example	example	NOUN
fuelectenerg-3309	341	32	a	a	DET
fuelectenerg-3309	341	33	method	method	NOUN
fuelectenerg-3309	341	34	to	to	PART
fuelectenerg-3309	341	35	code	code	VERB
fuelectenerg-3309	341	36	a	a	DET
fuelectenerg-3309	341	37	pseudorandom	pseudorandom	NOUN
fuelectenerg-3309	341	38	permutation	permutation	NOUN
fuelectenerg-3309	341	39	in	in	ADP
fuelectenerg-3309	341	40	p	p	PROPN
fuelectenerg-3309	341	41	(	(	PUNCT
fuelectenerg-3309	341	42	2	2	NUM
fuelectenerg-3309	341	43	m	m	NOUN
fuelectenerg-3309	341	44	)	)	PUNCT
fuelectenerg-3309	341	45	.	.	PUNCT
fuelectenerg-3309	342	1	for	for	ADP
fuelectenerg-3309	342	2	any	any	DET
fuelectenerg-3309	342	3	(	(	PUNCT
fuelectenerg-3309	342	4	ρ	ρ	PROPN
fuelectenerg-3309	342	5	,	,	PUNCT
fuelectenerg-3309	342	6	s	s	PART
fuelectenerg-3309	342	7	)	)	PUNCT
fuelectenerg-3309	342	8	∈	∈	PROPN
fuelectenerg-3309	342	9	p	p	X
fuelectenerg-3309	342	10	(	(	PUNCT
fuelectenerg-3309	342	11	m	m	NOUN
fuelectenerg-3309	342	12	)	)	PUNCT
fuelectenerg-3309	342	13	×	×	PROPN
fuelectenerg-3309	342	14	s(m	s(m	PROPN
fuelectenerg-3309	342	15	)	)	PUNCT
fuelectenerg-3309	342	16	and	and	CCONJ
fuelectenerg-3309	342	17	a	a	DET
fuelectenerg-3309	342	18	fixed	fix	VERB
fuelectenerg-3309	342	19	random	random	ADJ
fuelectenerg-3309	342	20	permutation	permutation	NOUN
fuelectenerg-3309	342	21	r	r	NOUN
fuelectenerg-3309	342	22	∈	∈	PROPN
fuelectenerg-3309	342	23	r(2	r(2	PROPN
fuelectenerg-3309	342	24	m	m	NOUN
fuelectenerg-3309	342	25	)	)	PUNCT
fuelectenerg-3309	342	26	we	we	PRON
fuelectenerg-3309	342	27	shuffle	shuffle	VERB
fuelectenerg-3309	342	28	the	the	DET
fuelectenerg-3309	342	29	image	image	NOUN
fuelectenerg-3309	342	30	of	of	ADP
fuelectenerg-3309	342	31	t2,ρ	t2,ρ	PROPN
fuelectenerg-3309	342	32	,	,	PUNCT
fuelectenerg-3309	342	33	s	s	VERB
fuelectenerg-3309	342	34	by	by	ADP
fuelectenerg-3309	342	35	the	the	DET
fuelectenerg-3309	342	36	composition	composition	NOUN
fuelectenerg-3309	342	37	map	map	NOUN
fuelectenerg-3309	342	38	wr,2t2,ρ	wr,2t2,ρ	PROPN
fuelectenerg-3309	342	39	,	,	PUNCT
fuelectenerg-3309	342	40	s	s	VERB
fuelectenerg-3309	342	41	for	for	ADP
fuelectenerg-3309	342	42	some	some	DET
fuelectenerg-3309	342	43	particular	particular	ADJ
fuelectenerg-3309	342	44	selection	selection	NOUN
fuelectenerg-3309	342	45	of	of	ADP
fuelectenerg-3309	342	46	r	r	NOUN
fuelectenerg-3309	342	47	∈	∈	PROPN
fuelectenerg-3309	342	48	r(28	r(28	NOUN
fuelectenerg-3309	342	49	)	)	PUNCT
fuelectenerg-3309	342	50	(	(	PUNCT
fuelectenerg-3309	342	51	see	see	VERB
fuelectenerg-3309	342	52	theorem	theorem	NOUN
fuelectenerg-3309	342	53	1	1	NUM
fuelectenerg-3309	342	54	)	)	PUNCT
fuelectenerg-3309	342	55	and	and	CCONJ
fuelectenerg-3309	342	56	we	we	PRON
fuelectenerg-3309	342	57	obtain	obtain	VERB
fuelectenerg-3309	342	58	a	a	DET
fuelectenerg-3309	342	59	pseudo	pseudo	NOUN
fuelectenerg-3309	342	60	-	-	ADJ
fuelectenerg-3309	342	61	random	random	ADJ
fuelectenerg-3309	342	62	permutation	permutation	NOUN
fuelectenerg-3309	342	63	coded	code	VERB
fuelectenerg-3309	342	64	by	by	ADP
fuelectenerg-3309	342	65	a	a	DET
fuelectenerg-3309	342	66	triple	triple	ADJ
fuelectenerg-3309	342	67	(	(	PUNCT
fuelectenerg-3309	342	68	ρ	ρ	PROPN
fuelectenerg-3309	342	69	,	,	PUNCT
fuelectenerg-3309	342	70	s	s	X
fuelectenerg-3309	342	71	,	,	PUNCT
fuelectenerg-3309	342	72	r	r	NOUN
fuelectenerg-3309	342	73	)	)	PUNCT
fuelectenerg-3309	342	74	.	.	PUNCT
fuelectenerg-3309	343	1	example	example	NOUN
fuelectenerg-3309	344	1	9	9	NUM
fuelectenerg-3309	344	2	let	let	VERB
fuelectenerg-3309	344	3	ρ	ρ	PROPN
fuelectenerg-3309	344	4	=	=	SYM
fuelectenerg-3309	344	5	(	(	PUNCT
fuelectenerg-3309	344	6	5	5	NUM
fuelectenerg-3309	344	7	,	,	PUNCT
fuelectenerg-3309	344	8	7	7	NUM
fuelectenerg-3309	344	9	,	,	PUNCT
fuelectenerg-3309	344	10	6	6	NUM
fuelectenerg-3309	344	11	,	,	PUNCT
fuelectenerg-3309	344	12	3	3	NUM
fuelectenerg-3309	344	13	,	,	PUNCT
fuelectenerg-3309	344	14	4	4	NUM
fuelectenerg-3309	344	15	,	,	PUNCT
fuelectenerg-3309	344	16	8	8	NUM
fuelectenerg-3309	344	17	,	,	PUNCT
fuelectenerg-3309	344	18	1	1	NUM
fuelectenerg-3309	344	19	,	,	PUNCT
fuelectenerg-3309	344	20	2	2	NUM
fuelectenerg-3309	344	21	)	)	PUNCT
fuelectenerg-3309	344	22	and	and	CCONJ
fuelectenerg-3309	344	23	s	s	VERB
fuelectenerg-3309	344	24	=	=	X
fuelectenerg-3309	344	25	(	(	PUNCT
fuelectenerg-3309	344	26	1	1	NUM
fuelectenerg-3309	344	27	,	,	PUNCT
fuelectenerg-3309	344	28	1	1	NUM
fuelectenerg-3309	344	29	,	,	PUNCT
fuelectenerg-3309	344	30	1	1	NUM
fuelectenerg-3309	344	31	,	,	PUNCT
fuelectenerg-3309	344	32	4	4	NUM
fuelectenerg-3309	344	33	,	,	PUNCT
fuelectenerg-3309	344	34	5	5	NUM
fuelectenerg-3309	344	35	,	,	PUNCT
fuelectenerg-3309	344	36	2	2	NUM
fuelectenerg-3309	344	37	,	,	PUNCT
fuelectenerg-3309	344	38	7	7	NUM
fuelectenerg-3309	344	39	,	,	PUNCT
fuelectenerg-3309	344	40	3	3	NUM
fuelectenerg-3309	344	41	)	)	PUNCT
fuelectenerg-3309	344	42	.	.	PUNCT
fuelectenerg-3309	345	1	figure	figure	NOUN
fuelectenerg-3309	345	2	1	1	NUM
fuelectenerg-3309	345	3	shows	show	VERB
fuelectenerg-3309	345	4	how	how	SCONJ
fuelectenerg-3309	345	5	the	the	DET
fuelectenerg-3309	345	6	bijective	bijective	ADJ
fuelectenerg-3309	345	7	map	map	NOUN
fuelectenerg-3309	345	8	t2,ρ	t2,ρ	PROPN
fuelectenerg-3309	345	9	,	,	PUNCT
fuelectenerg-3309	345	10	s	s	PART
fuelectenerg-3309	345	11	of	of	ADP
fuelectenerg-3309	345	12	theorem	theorem	ADJ
fuelectenerg-3309	345	13	2	2	NUM
fuelectenerg-3309	345	14	shuffles	shuffle	VERB
fuelectenerg-3309	345	15	the	the	DET
fuelectenerg-3309	345	16	elements	element	NOUN
fuelectenerg-3309	345	17	of	of	ADP
fuelectenerg-3309	345	18	the	the	DET
fuelectenerg-3309	345	19	set	set	NOUN
fuelectenerg-3309	345	20	i8	i8	NOUN
fuelectenerg-3309	345	21	=	=	SYM
fuelectenerg-3309	345	22	{	{	PUNCT
fuelectenerg-3309	345	23	0	0	NUM
fuelectenerg-3309	345	24	,	,	PUNCT
fuelectenerg-3309	345	25	...	...	PUNCT
fuelectenerg-3309	345	26	,	,	PUNCT
fuelectenerg-3309	345	27	28	28	NUM
fuelectenerg-3309	345	28	−	−	NOUN
fuelectenerg-3309	345	29	1	1	NUM
fuelectenerg-3309	345	30	}	}	PUNCT
fuelectenerg-3309	345	31	.	.	PUNCT
fuelectenerg-3309	346	1	in	in	ADP
fuelectenerg-3309	346	2	figure	figure	NOUN
fuelectenerg-3309	346	3	2	2	NUM
fuelectenerg-3309	346	4	we	we	PRON
fuelectenerg-3309	346	5	use	use	VERB
fuelectenerg-3309	346	6	a	a	DET
fuelectenerg-3309	346	7	fixed	fix	VERB
fuelectenerg-3309	346	8	element	element	NOUN
fuelectenerg-3309	346	9	r	r	PROPN
fuelectenerg-3309	346	10	∈	∈	PROPN
fuelectenerg-3309	346	11	r(28	r(28	NOUN
fuelectenerg-3309	346	12	)	)	PUNCT
fuelectenerg-3309	346	13	(	(	PUNCT
fuelectenerg-3309	346	14	see	see	VERB
fuelectenerg-3309	346	15	theorem	theorem	NOUN
fuelectenerg-3309	346	16	1	1	NUM
fuelectenerg-3309	346	17	)	)	PUNCT
fuelectenerg-3309	346	18	and	and	CCONJ
fuelectenerg-3309	346	19	we	we	PRON
fuelectenerg-3309	346	20	shuffle	shuffle	VERB
fuelectenerg-3309	346	21	the	the	DET
fuelectenerg-3309	346	22	set	set	VERB
fuelectenerg-3309	346	23	i8	i8	NOUN
fuelectenerg-3309	346	24	by	by	ADP
fuelectenerg-3309	346	25	means	mean	NOUN
fuelectenerg-3309	346	26	of	of	ADP
fuelectenerg-3309	346	27	the	the	DET
fuelectenerg-3309	346	28	composition	composition	NOUN
fuelectenerg-3309	346	29	operator	operator	NOUN
fuelectenerg-3309	346	30	wr,2t2ρ	wr,2t2ρ	VERB
fuelectenerg-3309	346	31	,	,	PUNCT
fuelectenerg-3309	346	32	s.	s.	PROPN
fuelectenerg-3309	346	33	in	in	ADP
fuelectenerg-3309	346	34	this	this	DET
fuelectenerg-3309	346	35	case	case	NOUN
fuelectenerg-3309	346	36	,	,	PUNCT
fuelectenerg-3309	346	37	the	the	DET
fuelectenerg-3309	346	38	graph	graph	NOUN
fuelectenerg-3309	346	39	appears	appear	VERB
fuelectenerg-3309	346	40	to	to	PART
fuelectenerg-3309	346	41	be	be	AUX
fuelectenerg-3309	346	42	more	more	ADV
fuelectenerg-3309	346	43	”	"	PUNCT
fuelectenerg-3309	346	44	randomly	randomly	ADV
fuelectenerg-3309	346	45	”	"	PUNCT
fuelectenerg-3309	346	46	distributed	distribute	VERB
fuelectenerg-3309	346	47	than	than	ADP
fuelectenerg-3309	346	48	the	the	DET
fuelectenerg-3309	346	49	graph	graph	NOUN
fuelectenerg-3309	346	50	of	of	ADP
fuelectenerg-3309	346	51	figure	figure	NOUN
fuelectenerg-3309	346	52	1	1	NUM
fuelectenerg-3309	346	53	.	.	PUNCT
fuelectenerg-3309	347	1	in	in	ADP
fuelectenerg-3309	347	2	conclusion	conclusion	NOUN
fuelectenerg-3309	347	3	,	,	PUNCT
fuelectenerg-3309	347	4	we	we	PRON
fuelectenerg-3309	347	5	demonstrated	demonstrate	VERB
fuelectenerg-3309	347	6	a	a	DET
fuelectenerg-3309	347	7	variety	variety	NOUN
fuelectenerg-3309	347	8	of	of	ADP
fuelectenerg-3309	347	9	new	new	ADJ
fuelectenerg-3309	347	10	enumeration	enumeration	NOUN
fuelectenerg-3309	347	11	/	/	SYM
fuelectenerg-3309	347	12	shuffling	shuffle	VERB
fuelectenerg-3309	347	13	methods	method	NOUN
fuelectenerg-3309	347	14	for	for	ADP
fuelectenerg-3309	347	15	the	the	DET
fuelectenerg-3309	347	16	group	group	NOUN
fuelectenerg-3309	347	17	of	of	ADP
fuelectenerg-3309	347	18	permutations	permutation	NOUN
fuelectenerg-3309	347	19	.	.	PUNCT
fuelectenerg-3309	348	1	we	we	PRON
fuelectenerg-3309	348	2	also	also	ADV
fuelectenerg-3309	348	3	proposed	propose	VERB
fuelectenerg-3309	348	4	a	a	DET
fuelectenerg-3309	348	5	class	class	NOUN
fuelectenerg-3309	348	6	of	of	ADP
fuelectenerg-3309	348	7	bijections	bijection	NOUN
fuelectenerg-3309	348	8	for	for	ADP
fuelectenerg-3309	348	9	sets	set	NOUN
fuelectenerg-3309	348	10	of	of	ADP
fuelectenerg-3309	348	11	natural	natural	ADJ
fuelectenerg-3309	348	12	numbers	number	NOUN
fuelectenerg-3309	348	13	based	base	VERB
fuelectenerg-3309	348	14	on	on	ADP
fuelectenerg-3309	348	15	efficient	efficient	ADJ
fuelectenerg-3309	348	16	coding	code	VERB
fuelectenerg-3309	348	17	methods	method	NOUN
fuelectenerg-3309	348	18	for	for	ADP
fuelectenerg-3309	348	19	252	252	NUM
fuelectenerg-3309	348	20	c.	c.	NOUN
fuelectenerg-3309	348	21	karanikas	karanikas	PROPN
fuelectenerg-3309	348	22	,	,	PUNCT
fuelectenerg-3309	348	23	n.	n.	PROPN
fuelectenerg-3309	348	24	atreas	atreas	PROPN
fuelectenerg-3309	348	25	enumeration	enumeration	PROPN
fuelectenerg-3309	348	26	and	and	CCONJ
fuelectenerg-3309	348	27	coding	code	VERB
fuelectenerg-3309	348	28	permutations	permutation	NOUN
fuelectenerg-3309	348	29	and	and	CCONJ
fuelectenerg-3309	348	30	reversible	reversible	ADJ
fuelectenerg-3309	348	31	logical	logical	ADJ
fuelectenerg-3309	348	32	circuits	circuit	NOUN
fuelectenerg-3309	348	33	253	253	NUM
fuelectenerg-3309	348	34	14	14	NUM
fuelectenerg-3309	348	35	n.	n.	NOUN
fuelectenerg-3309	348	36	atreas	atreas	PROPN
fuelectenerg-3309	348	37	and	and	CCONJ
fuelectenerg-3309	348	38	c.	c.	PROPN
fuelectenerg-3309	348	39	karanikas	karanikas	PROPN
fuelectenerg-3309	348	40	fig	fig	PROPN
fuelectenerg-3309	348	41	.	.	PUNCT
fuelectenerg-3309	349	1	2	2	NUM
fuelectenerg-3309	349	2	:	:	PUNCT
fuelectenerg-3309	349	3	the	the	DET
fuelectenerg-3309	349	4	set	set	NOUN
fuelectenerg-3309	349	5	of	of	ADP
fuelectenerg-3309	349	6	points	point	NOUN
fuelectenerg-3309	349	7	{	{	PUNCT
fuelectenerg-3309	349	8	(	(	PUNCT
fuelectenerg-3309	349	9	n	n	CCONJ
fuelectenerg-3309	349	10	,	,	PUNCT
fuelectenerg-3309	349	11	wr,2t2,ρ	wr,2t2,ρ	PROPN
fuelectenerg-3309	349	12	,	,	PUNCT
fuelectenerg-3309	349	13	s(n	s(n	PROPN
fuelectenerg-3309	349	14	)	)	PUNCT
fuelectenerg-3309	349	15	)	)	PUNCT
fuelectenerg-3309	349	16	:	:	PUNCT
fuelectenerg-3309	350	1	n	n	X
fuelectenerg-3309	350	2	∈	∈	PROPN
fuelectenerg-3309	350	3	i8	i8	NOUN
fuelectenerg-3309	350	4	}	}	PUNCT
fuelectenerg-3309	350	5	for	for	ADP
fuelectenerg-3309	350	6	some	some	DET
fuelectenerg-3309	350	7	r	r	NOUN
fuelectenerg-3309	350	8	∈	∈	PROPN
fuelectenerg-3309	350	9	r(28	r(28	NOUN
fuelectenerg-3309	350	10	)	)	PUNCT
fuelectenerg-3309	350	11	and	and	CCONJ
fuelectenerg-3309	350	12	(	(	PUNCT
fuelectenerg-3309	350	13	ρ	ρ	PROPN
fuelectenerg-3309	350	14	,	,	PUNCT
fuelectenerg-3309	350	15	s	s	PART
fuelectenerg-3309	350	16	)	)	PUNCT
fuelectenerg-3309	350	17	as	as	ADP
fuelectenerg-3309	350	18	in	in	ADP
fuelectenerg-3309	350	19	example	example	NOUN
fuelectenerg-3309	350	20	9	9	NUM
fuelectenerg-3309	350	21	.	.	PUNCT
fuelectenerg-3309	350	22	sparse	sparse	ADJ
fuelectenerg-3309	350	23	boolean	boolean	ADJ
fuelectenerg-3309	350	24	matrices	matrix	NOUN
fuelectenerg-3309	350	25	.	.	PUNCT
fuelectenerg-3309	351	1	we	we	PRON
fuelectenerg-3309	351	2	also	also	ADV
fuelectenerg-3309	351	3	discussed	discuss	VERB
fuelectenerg-3309	351	4	possible	possible	ADJ
fuelectenerg-3309	351	5	connections	connection	NOUN
fuelectenerg-3309	351	6	of	of	ADP
fuelectenerg-3309	351	7	the	the	DET
fuelectenerg-3309	351	8	shuffling	shuffle	VERB
fuelectenerg-3309	351	9	problem	problem	NOUN
fuelectenerg-3309	351	10	with	with	ADP
fuelectenerg-3309	351	11	the	the	DET
fuelectenerg-3309	351	12	random	random	ADJ
fuelectenerg-3309	351	13	permutation	permutation	NOUN
fuelectenerg-3309	351	14	generation	generation	NOUN
fuelectenerg-3309	351	15	problem	problem	NOUN
fuelectenerg-3309	351	16	.	.	PUNCT
fuelectenerg-3309	352	1	according	accord	VERB
fuelectenerg-3309	352	2	to	to	ADP
fuelectenerg-3309	352	3	[	[	X
fuelectenerg-3309	352	4	8	8	NUM
fuelectenerg-3309	352	5	,	,	PUNCT
fuelectenerg-3309	352	6	9	9	NUM
fuelectenerg-3309	352	7	]	]	PUNCT
fuelectenerg-3309	352	8	,	,	PUNCT
fuelectenerg-3309	352	9	any	any	DET
fuelectenerg-3309	352	10	permutation	permutation	NOUN
fuelectenerg-3309	352	11	in	in	ADP
fuelectenerg-3309	352	12	p	p	PROPN
fuelectenerg-3309	352	13	(	(	PUNCT
fuelectenerg-3309	352	14	m	m	NOUN
fuelectenerg-3309	352	15	)	)	PUNCT
fuelectenerg-3309	352	16	can	can	AUX
fuelectenerg-3309	352	17	be	be	AUX
fuelectenerg-3309	352	18	almost	almost	ADV
fuelectenerg-3309	352	19	uniformly	uniformly	ADV
fuelectenerg-3309	352	20	randomly	randomly	ADV
fuelectenerg-3309	352	21	distributed	distribute	VERB
fuelectenerg-3309	352	22	using	use	VERB
fuelectenerg-3309	352	23	mlog(m)/2	mlog(m)/2	NOUN
fuelectenerg-3309	352	24	.	.	PUNCT
fuelectenerg-3309	353	1	this	this	DET
fuelectenerg-3309	353	2	observation	observation	NOUN
fuelectenerg-3309	353	3	may	may	AUX
fuelectenerg-3309	353	4	be	be	AUX
fuelectenerg-3309	353	5	important	important	ADJ
fuelectenerg-3309	353	6	for	for	ADP
fuelectenerg-3309	353	7	establishing	establish	VERB
fuelectenerg-3309	353	8	a	a	DET
fuelectenerg-3309	353	9	connection	connection	NOUN
fuelectenerg-3309	353	10	between	between	ADP
fuelectenerg-3309	353	11	our	our	PRON
fuelectenerg-3309	353	12	shuffling	shuffling	NOUN
fuelectenerg-3309	353	13	method	method	NOUN
fuelectenerg-3309	353	14	and	and	CCONJ
fuelectenerg-3309	353	15	the	the	DET
fuelectenerg-3309	353	16	random	random	ADJ
fuelectenerg-3309	353	17	permutation	permutation	NOUN
fuelectenerg-3309	353	18	generation	generation	NOUN
fuelectenerg-3309	353	19	problem	problem	NOUN
fuelectenerg-3309	353	20	in	in	ADP
fuelectenerg-3309	353	21	future.we	future.we	NOUN
fuelectenerg-3309	353	22	believe	believe	VERB
fuelectenerg-3309	353	23	that	that	SCONJ
fuelectenerg-3309	353	24	this	this	DET
fuelectenerg-3309	353	25	direction	direction	NOUN
fuelectenerg-3309	353	26	is	be	AUX
fuelectenerg-3309	353	27	very	very	ADV
fuelectenerg-3309	353	28	promising	promising	ADJ
fuelectenerg-3309	353	29	.	.	PUNCT
fuelectenerg-3309	354	1	references	reference	NOUN
fuelectenerg-3309	354	2	[	[	X
fuelectenerg-3309	354	3	1	1	NUM
fuelectenerg-3309	354	4	]	]	PUNCT
fuelectenerg-3309	354	5	k.	k.	PROPN
fuelectenerg-3309	354	6	n.	n.	PROPN
fuelectenerg-3309	354	7	patel	patel	PROPN
fuelectenerg-3309	354	8	,	,	PUNCT
fuelectenerg-3309	354	9	j.	j.	PROPN
fuelectenerg-3309	354	10	p.	p.	PROPN
fuelectenerg-3309	354	11	hayes	hayes	PROPN
fuelectenerg-3309	354	12	,	,	PUNCT
fuelectenerg-3309	354	13	and	and	CCONJ
fuelectenerg-3309	354	14	i.	i.	PROPN
fuelectenerg-3309	354	15	l.	l.	PROPN
fuelectenerg-3309	354	16	markov	markov	PROPN
fuelectenerg-3309	354	17	,	,	PUNCT
fuelectenerg-3309	354	18	“	"	PUNCT
fuelectenerg-3309	354	19	fault	fault	VERB
fuelectenerg-3309	354	20	testing	testing	NOUN
fuelectenerg-3309	354	21	for	for	ADP
fuelectenerg-3309	354	22	reversible	reversible	ADJ
fuelectenerg-3309	354	23	circuits	circuit	NOUN
fuelectenerg-3309	354	24	,	,	PUNCT
fuelectenerg-3309	354	25	”	"	PUNCT
fuelectenerg-3309	354	26	in	in	ADP
fuelectenerg-3309	354	27	ieee	ieee	PROPN
fuelectenerg-3309	354	28	vlsi	vlsi	PROPN
fuelectenerg-3309	354	29	test	test	PROPN
fuelectenerg-3309	354	30	symposium	symposium	NOUN
fuelectenerg-3309	354	31	,	,	PUNCT
fuelectenerg-3309	354	32	napa	napa	ADJ
fuelectenerg-3309	354	33	valley	valley	NOUN
fuelectenerg-3309	354	34	,	,	PUNCT
fuelectenerg-3309	354	35	california	california	PROPN
fuelectenerg-3309	354	36	,	,	PUNCT
fuelectenerg-3309	354	37	2003	2003	NUM
fuelectenerg-3309	354	38	,	,	PUNCT
fuelectenerg-3309	354	39	pp	pp	ADJ
fuelectenerg-3309	354	40	.	.	PUNCT
fuelectenerg-3309	355	1	410–417	410–417	NUM
fuelectenerg-3309	355	2	.	.	PUNCT
fuelectenerg-3309	356	1	[	[	X
fuelectenerg-3309	356	2	2	2	NUM
fuelectenerg-3309	356	3	]	]	X
fuelectenerg-3309	356	4	n.	n.	NOUN
fuelectenerg-3309	356	5	atreas	atreas	PROPN
fuelectenerg-3309	356	6	and	and	CCONJ
fuelectenerg-3309	356	7	c.	c.	PROPN
fuelectenerg-3309	356	8	karanikas	karanikas	PROPN
fuelectenerg-3309	356	9	,	,	PUNCT
fuelectenerg-3309	356	10	“	"	PUNCT
fuelectenerg-3309	356	11	boolean	boolean	ADJ
fuelectenerg-3309	356	12	invertible	invertible	ADJ
fuelectenerg-3309	356	13	matrices	matrix	NOUN
fuelectenerg-3309	356	14	identified	identify	VERB
fuelectenerg-3309	356	15	from	from	ADP
fuelectenerg-3309	356	16	two	two	NUM
fuelectenerg-3309	356	17	permutations	permutation	NOUN
fuelectenerg-3309	356	18	and	and	CCONJ
fuelectenerg-3309	356	19	their	their	PRON
fuelectenerg-3309	356	20	corresponding	corresponding	ADJ
fuelectenerg-3309	356	21	haar	haar	NOUN
fuelectenerg-3309	356	22	-	-	PUNCT
fuelectenerg-3309	356	23	type	type	NOUN
fuelectenerg-3309	356	24	matrices	matrix	NOUN
fuelectenerg-3309	356	25	,	,	PUNCT
fuelectenerg-3309	356	26	”	"	PUNCT
fuelectenerg-3309	356	27	linear	linear	ADJ
fuelectenerg-3309	356	28	algebra	algebra	PROPN
fuelectenerg-3309	356	29	appl	appl	NOUN
fuelectenerg-3309	356	30	.	.	PUNCT
fuelectenerg-3309	356	31	,	,	PUNCT
fuelectenerg-3309	356	32	vol	vol	NOUN
fuelectenerg-3309	356	33	.	.	PROPN
fuelectenerg-3309	356	34	435	435	NUM
fuelectenerg-3309	356	35	,	,	PUNCT
fuelectenerg-3309	356	36	no	no	INTJ
fuelectenerg-3309	356	37	.	.	NOUN
fuelectenerg-3309	356	38	1	1	NUM
fuelectenerg-3309	356	39	,	,	PUNCT
fuelectenerg-3309	356	40	pp	pp	ADJ
fuelectenerg-3309	356	41	.	.	PUNCT
fuelectenerg-3309	357	1	95–105	95–105	NUM
fuelectenerg-3309	357	2	,	,	PUNCT
fuelectenerg-3309	357	3	2011	2011	NUM
fuelectenerg-3309	357	4	.	.	PUNCT
fuelectenerg-3309	358	1	[	[	X
fuelectenerg-3309	358	2	3	3	NUM
fuelectenerg-3309	358	3	]	]	PUNCT
fuelectenerg-3309	358	4	—	—	PUNCT
fuelectenerg-3309	358	5	—	—	PUNCT
fuelectenerg-3309	358	6	,	,	PUNCT
fuelectenerg-3309	358	7	“	"	PUNCT
fuelectenerg-3309	358	8	multiscale	multiscale	ADJ
fuelectenerg-3309	358	9	haar	haar	X
fuelectenerg-3309	358	10	unitary	unitary	ADJ
fuelectenerg-3309	358	11	matrices	matrix	NOUN
fuelectenerg-3309	358	12	with	with	ADP
fuelectenerg-3309	358	13	the	the	DET
fuelectenerg-3309	358	14	corresponding	corresponding	ADJ
fuelectenerg-3309	358	15	riesz	riesz	NOUN
fuelectenerg-3309	358	16	products	product	NOUN
fuelectenerg-3309	358	17	and	and	CCONJ
fuelectenerg-3309	358	18	a	a	DET
fuelectenerg-3309	358	19	characterization	characterization	NOUN
fuelectenerg-3309	358	20	of	of	ADP
fuelectenerg-3309	358	21	cantor	cantor	NOUN
fuelectenerg-3309	358	22	-	-	PUNCT
fuelectenerg-3309	358	23	type	type	NOUN
fuelectenerg-3309	358	24	languages	language	NOUN
fuelectenerg-3309	358	25	,	,	PUNCT
fuelectenerg-3309	358	26	”	"	PUNCT
fuelectenerg-3309	358	27	j.	j.	PROPN
fuelectenerg-3309	358	28	fourier	fourier	PROPN
fuelectenerg-3309	358	29	anal	anal	PROPN
fuelectenerg-3309	358	30	.	.	PUNCT
fuelectenerg-3309	359	1	appl	appl	PROPN
fuelectenerg-3309	359	2	.	.	PROPN
fuelectenerg-3309	359	3	,	,	PUNCT
fuelectenerg-3309	359	4	vol	vol	NOUN
fuelectenerg-3309	359	5	.	.	PROPN
fuelectenerg-3309	359	6	13	13	NUM
fuelectenerg-3309	359	7	,	,	PUNCT
fuelectenerg-3309	359	8	no	no	INTJ
fuelectenerg-3309	359	9	.	.	NOUN
fuelectenerg-3309	359	10	2	2	NUM
fuelectenerg-3309	359	11	,	,	PUNCT
fuelectenerg-3309	359	12	pp	pp	ADJ
fuelectenerg-3309	359	13	.	.	PUNCT
fuelectenerg-3309	360	1	197–210	197–210	NUM
fuelectenerg-3309	360	2	,	,	PUNCT
fuelectenerg-3309	360	3	2007	2007	NUM
fuelectenerg-3309	360	4	.	.	PUNCT
fuelectenerg-3309	361	1	[	[	X
fuelectenerg-3309	361	2	4	4	NUM
fuelectenerg-3309	361	3	]	]	PUNCT
fuelectenerg-3309	361	4	—	—	PUNCT
fuelectenerg-3309	361	5	—	—	PUNCT
fuelectenerg-3309	361	6	,	,	PUNCT
fuelectenerg-3309	361	7	“	"	PUNCT
fuelectenerg-3309	361	8	haar	haar	NOUN
fuelectenerg-3309	361	9	-	-	PUNCT
fuelectenerg-3309	361	10	type	type	NOUN
fuelectenerg-3309	361	11	orthonormal	orthonormal	ADJ
fuelectenerg-3309	361	12	systems	system	NOUN
fuelectenerg-3309	361	13	,	,	PUNCT
fuelectenerg-3309	361	14	data	datum	NOUN
fuelectenerg-3309	361	15	presentation	presentation	NOUN
fuelectenerg-3309	361	16	as	as	ADP
fuelectenerg-3309	361	17	riesz	riesz	NOUN
fuelectenerg-3309	361	18	products	product	NOUN
fuelectenerg-3309	361	19	and	and	CCONJ
fuelectenerg-3309	361	20	a	a	DET
fuelectenerg-3309	361	21	recognition	recognition	NOUN
fuelectenerg-3309	361	22	on	on	ADP
fuelectenerg-3309	361	23	symbolic	symbolic	ADJ
fuelectenerg-3309	361	24	sequences	sequence	NOUN
fuelectenerg-3309	361	25	,	,	PUNCT
fuelectenerg-3309	361	26	”	"	PUNCT
fuelectenerg-3309	361	27	contemporary	contemporary	ADJ
fuelectenerg-3309	361	28	math	math	NOUN
fuelectenerg-3309	361	29	.	.	PUNCT
fuelectenerg-3309	361	30	,	,	PUNCT
fuelectenerg-3309	361	31	vol	vol	NOUN
fuelectenerg-3309	361	32	.	.	PROPN
fuelectenerg-3309	361	33	451	451	NUM
fuelectenerg-3309	361	34	,	,	PUNCT
fuelectenerg-3309	361	35	pp	pp	ADJ
fuelectenerg-3309	361	36	.	.	PUNCT
fuelectenerg-3309	362	1	1–9	1–9	NUM
fuelectenerg-3309	362	2	,	,	PUNCT
fuelectenerg-3309	362	3	2008	2008	NUM
fuelectenerg-3309	362	4	.	.	PUNCT
fuelectenerg-3309	363	1	[	[	X
fuelectenerg-3309	363	2	5	5	NUM
fuelectenerg-3309	363	3	]	]	PUNCT
fuelectenerg-3309	363	4	—	—	PUNCT
fuelectenerg-3309	363	5	—	—	PUNCT
fuelectenerg-3309	363	6	,	,	PUNCT
fuelectenerg-3309	363	7	“	"	PUNCT
fuelectenerg-3309	363	8	discrete	discrete	ADJ
fuelectenerg-3309	363	9	type	type	NOUN
fuelectenerg-3309	363	10	riesz	riesz	NOUN
fuelectenerg-3309	363	11	products	product	NOUN
fuelectenerg-3309	363	12	,	,	PUNCT
fuelectenerg-3309	363	13	”	"	PUNCT
fuelectenerg-3309	363	14	in	in	ADP
fuelectenerg-3309	363	15	walsh	walsh	NOUN
fuelectenerg-3309	363	16	and	and	CCONJ
fuelectenerg-3309	363	17	dyadic	dyadic	ADJ
fuelectenerg-3309	363	18	analysis	analysis	NOUN
fuelectenerg-3309	363	19	,	,	PUNCT
fuelectenerg-3309	363	20	2008	2008	NUM
fuelectenerg-3309	363	21	,	,	PUNCT
fuelectenerg-3309	363	22	pp	pp	ADJ
fuelectenerg-3309	363	23	.	.	PUNCT
fuelectenerg-3309	364	1	137–143	137–143	NUM
fuelectenerg-3309	364	2	.	.	PUNCT
fuelectenerg-3309	364	3	254	254	NUM
fuelectenerg-3309	364	4	c.	c.	PROPN
fuelectenerg-3309	364	5	karanikas	karanikas	PROPN
fuelectenerg-3309	364	6	,	,	PUNCT
fuelectenerg-3309	364	7	n.	n.	PROPN
fuelectenerg-3309	364	8	atreas	atreas	PROPN
fuelectenerg-3309	364	9	enumeration	enumeration	PROPN
fuelectenerg-3309	364	10	and	and	CCONJ
fuelectenerg-3309	364	11	coding	code	VERB
fuelectenerg-3309	364	12	permutations	permutation	NOUN
fuelectenerg-3309	364	13	and	and	CCONJ
fuelectenerg-3309	364	14	reversible	reversible	ADJ
fuelectenerg-3309	364	15	logical	logical	ADJ
fuelectenerg-3309	364	16	circuits	circuit	NOUN
fuelectenerg-3309	364	17	255	255	NUM
fuelectenerg-3309	364	18	14	14	NUM
fuelectenerg-3309	364	19	n.	n.	NOUN
fuelectenerg-3309	364	20	atreas	atreas	PROPN
fuelectenerg-3309	364	21	and	and	CCONJ
fuelectenerg-3309	364	22	c.	c.	PROPN
fuelectenerg-3309	364	23	karanikas	karanikas	PROPN
fuelectenerg-3309	364	24	fig	fig	PROPN
fuelectenerg-3309	364	25	.	.	PUNCT
fuelectenerg-3309	365	1	2	2	NUM
fuelectenerg-3309	365	2	:	:	PUNCT
fuelectenerg-3309	365	3	the	the	DET
fuelectenerg-3309	365	4	set	set	NOUN
fuelectenerg-3309	365	5	of	of	ADP
fuelectenerg-3309	365	6	points	point	NOUN
fuelectenerg-3309	365	7	{	{	PUNCT
fuelectenerg-3309	365	8	(	(	PUNCT
fuelectenerg-3309	365	9	n	n	CCONJ
fuelectenerg-3309	365	10	,	,	PUNCT
fuelectenerg-3309	365	11	wr,2t2,ρ	wr,2t2,ρ	PROPN
fuelectenerg-3309	365	12	,	,	PUNCT
fuelectenerg-3309	365	13	s(n	s(n	PROPN
fuelectenerg-3309	365	14	)	)	PUNCT
fuelectenerg-3309	365	15	)	)	PUNCT
fuelectenerg-3309	365	16	:	:	PUNCT
fuelectenerg-3309	366	1	n	n	X
fuelectenerg-3309	366	2	∈	∈	PROPN
fuelectenerg-3309	366	3	i8	i8	NOUN
fuelectenerg-3309	366	4	}	}	PUNCT
fuelectenerg-3309	366	5	for	for	ADP
fuelectenerg-3309	366	6	some	some	DET
fuelectenerg-3309	366	7	r	r	NOUN
fuelectenerg-3309	366	8	∈	∈	PROPN
fuelectenerg-3309	366	9	r(28	r(28	NOUN
fuelectenerg-3309	366	10	)	)	PUNCT
fuelectenerg-3309	366	11	and	and	CCONJ
fuelectenerg-3309	366	12	(	(	PUNCT
fuelectenerg-3309	366	13	ρ	ρ	PROPN
fuelectenerg-3309	366	14	,	,	PUNCT
fuelectenerg-3309	366	15	s	s	PART
fuelectenerg-3309	366	16	)	)	PUNCT
fuelectenerg-3309	366	17	as	as	ADP
fuelectenerg-3309	366	18	in	in	ADP
fuelectenerg-3309	366	19	example	example	NOUN
fuelectenerg-3309	366	20	9	9	NUM
fuelectenerg-3309	366	21	.	.	PUNCT
fuelectenerg-3309	366	22	sparse	sparse	ADJ
fuelectenerg-3309	366	23	boolean	boolean	ADJ
fuelectenerg-3309	366	24	matrices	matrix	NOUN
fuelectenerg-3309	366	25	.	.	PUNCT
fuelectenerg-3309	367	1	we	we	PRON
fuelectenerg-3309	367	2	also	also	ADV
fuelectenerg-3309	367	3	discussed	discuss	VERB
fuelectenerg-3309	367	4	possible	possible	ADJ
fuelectenerg-3309	367	5	connections	connection	NOUN
fuelectenerg-3309	367	6	of	of	ADP
fuelectenerg-3309	367	7	the	the	DET
fuelectenerg-3309	367	8	shuffling	shuffle	VERB
fuelectenerg-3309	367	9	problem	problem	NOUN
fuelectenerg-3309	367	10	with	with	ADP
fuelectenerg-3309	367	11	the	the	DET
fuelectenerg-3309	367	12	random	random	ADJ
fuelectenerg-3309	367	13	permutation	permutation	NOUN
fuelectenerg-3309	367	14	generation	generation	NOUN
fuelectenerg-3309	367	15	problem	problem	NOUN
fuelectenerg-3309	367	16	.	.	PUNCT
fuelectenerg-3309	368	1	according	accord	VERB
fuelectenerg-3309	368	2	to	to	ADP
fuelectenerg-3309	368	3	[	[	X
fuelectenerg-3309	368	4	8	8	NUM
fuelectenerg-3309	368	5	,	,	PUNCT
fuelectenerg-3309	368	6	9	9	NUM
fuelectenerg-3309	368	7	]	]	PUNCT
fuelectenerg-3309	368	8	,	,	PUNCT
fuelectenerg-3309	368	9	any	any	DET
fuelectenerg-3309	368	10	permutation	permutation	NOUN
fuelectenerg-3309	368	11	in	in	ADP
fuelectenerg-3309	368	12	p	p	PROPN
fuelectenerg-3309	368	13	(	(	PUNCT
fuelectenerg-3309	368	14	m	m	NOUN
fuelectenerg-3309	368	15	)	)	PUNCT
fuelectenerg-3309	368	16	can	can	AUX
fuelectenerg-3309	368	17	be	be	AUX
fuelectenerg-3309	368	18	almost	almost	ADV
fuelectenerg-3309	368	19	uniformly	uniformly	ADV
fuelectenerg-3309	368	20	randomly	randomly	ADV
fuelectenerg-3309	368	21	distributed	distribute	VERB
fuelectenerg-3309	368	22	using	use	VERB
fuelectenerg-3309	368	23	mlog(m)/2	mlog(m)/2	NOUN
fuelectenerg-3309	368	24	.	.	PUNCT
fuelectenerg-3309	369	1	this	this	DET
fuelectenerg-3309	369	2	observation	observation	NOUN
fuelectenerg-3309	369	3	may	may	AUX
fuelectenerg-3309	369	4	be	be	AUX
fuelectenerg-3309	369	5	important	important	ADJ
fuelectenerg-3309	369	6	for	for	ADP
fuelectenerg-3309	369	7	establishing	establish	VERB
fuelectenerg-3309	369	8	a	a	DET
fuelectenerg-3309	369	9	connection	connection	NOUN
fuelectenerg-3309	369	10	between	between	ADP
fuelectenerg-3309	369	11	our	our	PRON
fuelectenerg-3309	369	12	shuffling	shuffling	NOUN
fuelectenerg-3309	369	13	method	method	NOUN
fuelectenerg-3309	369	14	and	and	CCONJ
fuelectenerg-3309	369	15	the	the	DET
fuelectenerg-3309	369	16	random	random	ADJ
fuelectenerg-3309	369	17	permutation	permutation	NOUN
fuelectenerg-3309	369	18	generation	generation	NOUN
fuelectenerg-3309	369	19	problem	problem	NOUN
fuelectenerg-3309	369	20	in	in	ADP
fuelectenerg-3309	369	21	future.we	future.we	NOUN
fuelectenerg-3309	369	22	believe	believe	VERB
fuelectenerg-3309	369	23	that	that	SCONJ
fuelectenerg-3309	369	24	this	this	DET
fuelectenerg-3309	369	25	direction	direction	NOUN
fuelectenerg-3309	369	26	is	be	AUX
fuelectenerg-3309	369	27	very	very	ADV
fuelectenerg-3309	369	28	promising	promising	ADJ
fuelectenerg-3309	369	29	.	.	PUNCT
fuelectenerg-3309	370	1	references	reference	NOUN
fuelectenerg-3309	370	2	[	[	X
fuelectenerg-3309	370	3	1	1	NUM
fuelectenerg-3309	370	4	]	]	PUNCT
fuelectenerg-3309	370	5	k.	k.	PROPN
fuelectenerg-3309	370	6	n.	n.	PROPN
fuelectenerg-3309	370	7	patel	patel	PROPN
fuelectenerg-3309	370	8	,	,	PUNCT
fuelectenerg-3309	370	9	j.	j.	PROPN
fuelectenerg-3309	370	10	p.	p.	PROPN
fuelectenerg-3309	370	11	hayes	hayes	PROPN
fuelectenerg-3309	370	12	,	,	PUNCT
fuelectenerg-3309	370	13	and	and	CCONJ
fuelectenerg-3309	370	14	i.	i.	PROPN
fuelectenerg-3309	370	15	l.	l.	PROPN
fuelectenerg-3309	370	16	markov	markov	PROPN
fuelectenerg-3309	370	17	,	,	PUNCT
fuelectenerg-3309	370	18	“	"	PUNCT
fuelectenerg-3309	370	19	fault	fault	VERB
fuelectenerg-3309	370	20	testing	testing	NOUN
fuelectenerg-3309	370	21	for	for	ADP
fuelectenerg-3309	370	22	reversible	reversible	ADJ
fuelectenerg-3309	370	23	circuits	circuit	NOUN
fuelectenerg-3309	370	24	,	,	PUNCT
fuelectenerg-3309	370	25	”	"	PUNCT
fuelectenerg-3309	370	26	in	in	ADP
fuelectenerg-3309	370	27	ieee	ieee	PROPN
fuelectenerg-3309	370	28	vlsi	vlsi	PROPN
fuelectenerg-3309	370	29	test	test	PROPN
fuelectenerg-3309	370	30	symposium	symposium	NOUN
fuelectenerg-3309	370	31	,	,	PUNCT
fuelectenerg-3309	370	32	napa	napa	ADJ
fuelectenerg-3309	370	33	valley	valley	NOUN
fuelectenerg-3309	370	34	,	,	PUNCT
fuelectenerg-3309	370	35	california	california	PROPN
fuelectenerg-3309	370	36	,	,	PUNCT
fuelectenerg-3309	370	37	2003	2003	NUM
fuelectenerg-3309	370	38	,	,	PUNCT
fuelectenerg-3309	370	39	pp	pp	ADJ
fuelectenerg-3309	370	40	.	.	PUNCT
fuelectenerg-3309	371	1	410–417	410–417	NUM
fuelectenerg-3309	371	2	.	.	PUNCT
fuelectenerg-3309	372	1	[	[	X
fuelectenerg-3309	372	2	2	2	NUM
fuelectenerg-3309	372	3	]	]	X
fuelectenerg-3309	372	4	n.	n.	NOUN
fuelectenerg-3309	372	5	atreas	atreas	PROPN
fuelectenerg-3309	372	6	and	and	CCONJ
fuelectenerg-3309	372	7	c.	c.	PROPN
fuelectenerg-3309	372	8	karanikas	karanikas	PROPN
fuelectenerg-3309	372	9	,	,	PUNCT
fuelectenerg-3309	372	10	“	"	PUNCT
fuelectenerg-3309	372	11	boolean	boolean	ADJ
fuelectenerg-3309	372	12	invertible	invertible	ADJ
fuelectenerg-3309	372	13	matrices	matrix	NOUN
fuelectenerg-3309	372	14	identified	identify	VERB
fuelectenerg-3309	372	15	from	from	ADP
fuelectenerg-3309	372	16	two	two	NUM
fuelectenerg-3309	372	17	permutations	permutation	NOUN
fuelectenerg-3309	372	18	and	and	CCONJ
fuelectenerg-3309	372	19	their	their	PRON
fuelectenerg-3309	372	20	corresponding	corresponding	ADJ
fuelectenerg-3309	372	21	haar	haar	NOUN
fuelectenerg-3309	372	22	-	-	PUNCT
fuelectenerg-3309	372	23	type	type	NOUN
fuelectenerg-3309	372	24	matrices	matrix	NOUN
fuelectenerg-3309	372	25	,	,	PUNCT
fuelectenerg-3309	372	26	”	"	PUNCT
fuelectenerg-3309	372	27	linear	linear	ADJ
fuelectenerg-3309	372	28	algebra	algebra	PROPN
fuelectenerg-3309	372	29	appl	appl	NOUN
fuelectenerg-3309	372	30	.	.	PUNCT
fuelectenerg-3309	372	31	,	,	PUNCT
fuelectenerg-3309	372	32	vol	vol	NOUN
fuelectenerg-3309	372	33	.	.	PROPN
fuelectenerg-3309	372	34	435	435	NUM
fuelectenerg-3309	372	35	,	,	PUNCT
fuelectenerg-3309	372	36	no	no	INTJ
fuelectenerg-3309	372	37	.	.	NOUN
fuelectenerg-3309	372	38	1	1	NUM
fuelectenerg-3309	372	39	,	,	PUNCT
fuelectenerg-3309	372	40	pp	pp	ADJ
fuelectenerg-3309	372	41	.	.	PUNCT
fuelectenerg-3309	373	1	95–105	95–105	NUM
fuelectenerg-3309	373	2	,	,	PUNCT
fuelectenerg-3309	373	3	2011	2011	NUM
fuelectenerg-3309	373	4	.	.	PUNCT
fuelectenerg-3309	374	1	[	[	X
fuelectenerg-3309	374	2	3	3	NUM
fuelectenerg-3309	374	3	]	]	PUNCT
fuelectenerg-3309	374	4	—	—	PUNCT
fuelectenerg-3309	374	5	—	—	PUNCT
fuelectenerg-3309	374	6	,	,	PUNCT
fuelectenerg-3309	374	7	“	"	PUNCT
fuelectenerg-3309	374	8	multiscale	multiscale	ADJ
fuelectenerg-3309	374	9	haar	haar	X
fuelectenerg-3309	374	10	unitary	unitary	ADJ
fuelectenerg-3309	374	11	matrices	matrix	NOUN
fuelectenerg-3309	374	12	with	with	ADP
fuelectenerg-3309	374	13	the	the	DET
fuelectenerg-3309	374	14	corresponding	corresponding	ADJ
fuelectenerg-3309	374	15	riesz	riesz	NOUN
fuelectenerg-3309	374	16	products	product	NOUN
fuelectenerg-3309	374	17	and	and	CCONJ
fuelectenerg-3309	374	18	a	a	DET
fuelectenerg-3309	374	19	characterization	characterization	NOUN
fuelectenerg-3309	374	20	of	of	ADP
fuelectenerg-3309	374	21	cantor	cantor	NOUN
fuelectenerg-3309	374	22	-	-	PUNCT
fuelectenerg-3309	374	23	type	type	NOUN
fuelectenerg-3309	374	24	languages	language	NOUN
fuelectenerg-3309	374	25	,	,	PUNCT
fuelectenerg-3309	374	26	”	"	PUNCT
fuelectenerg-3309	374	27	j.	j.	PROPN
fuelectenerg-3309	374	28	fourier	fourier	PROPN
fuelectenerg-3309	374	29	anal	anal	PROPN
fuelectenerg-3309	374	30	.	.	PUNCT
fuelectenerg-3309	375	1	appl	appl	PROPN
fuelectenerg-3309	375	2	.	.	PROPN
fuelectenerg-3309	375	3	,	,	PUNCT
fuelectenerg-3309	375	4	vol	vol	NOUN
fuelectenerg-3309	375	5	.	.	PROPN
fuelectenerg-3309	375	6	13	13	NUM
fuelectenerg-3309	375	7	,	,	PUNCT
fuelectenerg-3309	375	8	no	no	INTJ
fuelectenerg-3309	375	9	.	.	NOUN
fuelectenerg-3309	375	10	2	2	NUM
fuelectenerg-3309	375	11	,	,	PUNCT
fuelectenerg-3309	375	12	pp	pp	ADJ
fuelectenerg-3309	375	13	.	.	PUNCT
fuelectenerg-3309	376	1	197–210	197–210	NUM
fuelectenerg-3309	376	2	,	,	PUNCT
fuelectenerg-3309	376	3	2007	2007	NUM
fuelectenerg-3309	376	4	.	.	PUNCT
fuelectenerg-3309	377	1	[	[	X
fuelectenerg-3309	377	2	4	4	NUM
fuelectenerg-3309	377	3	]	]	PUNCT
fuelectenerg-3309	377	4	—	—	PUNCT
fuelectenerg-3309	377	5	—	—	PUNCT
fuelectenerg-3309	377	6	,	,	PUNCT
fuelectenerg-3309	377	7	“	"	PUNCT
fuelectenerg-3309	377	8	haar	haar	NOUN
fuelectenerg-3309	377	9	-	-	PUNCT
fuelectenerg-3309	377	10	type	type	NOUN
fuelectenerg-3309	377	11	orthonormal	orthonormal	ADJ
fuelectenerg-3309	377	12	systems	system	NOUN
fuelectenerg-3309	377	13	,	,	PUNCT
fuelectenerg-3309	377	14	data	datum	NOUN
fuelectenerg-3309	377	15	presentation	presentation	NOUN
fuelectenerg-3309	377	16	as	as	ADP
fuelectenerg-3309	377	17	riesz	riesz	NOUN
fuelectenerg-3309	377	18	products	product	NOUN
fuelectenerg-3309	377	19	and	and	CCONJ
fuelectenerg-3309	377	20	a	a	DET
fuelectenerg-3309	377	21	recognition	recognition	NOUN
fuelectenerg-3309	377	22	on	on	ADP
fuelectenerg-3309	377	23	symbolic	symbolic	ADJ
fuelectenerg-3309	377	24	sequences	sequence	NOUN
fuelectenerg-3309	377	25	,	,	PUNCT
fuelectenerg-3309	377	26	”	"	PUNCT
fuelectenerg-3309	377	27	contemporary	contemporary	ADJ
fuelectenerg-3309	377	28	math	math	NOUN
fuelectenerg-3309	377	29	.	.	PUNCT
fuelectenerg-3309	377	30	,	,	PUNCT
fuelectenerg-3309	377	31	vol	vol	NOUN
fuelectenerg-3309	377	32	.	.	PROPN
fuelectenerg-3309	377	33	451	451	NUM
fuelectenerg-3309	377	34	,	,	PUNCT
fuelectenerg-3309	377	35	pp	pp	ADJ
fuelectenerg-3309	377	36	.	.	PUNCT
fuelectenerg-3309	378	1	1–9	1–9	NUM
fuelectenerg-3309	378	2	,	,	PUNCT
fuelectenerg-3309	378	3	2008	2008	NUM
fuelectenerg-3309	378	4	.	.	PUNCT
fuelectenerg-3309	379	1	[	[	X
fuelectenerg-3309	379	2	5	5	NUM
fuelectenerg-3309	379	3	]	]	PUNCT
fuelectenerg-3309	379	4	—	—	PUNCT
fuelectenerg-3309	379	5	—	—	PUNCT
fuelectenerg-3309	379	6	,	,	PUNCT
fuelectenerg-3309	379	7	“	"	PUNCT
fuelectenerg-3309	379	8	discrete	discrete	ADJ
fuelectenerg-3309	379	9	type	type	NOUN
fuelectenerg-3309	379	10	riesz	riesz	NOUN
fuelectenerg-3309	379	11	products	product	NOUN
fuelectenerg-3309	379	12	,	,	PUNCT
fuelectenerg-3309	379	13	”	"	PUNCT
fuelectenerg-3309	379	14	in	in	ADP
fuelectenerg-3309	379	15	walsh	walsh	NOUN
fuelectenerg-3309	379	16	and	and	CCONJ
fuelectenerg-3309	379	17	dyadic	dyadic	ADJ
fuelectenerg-3309	379	18	analysis	analysis	NOUN
fuelectenerg-3309	379	19	,	,	PUNCT
fuelectenerg-3309	379	20	2008	2008	NUM
fuelectenerg-3309	379	21	,	,	PUNCT
fuelectenerg-3309	379	22	pp	pp	ADJ
fuelectenerg-3309	379	23	.	.	PUNCT
fuelectenerg-3309	380	1	137–143	137–143	NUM
fuelectenerg-3309	380	2	.	.	PUNCT
fuelectenerg-3309	381	1	enumeration	enumeration	NOUN
fuelectenerg-3309	381	2	and	and	CCONJ
fuelectenerg-3309	381	3	coding	code	VERB
fuelectenerg-3309	381	4	permutations	permutation	NOUN
fuelectenerg-3309	381	5	and	and	CCONJ
fuelectenerg-3309	381	6	reversible	reversible	ADJ
fuelectenerg-3309	381	7	logical	logical	ADJ
fuelectenerg-3309	381	8	circuits	circuit	NOUN
fuelectenerg-3309	381	9	15	15	NUM
fuelectenerg-3309	381	10	[	[	SYM
fuelectenerg-3309	381	11	6	6	NUM
fuelectenerg-3309	381	12	]	]	X
fuelectenerg-3309	381	13	n.	n.	PROPN
fuelectenerg-3309	381	14	atreas	atreas	PROPN
fuelectenerg-3309	381	15	,	,	PUNCT
fuelectenerg-3309	381	16	c.	c.	PROPN
fuelectenerg-3309	381	17	karanikas	karanikas	PROPN
fuelectenerg-3309	381	18	,	,	PUNCT
fuelectenerg-3309	381	19	and	and	CCONJ
fuelectenerg-3309	381	20	p.	p.	PROPN
fuelectenerg-3309	381	21	polychronidou	polychronidou	NOUN
fuelectenerg-3309	381	22	,	,	PUNCT
fuelectenerg-3309	381	23	“	"	PUNCT
fuelectenerg-3309	381	24	a	a	DET
fuelectenerg-3309	381	25	class	class	NOUN
fuelectenerg-3309	381	26	of	of	ADP
fuelectenerg-3309	381	27	sparse	sparse	ADJ
fuelectenerg-3309	381	28	unimodular	unimodular	ADJ
fuelectenerg-3309	381	29	matrices	matrix	NOUN
fuelectenerg-3309	381	30	generating	generate	VERB
fuelectenerg-3309	381	31	multiresolution	multiresolution	NOUN
fuelectenerg-3309	381	32	and	and	CCONJ
fuelectenerg-3309	381	33	sampling	sample	VERB
fuelectenerg-3309	381	34	analysis	analysis	NOUN
fuelectenerg-3309	381	35	for	for	ADP
fuelectenerg-3309	381	36	data	datum	NOUN
fuelectenerg-3309	381	37	of	of	ADP
fuelectenerg-3309	381	38	any	any	DET
fuelectenerg-3309	381	39	length	length	NOUN
fuelectenerg-3309	381	40	,	,	PUNCT
fuelectenerg-3309	381	41	”	"	PUNCT
fuelectenerg-3309	381	42	siam	siam	PROPN
fuelectenerg-3309	381	43	j.	j.	PROPN
fuelectenerg-3309	381	44	matrix	matrix	PROPN
fuelectenerg-3309	381	45	anal	anal	PROPN
fuelectenerg-3309	381	46	.	.	PUNCT
fuelectenerg-3309	382	1	appl	appl	PROPN
fuelectenerg-3309	382	2	.	.	PROPN
fuelectenerg-3309	382	3	,	,	PUNCT
fuelectenerg-3309	382	4	,	,	PUNCT
fuelectenerg-3309	382	5	vol	vol	NOUN
fuelectenerg-3309	382	6	.	.	PROPN
fuelectenerg-3309	382	7	30	30	NUM
fuelectenerg-3309	382	8	,	,	PUNCT
fuelectenerg-3309	382	9	no	no	INTJ
fuelectenerg-3309	382	10	.	.	NOUN
fuelectenerg-3309	382	11	1	1	NUM
fuelectenerg-3309	382	12	,	,	PUNCT
fuelectenerg-3309	382	13	pp	pp	ADJ
fuelectenerg-3309	382	14	.	.	PUNCT
fuelectenerg-3309	383	1	312–323	312–323	NUM
fuelectenerg-3309	383	2	,	,	PUNCT
fuelectenerg-3309	383	3	2008	2008	NUM
fuelectenerg-3309	383	4	.	.	PUNCT
fuelectenerg-3309	384	1	[	[	X
fuelectenerg-3309	384	2	7	7	X
fuelectenerg-3309	384	3	]	]	X
fuelectenerg-3309	384	4	d.	d.	PROPN
fuelectenerg-3309	384	5	h.	h.	PROPN
fuelectenerg-3309	384	6	lehmer	lehmer	PROPN
fuelectenerg-3309	384	7	,	,	PUNCT
fuelectenerg-3309	384	8	“	"	PUNCT
fuelectenerg-3309	384	9	teaching	teach	VERB
fuelectenerg-3309	384	10	combinatorial	combinatorial	ADJ
fuelectenerg-3309	384	11	tricks	trick	NOUN
fuelectenerg-3309	384	12	to	to	ADP
fuelectenerg-3309	384	13	a	a	DET
fuelectenerg-3309	384	14	computer	computer	NOUN
fuelectenerg-3309	384	15	,	,	PUNCT
fuelectenerg-3309	384	16	”	"	PUNCT
fuelectenerg-3309	384	17	in	in	ADP
fuelectenerg-3309	384	18	proc	proc	NOUN
fuelectenerg-3309	384	19	.	.	PUNCT
fuelectenerg-3309	385	1	symbos	symbos	PROPN
fuelectenerg-3309	385	2	.	.	PUNCT
fuelectenerg-3309	386	1	appl	appl	PROPN
fuelectenerg-3309	386	2	.	.	PROPN
fuelectenerg-3309	386	3	math	math	PROPN
fuelectenerg-3309	386	4	.	.	PUNCT
fuelectenerg-3309	387	1	combinatorial	combinatorial	ADJ
fuelectenerg-3309	387	2	analysis	analysis	NOUN
fuelectenerg-3309	387	3	,	,	PUNCT
fuelectenerg-3309	387	4	vol	vol	NOUN
fuelectenerg-3309	387	5	.	.	PROPN
fuelectenerg-3309	387	6	10	10	NUM
fuelectenerg-3309	387	7	,	,	PUNCT
fuelectenerg-3309	387	8	1960	1960	NUM
fuelectenerg-3309	387	9	,	,	PUNCT
fuelectenerg-3309	387	10	pp	pp	ADP
fuelectenerg-3309	387	11	.	.	PUNCT
fuelectenerg-3309	388	1	179–193	179–193	NUM
fuelectenerg-3309	388	2	.	.	PUNCT
fuelectenerg-3309	389	1	[	[	X
fuelectenerg-3309	389	2	8	8	NUM
fuelectenerg-3309	389	3	]	]	X
fuelectenerg-3309	389	4	p.	p.	NOUN
fuelectenerg-3309	389	5	diaconis	diaconis	PROPN
fuelectenerg-3309	389	6	,	,	PUNCT
fuelectenerg-3309	389	7	g.	g.	PROPN
fuelectenerg-3309	389	8	graham	graham	PROPN
fuelectenerg-3309	389	9	,	,	PUNCT
fuelectenerg-3309	389	10	and	and	CCONJ
fuelectenerg-3309	389	11	s.	s.	PROPN
fuelectenerg-3309	389	12	p.	p.	PROPN
fuelectenerg-3309	389	13	holmes	holmes	PROPN
fuelectenerg-3309	389	14	,	,	PUNCT
fuelectenerg-3309	389	15	“	"	PUNCT
fuelectenerg-3309	389	16	statistical	statistical	ADJ
fuelectenerg-3309	389	17	problems	problem	NOUN
fuelectenerg-3309	389	18	involving	involve	VERB
fuelectenerg-3309	389	19	permutations	permutation	NOUN
fuelectenerg-3309	389	20	with	with	ADP
fuelectenerg-3309	389	21	restricted	restricted	ADJ
fuelectenerg-3309	389	22	positions	position	NOUN
fuelectenerg-3309	389	23	,	,	PUNCT
fuelectenerg-3309	389	24	”	"	PUNCT
fuelectenerg-3309	389	25	in	in	ADP
fuelectenerg-3309	389	26	lecture	lecture	NOUN
fuelectenerg-3309	389	27	notes	note	NOUN
fuelectenerg-3309	389	28	.	.	PUNCT
fuelectenerg-3309	390	1	monograph	monograph	NOUN
fuelectenerg-3309	390	2	series	series	PROPN
fuelectenerg-3309	390	3	,	,	PUNCT
fuelectenerg-3309	390	4	vol	vol	NOUN
fuelectenerg-3309	390	5	.	.	PROPN
fuelectenerg-3309	390	6	36	36	NUM
fuelectenerg-3309	390	7	,	,	PUNCT
fuelectenerg-3309	390	8	2001	2001	NUM
fuelectenerg-3309	390	9	,	,	PUNCT
fuelectenerg-3309	390	10	pp	pp	ADP
fuelectenerg-3309	390	11	.	.	PUNCT
fuelectenerg-3309	391	1	195–202	195–202	NUM
fuelectenerg-3309	391	2	.	.	PUNCT
fuelectenerg-3309	392	1	[	[	X
fuelectenerg-3309	392	2	9	9	NUM
fuelectenerg-3309	392	3	]	]	PUNCT
fuelectenerg-3309	392	4	p.	p.	NOUN
fuelectenerg-3309	392	5	diaconis	diaconis	NOUN
fuelectenerg-3309	392	6	and	and	CCONJ
fuelectenerg-3309	392	7	m.	m.	NOUN
fuelectenerg-3309	392	8	shahshahani	shahshahani	PROPN
fuelectenerg-3309	392	9	,	,	PUNCT
fuelectenerg-3309	392	10	“	"	PUNCT
fuelectenerg-3309	392	11	generating	generate	VERB
fuelectenerg-3309	392	12	a	a	DET
fuelectenerg-3309	392	13	random	random	ADJ
fuelectenerg-3309	392	14	permutation	permutation	NOUN
fuelectenerg-3309	392	15	with	with	ADP
fuelectenerg-3309	392	16	random	random	ADJ
fuelectenerg-3309	392	17	transposition	transposition	NOUN
fuelectenerg-3309	392	18	,	,	PUNCT
fuelectenerg-3309	392	19	”	"	PUNCT
fuelectenerg-3309	392	20	z.	z.	PROPN
fuelectenerg-3309	392	21	wahr	wahr	PROPN
fuelectenerg-3309	392	22	.	.	PUNCT
fuelectenerg-3309	393	1	verw	verw	PROPN
fuelectenerg-3309	393	2	.	.	PUNCT
fuelectenerg-3309	394	1	gebeite	gebeite	ADJ
fuelectenerg-3309	394	2	,	,	PUNCT
fuelectenerg-3309	394	3	vol	vol	NOUN
fuelectenerg-3309	394	4	.	.	PROPN
fuelectenerg-3309	395	1	57	57	NUM
fuelectenerg-3309	395	2	,	,	PUNCT
fuelectenerg-3309	395	3	no	no	INTJ
fuelectenerg-3309	395	4	.	.	NOUN
fuelectenerg-3309	395	5	2	2	NUM
fuelectenerg-3309	395	6	,	,	PUNCT
fuelectenerg-3309	395	7	pp	pp	ADJ
fuelectenerg-3309	395	8	.	.	PUNCT
fuelectenerg-3309	396	1	159–17	159–17	NUM
fuelectenerg-3309	396	2	,	,	PUNCT
fuelectenerg-3309	396	3	1981	1981	NUM
fuelectenerg-3309	396	4	.	.	PUNCT
fuelectenerg-3309	397	1	254	254	NUM
fuelectenerg-3309	397	2	c.	c.	PROPN
fuelectenerg-3309	397	3	karanikas	karanikas	PROPN
fuelectenerg-3309	397	4	,	,	PUNCT
fuelectenerg-3309	397	5	n.	n.	PROPN
fuelectenerg-3309	397	6	atreas	atreas	PROPN
fuelectenerg-3309	397	7	enumeration	enumeration	PROPN
fuelectenerg-3309	397	8	and	and	CCONJ
fuelectenerg-3309	397	9	coding	code	VERB
fuelectenerg-3309	397	10	permutations	permutation	NOUN
fuelectenerg-3309	397	11	and	and	CCONJ
fuelectenerg-3309	397	12	reversible	reversible	ADJ
fuelectenerg-3309	397	13	logical	logical	ADJ
fuelectenerg-3309	397	14	circuits	circuit	NOUN
fuelectenerg-3309	397	15	255	255	NUM