id	sid	tid	token	lemma	pos
ejpam-3860	1	1	european	european	PROPN
ejpam-3860	1	2	journal	journal	PROPN
ejpam-3860	1	3	of	of	ADP
ejpam-3860	1	4	pure	pure	ADJ
ejpam-3860	1	5	and	and	CCONJ
ejpam-3860	1	6	applied	apply	VERB
ejpam-3860	1	7	mathematics	mathematic	NOUN
ejpam-3860	1	8	vol	vol	NOUN
ejpam-3860	1	9	.	.	PUNCT
ejpam-3860	2	1	14	14	NUM
ejpam-3860	2	2	,	,	PUNCT
ejpam-3860	2	3	no	no	INTJ
ejpam-3860	2	4	.	.	NOUN
ejpam-3860	2	5	1	1	NUM
ejpam-3860	2	6	,	,	PUNCT
ejpam-3860	2	7	2021	2021	NUM
ejpam-3860	2	8	,	,	PUNCT
ejpam-3860	2	9	173	173	NUM
ejpam-3860	2	10	-	-	SYM
ejpam-3860	2	11	191	191	NUM
ejpam-3860	2	12	issn	issn	PROPN
ejpam-3860	2	13	1307	1307	NUM
ejpam-3860	2	14	-	-	SYM
ejpam-3860	2	15	5543	5543	NUM
ejpam-3860	2	16	–	–	PUNCT
ejpam-3860	3	1	ejpam.com	ejpam.com	X
ejpam-3860	3	2	published	publish	VERB
ejpam-3860	3	3	by	by	ADP
ejpam-3860	3	4	new	new	PROPN
ejpam-3860	3	5	york	york	PROPN
ejpam-3860	3	6	business	business	PROPN
ejpam-3860	3	7	global	global	PROPN
ejpam-3860	3	8	on	on	ADP
ejpam-3860	3	9	the	the	DET
ejpam-3860	3	10	independent	independent	ADJ
ejpam-3860	3	11	neighborhood	neighborhood	NOUN
ejpam-3860	3	12	polynomial	polynomial	NOUN
ejpam-3860	3	13	of	of	ADP
ejpam-3860	3	14	the	the	DET
ejpam-3860	3	15	cartesian	cartesian	ADJ
ejpam-3860	3	16	product	product	NOUN
ejpam-3860	3	17	of	of	ADP
ejpam-3860	3	18	some	some	DET
ejpam-3860	3	19	special	special	ADJ
ejpam-3860	3	20	graphs	graph	NOUN
ejpam-3860	3	21	normalah	normalah	NOUN
ejpam-3860	3	22	abdulcarim1,∗	abdulcarim1,∗	PROPN
ejpam-3860	3	23	,	,	PUNCT
ejpam-3860	3	24	susan	susan	PROPN
ejpam-3860	3	25	dagondon2	dagondon2	PROPN
ejpam-3860	3	26	,	,	PUNCT
ejpam-3860	3	27	emmy	emmy	ADJ
ejpam-3860	3	28	chacon2	chacon2	PROPN
ejpam-3860	3	29	1	1	NUM
ejpam-3860	3	30	department	department	NOUN
ejpam-3860	3	31	of	of	ADP
ejpam-3860	3	32	mathematics	mathematic	NOUN
ejpam-3860	3	33	,	,	PUNCT
ejpam-3860	3	34	college	college	NOUN
ejpam-3860	3	35	of	of	ADP
ejpam-3860	3	36	natural	natural	ADJ
ejpam-3860	3	37	sciences	science	NOUN
ejpam-3860	3	38	and	and	CCONJ
ejpam-3860	3	39	mathematics	mathematic	NOUN
ejpam-3860	3	40	,	,	PUNCT
ejpam-3860	3	41	mindanao	mindanao	PROPN
ejpam-3860	3	42	state	state	PROPN
ejpam-3860	3	43	university	university	PROPN
ejpam-3860	3	44	main	main	ADJ
ejpam-3860	3	45	campus	campus	NOUN
ejpam-3860	3	46	,	,	PUNCT
ejpam-3860	3	47	9700	9700	NUM
ejpam-3860	3	48	marawi	marawi	PROPN
ejpam-3860	3	49	city	city	PROPN
ejpam-3860	3	50	,	,	PUNCT
ejpam-3860	3	51	philippines	philippines	PROPN
ejpam-3860	3	52	2	2	NUM
ejpam-3860	3	53	department	department	NOUN
ejpam-3860	3	54	of	of	ADP
ejpam-3860	3	55	mathematics	mathematic	NOUN
ejpam-3860	3	56	and	and	CCONJ
ejpam-3860	3	57	statistics	statistic	NOUN
ejpam-3860	3	58	,	,	PUNCT
ejpam-3860	3	59	college	college	NOUN
ejpam-3860	3	60	of	of	ADP
ejpam-3860	3	61	science	science	NOUN
ejpam-3860	3	62	and	and	CCONJ
ejpam-3860	3	63	mathematics	mathematic	NOUN
ejpam-3860	3	64	,	,	PUNCT
ejpam-3860	3	65	center	center	NOUN
ejpam-3860	3	66	of	of	ADP
ejpam-3860	3	67	graph	graph	NOUN
ejpam-3860	3	68	theory	theory	NOUN
ejpam-3860	3	69	,	,	PUNCT
ejpam-3860	3	70	algebra	algebra	NOUN
ejpam-3860	3	71	,	,	PUNCT
ejpam-3860	3	72	and	and	CCONJ
ejpam-3860	3	73	analysis	analysis	NOUN
ejpam-3860	3	74	-	-	PUNCT
ejpam-3860	3	75	premier	premier	NOUN
ejpam-3860	3	76	research	research	NOUN
ejpam-3860	3	77	institute	institute	PROPN
ejpam-3860	3	78	of	of	ADP
ejpam-3860	3	79	science	science	NOUN
ejpam-3860	3	80	and	and	CCONJ
ejpam-3860	3	81	mathematics	mathematic	NOUN
ejpam-3860	3	82	,	,	PUNCT
ejpam-3860	3	83	mindanao	mindanao	PROPN
ejpam-3860	3	84	state	state	PROPN
ejpam-3860	3	85	university	university	PROPN
ejpam-3860	3	86	-	-	PUNCT
ejpam-3860	3	87	iligan	iligan	PROPN
ejpam-3860	3	88	institute	institute	PROPN
ejpam-3860	3	89	of	of	ADP
ejpam-3860	3	90	technology	technology	PROPN
ejpam-3860	3	91	,	,	PUNCT
ejpam-3860	3	92	9200	9200	NUM
ejpam-3860	3	93	iligan	iligan	ADJ
ejpam-3860	3	94	city	city	NOUN
ejpam-3860	3	95	,	,	PUNCT
ejpam-3860	3	96	philippines	philippine	NOUN
ejpam-3860	3	97	abstract	abstract	ADJ
ejpam-3860	3	98	.	.	PUNCT
ejpam-3860	4	1	two	two	NUM
ejpam-3860	4	2	vertices	vertex	NOUN
ejpam-3860	4	3	x	x	X
ejpam-3860	4	4	,	,	PUNCT
ejpam-3860	4	5	y	y	PROPN
ejpam-3860	4	6	of	of	ADP
ejpam-3860	4	7	a	a	DET
ejpam-3860	4	8	graph	graph	NOUN
ejpam-3860	4	9	g	g	NOUN
ejpam-3860	4	10	are	be	AUX
ejpam-3860	4	11	adjacent	adjacent	ADJ
ejpam-3860	4	12	,	,	PUNCT
ejpam-3860	4	13	or	or	CCONJ
ejpam-3860	4	14	neighbors	neighbor	NOUN
ejpam-3860	4	15	,	,	PUNCT
ejpam-3860	4	16	if	if	SCONJ
ejpam-3860	4	17	xy	xy	PROPN
ejpam-3860	4	18	is	be	AUX
ejpam-3860	4	19	an	an	DET
ejpam-3860	4	20	edge	edge	NOUN
ejpam-3860	4	21	of	of	ADP
ejpam-3860	4	22	g.	g.	PROPN
ejpam-3860	4	23	a	a	DET
ejpam-3860	4	24	set	set	NOUN
ejpam-3860	4	25	s	s	NOUN
ejpam-3860	4	26	of	of	ADP
ejpam-3860	4	27	vertices	vertex	NOUN
ejpam-3860	4	28	in	in	ADP
ejpam-3860	4	29	a	a	DET
ejpam-3860	4	30	graph	graph	NOUN
ejpam-3860	4	31	g	g	NOUN
ejpam-3860	4	32	is	be	AUX
ejpam-3860	4	33	a	a	DET
ejpam-3860	4	34	neighborhood	neighborhood	NOUN
ejpam-3860	4	35	set	set	VERB
ejpam-3860	4	36	if	if	SCONJ
ejpam-3860	4	37	g	g	NOUN
ejpam-3860	4	38	=	=	SYM
ejpam-3860	4	39	⋃	⋃	PROPN
ejpam-3860	4	40	v∈s	v∈s	ADJ
ejpam-3860	4	41	〈	〈	PROPN
ejpam-3860	4	42	n	n	PRON
ejpam-3860	4	43	[	[	X
ejpam-3860	4	44	v	v	NOUN
ejpam-3860	4	45	]	]	X
ejpam-3860	4	46	〉	〉	NOUN
ejpam-3860	4	47	where	where	SCONJ
ejpam-3860	4	48	〈	〈	PROPN
ejpam-3860	4	49	n	n	PRON
ejpam-3860	4	50	[	[	X
ejpam-3860	4	51	v	v	NOUN
ejpam-3860	4	52	]	]	X
ejpam-3860	4	53	〉	〉	PROPN
ejpam-3860	4	54	is	be	AUX
ejpam-3860	4	55	the	the	DET
ejpam-3860	4	56	subgraph	subgraph	NOUN
ejpam-3860	4	57	induced	induce	VERB
ejpam-3860	4	58	by	by	ADP
ejpam-3860	4	59	v	v	NOUN
ejpam-3860	4	60	and	and	CCONJ
ejpam-3860	4	61	all	all	DET
ejpam-3860	4	62	the	the	DET
ejpam-3860	4	63	vertices	vertex	NOUN
ejpam-3860	4	64	adjacent	adjacent	ADJ
ejpam-3860	4	65	to	to	ADP
ejpam-3860	4	66	v.	v.	INTJ
ejpam-3860	4	67	if	if	SCONJ
ejpam-3860	4	68	no	no	DET
ejpam-3860	4	69	two	two	NUM
ejpam-3860	4	70	of	of	ADP
ejpam-3860	4	71	the	the	DET
ejpam-3860	4	72	elements	element	NOUN
ejpam-3860	4	73	of	of	ADP
ejpam-3860	4	74	s	s	NOUN
ejpam-3860	4	75	are	be	AUX
ejpam-3860	4	76	adjacent	adjacent	ADJ
ejpam-3860	4	77	,	,	PUNCT
ejpam-3860	4	78	then	then	ADV
ejpam-3860	4	79	s	s	VERB
ejpam-3860	4	80	is	be	AUX
ejpam-3860	4	81	called	call	VERB
ejpam-3860	4	82	an	an	DET
ejpam-3860	4	83	independent	independent	ADJ
ejpam-3860	4	84	neighborhood	neighborhood	NOUN
ejpam-3860	4	85	set	set	NOUN
ejpam-3860	4	86	.	.	PUNCT
ejpam-3860	5	1	the	the	DET
ejpam-3860	5	2	independent	independent	ADJ
ejpam-3860	5	3	neighborhood	neighborhood	NOUN
ejpam-3860	5	4	polynomial	polynomial	NOUN
ejpam-3860	5	5	of	of	ADP
ejpam-3860	5	6	g	g	NOUN
ejpam-3860	5	7	of	of	ADP
ejpam-3860	5	8	order	order	NOUN
ejpam-3860	5	9	m	m	NOUN
ejpam-3860	5	10	is	be	AUX
ejpam-3860	5	11	ni(g	ni(g	NOUN
ejpam-3860	5	12	,	,	PUNCT
ejpam-3860	5	13	x	x	X
ejpam-3860	5	14	)	)	PUNCT
ejpam-3860	5	15	=	=	PUNCT
ejpam-3860	5	16	m∑	m∑	PRON
ejpam-3860	5	17	j	j	X
ejpam-3860	5	18	=	=	NOUN
ejpam-3860	5	19	ηi(g	ηi(g	NOUN
ejpam-3860	5	20	)	)	PUNCT
ejpam-3860	6	1	ni(g	ni(g	PUNCT
ejpam-3860	6	2	,	,	PUNCT
ejpam-3860	6	3	j)x	j)x	PROPN
ejpam-3860	6	4	j	j	PROPN
ejpam-3860	7	1	where	where	SCONJ
ejpam-3860	7	2	ni(g	ni(g	NUM
ejpam-3860	7	3	,	,	PUNCT
ejpam-3860	7	4	j	j	NOUN
ejpam-3860	7	5	)	)	PUNCT
ejpam-3860	7	6	is	be	AUX
ejpam-3860	7	7	the	the	DET
ejpam-3860	7	8	number	number	NOUN
ejpam-3860	7	9	of	of	ADP
ejpam-3860	7	10	independent	independent	ADJ
ejpam-3860	7	11	neighborhood	neighborhood	NOUN
ejpam-3860	7	12	set	set	NOUN
ejpam-3860	7	13	of	of	ADP
ejpam-3860	7	14	g	g	NOUN
ejpam-3860	7	15	of	of	ADP
ejpam-3860	7	16	size	size	NOUN
ejpam-3860	7	17	j	j	PROPN
ejpam-3860	7	18	and	and	CCONJ
ejpam-3860	7	19	ηi(g	ηi(g	NOUN
ejpam-3860	7	20	)	)	PUNCT
ejpam-3860	7	21	is	be	AUX
ejpam-3860	7	22	the	the	DET
ejpam-3860	7	23	minimum	minimum	ADJ
ejpam-3860	7	24	cardinality	cardinality	NOUN
ejpam-3860	7	25	of	of	ADP
ejpam-3860	7	26	an	an	DET
ejpam-3860	7	27	independent	independent	ADJ
ejpam-3860	7	28	neighborhood	neighborhood	NOUN
ejpam-3860	7	29	set	set	NOUN
ejpam-3860	7	30	of	of	ADP
ejpam-3860	7	31	g.	g.	PROPN
ejpam-3860	7	32	this	this	DET
ejpam-3860	7	33	paper	paper	NOUN
ejpam-3860	7	34	investigates	investigate	VERB
ejpam-3860	7	35	the	the	DET
ejpam-3860	7	36	independent	independent	ADJ
ejpam-3860	7	37	neighborhood	neighborhood	NOUN
ejpam-3860	7	38	polynomial	polynomial	NOUN
ejpam-3860	7	39	of	of	ADP
ejpam-3860	7	40	the	the	DET
ejpam-3860	7	41	cartesian	cartesian	ADJ
ejpam-3860	7	42	product	product	NOUN
ejpam-3860	7	43	of	of	ADP
ejpam-3860	7	44	some	some	DET
ejpam-3860	7	45	special	special	ADJ
ejpam-3860	7	46	graphs	graph	NOUN
ejpam-3860	7	47	.	.	PUNCT
ejpam-3860	8	1	2020	2020	NUM
ejpam-3860	8	2	mathematics	mathematic	NOUN
ejpam-3860	8	3	subject	subject	NOUN
ejpam-3860	8	4	classifications	classification	NOUN
ejpam-3860	8	5	:	:	PUNCT
ejpam-3860	8	6	05c31	05c31	NUM
ejpam-3860	8	7	,	,	PUNCT
ejpam-3860	8	8	05c69	05c69	NUM
ejpam-3860	8	9	,	,	PUNCT
ejpam-3860	8	10	05c76	05c76	DET
ejpam-3860	8	11	key	key	ADJ
ejpam-3860	8	12	words	word	NOUN
ejpam-3860	8	13	and	and	CCONJ
ejpam-3860	8	14	phrases	phrase	NOUN
ejpam-3860	8	15	:	:	PUNCT
ejpam-3860	8	16	independent	independent	ADJ
ejpam-3860	8	17	neighborhood	neighborhood	NOUN
ejpam-3860	8	18	set	set	NOUN
ejpam-3860	8	19	,	,	PUNCT
ejpam-3860	8	20	neighborhood	neighborhood	NOUN
ejpam-3860	8	21	polynomial	polynomial	ADJ
ejpam-3860	8	22	,	,	PUNCT
ejpam-3860	8	23	cartesian	cartesian	ADJ
ejpam-3860	8	24	product	product	NOUN
ejpam-3860	8	25	1	1	NUM
ejpam-3860	8	26	.	.	PUNCT
ejpam-3860	8	27	introduction	introduction	NOUN
ejpam-3860	8	28	the	the	DET
ejpam-3860	8	29	history	history	NOUN
ejpam-3860	8	30	of	of	ADP
ejpam-3860	8	31	graph	graph	NOUN
ejpam-3860	8	32	theory	theory	NOUN
ejpam-3860	8	33	may	may	AUX
ejpam-3860	8	34	be	be	AUX
ejpam-3860	8	35	specifically	specifically	ADV
ejpam-3860	8	36	traced	trace	VERB
ejpam-3860	8	37	to	to	ADP
ejpam-3860	8	38	1735	1735	NUM
ejpam-3860	8	39	when	when	SCONJ
ejpam-3860	8	40	the	the	DET
ejpam-3860	8	41	swiss	swiss	ADJ
ejpam-3860	8	42	mathematician	mathematician	NOUN
ejpam-3860	8	43	leonhard	leonhard	PROPN
ejpam-3860	8	44	euler	euler	PROPN
ejpam-3860	8	45	solve	solve	VERB
ejpam-3860	8	46	the	the	DET
ejpam-3860	8	47	königberg	königberg	PROPN
ejpam-3860	8	48	bridge	bridge	PROPN
ejpam-3860	8	49	problem	problem	NOUN
ejpam-3860	8	50	.	.	PUNCT
ejpam-3860	9	1	there	there	PRON
ejpam-3860	9	2	are	be	VERB
ejpam-3860	9	3	number	number	NOUN
ejpam-3860	9	4	of	of	ADP
ejpam-3860	9	5	applications	application	NOUN
ejpam-3860	9	6	of	of	ADP
ejpam-3860	9	7	graph	graph	NOUN
ejpam-3860	9	8	theory	theory	NOUN
ejpam-3860	9	9	that	that	PRON
ejpam-3860	9	10	have	have	AUX
ejpam-3860	9	11	been	be	AUX
ejpam-3860	9	12	widely	widely	ADV
ejpam-3860	9	13	studied	study	VERB
ejpam-3860	9	14	.	.	PUNCT
ejpam-3860	10	1	a	a	DET
ejpam-3860	10	2	graph	graph	NOUN
ejpam-3860	10	3	polynomial	polynomial	NOUN
ejpam-3860	10	4	is	be	AUX
ejpam-3860	10	5	one	one	NUM
ejpam-3860	10	6	of	of	ADP
ejpam-3860	10	7	the	the	DET
ejpam-3860	10	8	algebraic	algebraic	ADJ
ejpam-3860	10	9	reperesentations	reperesentation	NOUN
ejpam-3860	10	10	for	for	ADP
ejpam-3860	10	11	graph	graph	NOUN
ejpam-3860	10	12	.	.	PUNCT
ejpam-3860	11	1	in	in	ADP
ejpam-3860	11	2	this	this	DET
ejpam-3860	11	3	paper	paper	NOUN
ejpam-3860	11	4	,	,	PUNCT
ejpam-3860	11	5	we	we	PRON
ejpam-3860	11	6	study	study	VERB
ejpam-3860	11	7	a	a	DET
ejpam-3860	11	8	new	new	ADJ
ejpam-3860	11	9	type	type	NOUN
ejpam-3860	11	10	of	of	ADP
ejpam-3860	11	11	graph	graph	NOUN
ejpam-3860	11	12	polynomial	polynomial	NOUN
ejpam-3860	11	13	called	call	VERB
ejpam-3860	11	14	the	the	DET
ejpam-3860	11	15	independent	independent	ADJ
ejpam-3860	11	16	neighborhood	neighborhood	NOUN
ejpam-3860	11	17	polynomial	polynomial	NOUN
ejpam-3860	11	18	[	[	X
ejpam-3860	11	19	10	10	NUM
ejpam-3860	11	20	]	]	PUNCT
ejpam-3860	11	21	.	.	PUNCT
ejpam-3860	12	1	throughout	throughout	ADP
ejpam-3860	12	2	this	this	DET
ejpam-3860	12	3	paper	paper	NOUN
ejpam-3860	12	4	,	,	PUNCT
ejpam-3860	12	5	we	we	PRON
ejpam-3860	12	6	consider	consider	VERB
ejpam-3860	12	7	only	only	ADV
ejpam-3860	12	8	a	a	DET
ejpam-3860	12	9	finite	finite	ADJ
ejpam-3860	12	10	,	,	PUNCT
ejpam-3860	12	11	simple	simple	ADJ
ejpam-3860	12	12	,	,	PUNCT
ejpam-3860	12	13	undirected	undirected	ADJ
ejpam-3860	12	14	graphs	graph	NOUN
ejpam-3860	12	15	without	without	ADP
ejpam-3860	12	16	loops	loop	NOUN
ejpam-3860	12	17	and	and	CCONJ
ejpam-3860	12	18	multiple	multiple	ADJ
ejpam-3860	12	19	edges	edge	NOUN
ejpam-3860	12	20	.	.	PUNCT
ejpam-3860	13	1	∗corresponding	∗corresponde	VERB
ejpam-3860	13	2	author	author	NOUN
ejpam-3860	13	3	.	.	PUNCT
ejpam-3860	14	1	doi	doi	NOUN
ejpam-3860	14	2	:	:	PUNCT
ejpam-3860	14	3	https://doi.org/10.29020/nybg.ejpam.v14i1.3860	https://doi.org/10.29020/nybg.ejpam.v14i1.3860	NOUN
ejpam-3860	14	4	email	email	NOUN
ejpam-3860	14	5	addresses	address	VERB
ejpam-3860	14	6	:	:	PUNCT
ejpam-3860	14	7	n	n	PRON
ejpam-3860	14	8	abdulcarim@yahoo.com	abdulcarim@yahoo.com	X
ejpam-3860	14	9	(	(	PUNCT
ejpam-3860	14	10	n.	n.	PROPN
ejpam-3860	14	11	abdulcarim	abdulcarim	PROPN
ejpam-3860	14	12	)	)	PUNCT
ejpam-3860	14	13	,	,	PUNCT
ejpam-3860	14	14	susan.dagondon@g.msuiit.edu.ph	susan.dagondon@g.msuiit.edu.ph	PROPN
ejpam-3860	14	15	(	(	PUNCT
ejpam-3860	14	16	s.	s.	PROPN
ejpam-3860	14	17	dagondon	dagondon	PROPN
ejpam-3860	14	18	)	)	PUNCT
ejpam-3860	14	19	,	,	PUNCT
ejpam-3860	14	20	emmy.chacon@g.msuiit.edu.ph	emmy.chacon@g.msuiit.edu.ph	PROPN
ejpam-3860	14	21	(	(	PUNCT
ejpam-3860	14	22	e.	e.	PROPN
ejpam-3860	14	23	chacon	chacon	PROPN
ejpam-3860	14	24	)	)	PUNCT
ejpam-3860	14	25	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3860	15	1	173	173	NUM
ejpam-3860	15	2	c	c	X
ejpam-3860	15	3	©	©	PROPN
ejpam-3860	15	4	2021	2021	NUM
ejpam-3860	15	5	ejpam	ejpam	VERB
ejpam-3860	15	6	all	all	DET
ejpam-3860	15	7	rights	right	NOUN
ejpam-3860	15	8	reserved	reserve	VERB
ejpam-3860	15	9	.	.	PUNCT
ejpam-3860	16	1	n.	n.	PROPN
ejpam-3860	16	2	abdulcarim	abdulcarim	PROPN
ejpam-3860	16	3	,	,	PUNCT
ejpam-3860	16	4	s.	s.	PROPN
ejpam-3860	16	5	dagondon	dagondon	PROPN
ejpam-3860	16	6	,	,	PUNCT
ejpam-3860	16	7	e.	e.	PROPN
ejpam-3860	16	8	chacon	chacon	PROPN
ejpam-3860	16	9	/	/	SYM
ejpam-3860	16	10	eur	eur	PROPN
ejpam-3860	16	11	.	.	PUNCT
ejpam-3860	17	1	j.	j.	PROPN
ejpam-3860	17	2	pure	pure	PROPN
ejpam-3860	17	3	appl	appl	PROPN
ejpam-3860	17	4	.	.	PROPN
ejpam-3860	17	5	math	math	PROPN
ejpam-3860	17	6	,	,	PUNCT
ejpam-3860	17	7	14	14	NUM
ejpam-3860	17	8	(	(	PUNCT
ejpam-3860	17	9	1	1	NUM
ejpam-3860	17	10	)	)	PUNCT
ejpam-3860	17	11	(	(	PUNCT
ejpam-3860	17	12	2021	2021	NUM
ejpam-3860	17	13	)	)	PUNCT
ejpam-3860	17	14	,	,	PUNCT
ejpam-3860	17	15	173	173	NUM
ejpam-3860	17	16	-	-	SYM
ejpam-3860	17	17	191	191	NUM
ejpam-3860	17	18	174	174	NUM
ejpam-3860	17	19	a	a	DET
ejpam-3860	17	20	graph	graph	NOUN
ejpam-3860	17	21	g	g	NOUN
ejpam-3860	17	22	is	be	AUX
ejpam-3860	17	23	a	a	DET
ejpam-3860	17	24	pair	pair	NOUN
ejpam-3860	17	25	(	(	PUNCT
ejpam-3860	17	26	v	v	NOUN
ejpam-3860	17	27	(	(	PUNCT
ejpam-3860	17	28	g	g	NOUN
ejpam-3860	17	29	)	)	PUNCT
ejpam-3860	17	30	,	,	PUNCT
ejpam-3860	17	31	e(g	e(g	PROPN
ejpam-3860	17	32	)	)	PUNCT
ejpam-3860	17	33	)	)	PUNCT
ejpam-3860	18	1	consisting	consist	VERB
ejpam-3860	18	2	of	of	ADP
ejpam-3860	18	3	a	a	DET
ejpam-3860	18	4	nonempty	nonempty	ADJ
ejpam-3860	18	5	finite	finite	NOUN
ejpam-3860	18	6	set	set	NOUN
ejpam-3860	18	7	of	of	ADP
ejpam-3860	18	8	vertices	vertex	NOUN
ejpam-3860	18	9	v	v	X
ejpam-3860	18	10	(	(	PUNCT
ejpam-3860	18	11	g	g	NOUN
ejpam-3860	18	12	)	)	PUNCT
ejpam-3860	18	13	and	and	CCONJ
ejpam-3860	18	14	a	a	DET
ejpam-3860	18	15	set	set	NOUN
ejpam-3860	18	16	of	of	ADP
ejpam-3860	18	17	edges	edge	NOUN
ejpam-3860	18	18	e(g	e(g	PROPN
ejpam-3860	18	19	)	)	PUNCT
ejpam-3860	18	20	of	of	ADP
ejpam-3860	18	21	unordered	unordered	ADJ
ejpam-3860	18	22	pairs	pair	NOUN
ejpam-3860	18	23	of	of	ADP
ejpam-3860	18	24	elements	element	NOUN
ejpam-3860	18	25	of	of	ADP
ejpam-3860	18	26	v	v	NOUN
ejpam-3860	18	27	(	(	PUNCT
ejpam-3860	18	28	g	g	NOUN
ejpam-3860	18	29	)	)	PUNCT
ejpam-3860	18	30	.	.	PUNCT
ejpam-3860	19	1	the	the	DET
ejpam-3860	19	2	cardinalities	cardinality	NOUN
ejpam-3860	19	3	of	of	ADP
ejpam-3860	19	4	v	v	NOUN
ejpam-3860	19	5	(	(	PUNCT
ejpam-3860	19	6	g	g	NOUN
ejpam-3860	19	7	)	)	PUNCT
ejpam-3860	19	8	and	and	CCONJ
ejpam-3860	19	9	e(g	e(g	PROPN
ejpam-3860	19	10	)	)	PUNCT
ejpam-3860	19	11	are	be	AUX
ejpam-3860	19	12	called	call	VERB
ejpam-3860	19	13	the	the	DET
ejpam-3860	19	14	order	order	NOUN
ejpam-3860	19	15	and	and	CCONJ
ejpam-3860	19	16	size	size	NOUN
ejpam-3860	19	17	of	of	ADP
ejpam-3860	19	18	g	g	NOUN
ejpam-3860	19	19	,	,	PUNCT
ejpam-3860	19	20	respectively	respectively	ADV
ejpam-3860	19	21	.	.	PUNCT
ejpam-3860	20	1	we	we	PRON
ejpam-3860	20	2	write	write	VERB
ejpam-3860	20	3	x	x	PUNCT
ejpam-3860	20	4	=	=	PUNCT
ejpam-3860	20	5	uv	uv	NOUN
ejpam-3860	20	6	and	and	CCONJ
ejpam-3860	20	7	say	say	VERB
ejpam-3860	20	8	that	that	SCONJ
ejpam-3860	20	9	u	u	PROPN
ejpam-3860	20	10	and	and	CCONJ
ejpam-3860	20	11	v	v	NOUN
ejpam-3860	20	12	are	be	AUX
ejpam-3860	20	13	adjacent	adjacent	ADJ
ejpam-3860	20	14	vertices	vertex	NOUN
ejpam-3860	20	15	;	;	PUNCT
ejpam-3860	20	16	vertex	vertex	NOUN
ejpam-3860	20	17	u	u	NOUN
ejpam-3860	20	18	and	and	CCONJ
ejpam-3860	20	19	edge	edge	NOUN
ejpam-3860	20	20	x	x	VERB
ejpam-3860	20	21	are	be	AUX
ejpam-3860	20	22	incident	incident	NOUN
ejpam-3860	20	23	with	with	ADP
ejpam-3860	20	24	each	each	DET
ejpam-3860	20	25	other	other	ADJ
ejpam-3860	20	26	,	,	PUNCT
ejpam-3860	20	27	so	so	ADV
ejpam-3860	20	28	are	be	AUX
ejpam-3860	20	29	v	v	ADJ
ejpam-3860	20	30	and	and	CCONJ
ejpam-3860	20	31	x.	x.	NOUN
ejpam-3860	20	32	the	the	DET
ejpam-3860	20	33	two	two	NUM
ejpam-3860	20	34	vertices	vertex	NOUN
ejpam-3860	20	35	incident	incident	NOUN
ejpam-3860	20	36	with	with	ADP
ejpam-3860	20	37	an	an	DET
ejpam-3860	20	38	edge	edge	NOUN
ejpam-3860	20	39	are	be	AUX
ejpam-3860	20	40	its	its	PRON
ejpam-3860	20	41	endvertices	endvertice	NOUN
ejpam-3860	20	42	or	or	CCONJ
ejpam-3860	20	43	ends	end	NOUN
ejpam-3860	20	44	,	,	PUNCT
ejpam-3860	20	45	and	and	CCONJ
ejpam-3860	20	46	an	an	DET
ejpam-3860	20	47	edge	edge	NOUN
ejpam-3860	20	48	joins	join	VERB
ejpam-3860	20	49	its	its	PRON
ejpam-3860	20	50	ends	end	NOUN
ejpam-3860	20	51	.	.	PUNCT
ejpam-3860	21	1	two	two	NUM
ejpam-3860	21	2	vertices	vertex	NOUN
ejpam-3860	21	3	of	of	ADP
ejpam-3860	21	4	a	a	DET
ejpam-3860	21	5	graph	graph	NOUN
ejpam-3860	21	6	g	g	NOUN
ejpam-3860	21	7	are	be	AUX
ejpam-3860	21	8	said	say	VERB
ejpam-3860	21	9	to	to	PART
ejpam-3860	21	10	be	be	AUX
ejpam-3860	21	11	neighbors	neighbor	NOUN
ejpam-3860	21	12	if	if	SCONJ
ejpam-3860	21	13	they	they	PRON
ejpam-3860	21	14	are	be	AUX
ejpam-3860	21	15	adjacent	adjacent	ADJ
ejpam-3860	21	16	in	in	ADP
ejpam-3860	21	17	g.	g.	PROPN
ejpam-3860	21	18	the	the	DET
ejpam-3860	21	19	neighborhood	neighborhood	NOUN
ejpam-3860	21	20	of	of	ADP
ejpam-3860	21	21	a	a	DET
ejpam-3860	21	22	vertex	vertex	NOUN
ejpam-3860	21	23	v	v	ADP
ejpam-3860	21	24	∈	∈	NOUN
ejpam-3860	21	25	v	v	NOUN
ejpam-3860	21	26	is	be	AUX
ejpam-3860	21	27	the	the	DET
ejpam-3860	21	28	set	set	NOUN
ejpam-3860	21	29	ng(v	ng(v	PUNCT
ejpam-3860	21	30	)	)	PUNCT
ejpam-3860	21	31	=	=	PRON
ejpam-3860	22	1	{	{	PUNCT
ejpam-3860	22	2	w	w	NOUN
ejpam-3860	22	3	:	:	PUNCT
ejpam-3860	22	4	w	w	PROPN
ejpam-3860	22	5	∈	∈	PROPN
ejpam-3860	22	6	v	v	NOUN
ejpam-3860	22	7	and	and	CCONJ
ejpam-3860	22	8	vw	vw	PROPN
ejpam-3860	22	9	∈	∈	PROPN
ejpam-3860	22	10	e(g	e(g	PROPN
ejpam-3860	22	11	)	)	PUNCT
ejpam-3860	22	12	}	}	PUNCT
ejpam-3860	22	13	.	.	PUNCT
ejpam-3860	23	1	a	a	DET
ejpam-3860	23	2	vertex	vertex	NOUN
ejpam-3860	23	3	v	v	NOUN
ejpam-3860	23	4	is	be	AUX
ejpam-3860	23	5	pendant	pendant	ADJ
ejpam-3860	23	6	if	if	SCONJ
ejpam-3860	23	7	its	its	PRON
ejpam-3860	23	8	neighborhood	neighborhood	NOUN
ejpam-3860	23	9	contains	contain	VERB
ejpam-3860	23	10	only	only	ADV
ejpam-3860	23	11	one	one	NUM
ejpam-3860	23	12	vertex	vertex	NOUN
ejpam-3860	23	13	;	;	PUNCT
ejpam-3860	23	14	and	and	CCONJ
ejpam-3860	23	15	edge	edge	NOUN
ejpam-3860	23	16	e	e	NOUN
ejpam-3860	23	17	=	=	NOUN
ejpam-3860	23	18	uv	uv	NOUN
ejpam-3860	23	19	is	be	AUX
ejpam-3860	23	20	pendant	pendant	ADJ
ejpam-3860	23	21	if	if	SCONJ
ejpam-3860	23	22	one	one	NUM
ejpam-3860	23	23	of	of	ADP
ejpam-3860	23	24	its	its	PRON
ejpam-3860	23	25	endvertices	endvertice	NOUN
ejpam-3860	23	26	is	be	AUX
ejpam-3860	23	27	a	a	DET
ejpam-3860	23	28	pendant	pendant	ADJ
ejpam-3860	23	29	vertex	vertex	NOUN
ejpam-3860	23	30	.	.	PUNCT
ejpam-3860	24	1	a	a	DET
ejpam-3860	24	2	graph	graph	NOUN
ejpam-3860	24	3	h	h	NOUN
ejpam-3860	24	4	is	be	AUX
ejpam-3860	24	5	called	call	VERB
ejpam-3860	24	6	a	a	DET
ejpam-3860	24	7	subgraph	subgraph	NOUN
ejpam-3860	24	8	of	of	ADP
ejpam-3860	24	9	g	g	NOUN
ejpam-3860	24	10	,	,	PUNCT
ejpam-3860	24	11	written	write	VERB
ejpam-3860	24	12	h	h	NOUN
ejpam-3860	24	13	⊆	⊆	NUM
ejpam-3860	24	14	g	g	NOUN
ejpam-3860	24	15	,	,	PUNCT
ejpam-3860	24	16	if	if	SCONJ
ejpam-3860	24	17	v	v	X
ejpam-3860	24	18	(	(	PUNCT
ejpam-3860	24	19	h	h	NOUN
ejpam-3860	24	20	)	)	PUNCT
ejpam-3860	24	21	⊆	⊆	NUM
ejpam-3860	24	22	v	v	NOUN
ejpam-3860	24	23	(	(	PUNCT
ejpam-3860	24	24	g	g	NOUN
ejpam-3860	24	25	)	)	PUNCT
ejpam-3860	24	26	and	and	CCONJ
ejpam-3860	24	27	e(h	e(h	NOUN
ejpam-3860	24	28	)	)	PUNCT
ejpam-3860	24	29	⊆	⊆	NUM
ejpam-3860	24	30	e(g	e(g	PROPN
ejpam-3860	24	31	)	)	PUNCT
ejpam-3860	24	32	.	.	PUNCT
ejpam-3860	25	1	if	if	SCONJ
ejpam-3860	25	2	h	h	NOUN
ejpam-3860	25	3	⊆	⊆	NUM
ejpam-3860	25	4	g	g	NOUN
ejpam-3860	25	5	and	and	CCONJ
ejpam-3860	25	6	either	either	CCONJ
ejpam-3860	25	7	v	v	NOUN
ejpam-3860	25	8	(	(	PUNCT
ejpam-3860	25	9	h	h	NOUN
ejpam-3860	25	10	)	)	PUNCT
ejpam-3860	25	11	is	be	AUX
ejpam-3860	25	12	a	a	DET
ejpam-3860	25	13	proper	proper	ADJ
ejpam-3860	25	14	subset	subset	NOUN
ejpam-3860	25	15	of	of	ADP
ejpam-3860	25	16	v	v	NOUN
ejpam-3860	25	17	(	(	PUNCT
ejpam-3860	25	18	g	g	NOUN
ejpam-3860	25	19	)	)	PUNCT
ejpam-3860	25	20	or	or	CCONJ
ejpam-3860	25	21	e(h	e(h	PROPN
ejpam-3860	25	22	)	)	PUNCT
ejpam-3860	25	23	is	be	AUX
ejpam-3860	25	24	a	a	DET
ejpam-3860	25	25	proper	proper	ADJ
ejpam-3860	25	26	subset	subset	NOUN
ejpam-3860	25	27	of	of	ADP
ejpam-3860	25	28	e(g	e(g	PROPN
ejpam-3860	25	29	)	)	PUNCT
ejpam-3860	25	30	,	,	PUNCT
ejpam-3860	25	31	then	then	ADV
ejpam-3860	25	32	h	h	PROPN
ejpam-3860	25	33	is	be	AUX
ejpam-3860	25	34	a	a	DET
ejpam-3860	25	35	proper	proper	ADJ
ejpam-3860	25	36	subgraph	subgraph	NOUN
ejpam-3860	25	37	of	of	ADP
ejpam-3860	25	38	g.	g.	PROPN
ejpam-3860	25	39	a	a	DET
ejpam-3860	25	40	subgraph	subgraph	NOUN
ejpam-3860	25	41	f	f	PROPN
ejpam-3860	25	42	of	of	ADP
ejpam-3860	25	43	a	a	DET
ejpam-3860	25	44	graph	graph	NOUN
ejpam-3860	25	45	g	g	NOUN
ejpam-3860	25	46	is	be	AUX
ejpam-3860	25	47	called	call	VERB
ejpam-3860	25	48	an	an	DET
ejpam-3860	25	49	induced	induced	ADJ
ejpam-3860	25	50	subgraph	subgraph	NOUN
ejpam-3860	25	51	of	of	ADP
ejpam-3860	25	52	g	g	NOUN
ejpam-3860	25	53	,	,	PUNCT
ejpam-3860	25	54	denoted	denote	VERB
ejpam-3860	25	55	by	by	ADP
ejpam-3860	25	56	〈	〈	PROPN
ejpam-3860	25	57	f	f	PROPN
ejpam-3860	25	58	〉	〉	PROPN
ejpam-3860	25	59	,	,	PUNCT
ejpam-3860	25	60	if	if	SCONJ
ejpam-3860	25	61	whenever	whenever	SCONJ
ejpam-3860	25	62	u	u	NOUN
ejpam-3860	25	63	and	and	CCONJ
ejpam-3860	25	64	v	v	NOUN
ejpam-3860	25	65	are	be	AUX
ejpam-3860	25	66	vertices	vertex	NOUN
ejpam-3860	25	67	of	of	ADP
ejpam-3860	25	68	f	f	PROPN
ejpam-3860	25	69	and	and	CCONJ
ejpam-3860	25	70	uv	uv	NOUN
ejpam-3860	25	71	is	be	AUX
ejpam-3860	25	72	an	an	DET
ejpam-3860	25	73	edge	edge	NOUN
ejpam-3860	25	74	of	of	ADP
ejpam-3860	25	75	g	g	NOUN
ejpam-3860	25	76	,	,	PUNCT
ejpam-3860	25	77	then	then	ADV
ejpam-3860	25	78	uv	uv	NOUN
ejpam-3860	25	79	is	be	AUX
ejpam-3860	25	80	an	an	DET
ejpam-3860	25	81	edge	edge	NOUN
ejpam-3860	25	82	of	of	ADP
ejpam-3860	25	83	f	f	PROPN
ejpam-3860	25	84	as	as	ADV
ejpam-3860	25	85	well	well	ADV
ejpam-3860	25	86	.	.	PUNCT
ejpam-3860	26	1	a	a	DET
ejpam-3860	26	2	path	path	NOUN
ejpam-3860	26	3	is	be	AUX
ejpam-3860	26	4	a	a	DET
ejpam-3860	26	5	nonempty	nonempty	ADJ
ejpam-3860	26	6	graph	graph	NOUN
ejpam-3860	26	7	p	p	X
ejpam-3860	26	8	=	=	X
ejpam-3860	26	9	(	(	PUNCT
ejpam-3860	26	10	v	v	NOUN
ejpam-3860	26	11	,	,	PUNCT
ejpam-3860	26	12	e	e	NOUN
ejpam-3860	26	13	)	)	PUNCT
ejpam-3860	26	14	of	of	ADP
ejpam-3860	26	15	the	the	DET
ejpam-3860	26	16	form	form	NOUN
ejpam-3860	26	17	v	v	NOUN
ejpam-3860	26	18	=	=	SYM
ejpam-3860	26	19	{	{	PUNCT
ejpam-3860	26	20	v1	v1	PROPN
ejpam-3860	26	21	,	,	PUNCT
ejpam-3860	26	22	·	·	PUNCT
ejpam-3860	26	23	·	·	PUNCT
ejpam-3860	26	24	·	·	PUNCT
ejpam-3860	26	25	,	,	PUNCT
ejpam-3860	26	26	vm	vm	NOUN
ejpam-3860	26	27	}	}	PUNCT
ejpam-3860	26	28	e	e	X
ejpam-3860	26	29	=	=	PRON
ejpam-3860	26	30	{	{	PUNCT
ejpam-3860	26	31	v1v2	v1v2	PROPN
ejpam-3860	26	32	,	,	PUNCT
ejpam-3860	26	33	v2v3	v2v3	PROPN
ejpam-3860	26	34	,	,	PUNCT
ejpam-3860	26	35	·	·	PUNCT
ejpam-3860	26	36	·	·	PUNCT
ejpam-3860	26	37	·	·	PUNCT
ejpam-3860	26	38	,	,	PUNCT
ejpam-3860	26	39	vm−1vm	vm−1vm	NOUN
ejpam-3860	26	40	}	}	PUNCT
ejpam-3860	26	41	,	,	PUNCT
ejpam-3860	26	42	where	where	SCONJ
ejpam-3860	26	43	the	the	DET
ejpam-3860	26	44	vi	vi	NOUN
ejpam-3860	26	45	are	be	AUX
ejpam-3860	26	46	all	all	ADV
ejpam-3860	26	47	distinct	distinct	ADJ
ejpam-3860	26	48	.	.	PUNCT
ejpam-3860	27	1	in	in	ADP
ejpam-3860	27	2	this	this	DET
ejpam-3860	27	3	research	research	NOUN
ejpam-3860	27	4	,	,	PUNCT
ejpam-3860	27	5	we	we	PRON
ejpam-3860	27	6	focused	focus	VERB
ejpam-3860	27	7	to	to	PART
ejpam-3860	27	8	determine	determine	VERB
ejpam-3860	27	9	the	the	DET
ejpam-3860	27	10	independent	independent	ADJ
ejpam-3860	27	11	neighborhood	neighborhood	NOUN
ejpam-3860	27	12	sets	set	NOUN
ejpam-3860	27	13	of	of	ADP
ejpam-3860	27	14	the	the	DET
ejpam-3860	27	15	cartesian	cartesian	ADJ
ejpam-3860	27	16	product	product	NOUN
ejpam-3860	27	17	of	of	ADP
ejpam-3860	27	18	some	some	DET
ejpam-3860	27	19	special	special	ADJ
ejpam-3860	27	20	graphs	graph	NOUN
ejpam-3860	27	21	with	with	ADP
ejpam-3860	27	22	path	path	NOUN
ejpam-3860	27	23	and	and	CCONJ
ejpam-3860	27	24	represent	represent	VERB
ejpam-3860	27	25	them	they	PRON
ejpam-3860	27	26	in	in	ADP
ejpam-3860	27	27	a	a	DET
ejpam-3860	27	28	graph	graph	NOUN
ejpam-3860	27	29	polynomial	polynomial	NOUN
ejpam-3860	27	30	called	call	VERB
ejpam-3860	27	31	independent	independent	ADJ
ejpam-3860	27	32	neighborhood	neighborhood	NOUN
ejpam-3860	27	33	polynomial	polynomial	NOUN
ejpam-3860	27	34	.	.	PUNCT
ejpam-3860	28	1	the	the	DET
ejpam-3860	28	2	readers	reader	NOUN
ejpam-3860	28	3	may	may	AUX
ejpam-3860	28	4	also	also	ADV
ejpam-3860	28	5	read	read	VERB
ejpam-3860	28	6	on	on	ADP
ejpam-3860	28	7	the	the	DET
ejpam-3860	28	8	following	following	ADJ
ejpam-3860	28	9	references	reference	NOUN
ejpam-3860	28	10	:	:	PUNCT
ejpam-3860	29	1	[	[	X
ejpam-3860	29	2	1],[2],[3	1],[2],[3	X
ejpam-3860	29	3	]	]	X
ejpam-3860	29	4	,	,	PUNCT
ejpam-3860	30	1	[	[	X
ejpam-3860	30	2	5],[9],[11	5],[9],[11	X
ejpam-3860	30	3	]	]	PUNCT
ejpam-3860	30	4	and	and	CCONJ
ejpam-3860	30	5	[	[	X
ejpam-3860	30	6	6	6	NUM
ejpam-3860	30	7	]	]	PUNCT
ejpam-3860	30	8	.	.	PUNCT
ejpam-3860	31	1	2	2	X
ejpam-3860	31	2	.	.	X
ejpam-3860	31	3	preliminaries	preliminary	NOUN
ejpam-3860	31	4	definition	definition	NOUN
ejpam-3860	31	5	1	1	NUM
ejpam-3860	31	6	.	.	PUNCT
ejpam-3860	32	1	[	[	X
ejpam-3860	32	2	7	7	X
ejpam-3860	32	3	]	]	X
ejpam-3860	32	4	a	a	DET
ejpam-3860	32	5	graph	graph	NOUN
ejpam-3860	32	6	g	g	NOUN
ejpam-3860	32	7	is	be	AUX
ejpam-3860	32	8	a	a	DET
ejpam-3860	32	9	bipartite	bipartite	ADJ
ejpam-3860	32	10	graph	graph	NOUN
ejpam-3860	32	11	,	,	PUNCT
ejpam-3860	32	12	denoted	denote	VERB
ejpam-3860	32	13	by	by	ADP
ejpam-3860	32	14	km	km	PROPN
ejpam-3860	32	15	,	,	PUNCT
ejpam-3860	32	16	n	n	CCONJ
ejpam-3860	32	17	,	,	PUNCT
ejpam-3860	32	18	if	if	SCONJ
ejpam-3860	32	19	v	v	X
ejpam-3860	32	20	(	(	PUNCT
ejpam-3860	32	21	g	g	NOUN
ejpam-3860	32	22	)	)	PUNCT
ejpam-3860	32	23	can	can	AUX
ejpam-3860	32	24	be	be	AUX
ejpam-3860	32	25	partitioned	partition	VERB
ejpam-3860	32	26	into	into	ADP
ejpam-3860	32	27	two	two	NUM
ejpam-3860	32	28	subsets	subset	NOUN
ejpam-3860	32	29	vm	vm	PROPN
ejpam-3860	32	30	and	and	CCONJ
ejpam-3860	32	31	vn	vn	PROPN
ejpam-3860	32	32	of	of	ADP
ejpam-3860	32	33	order	order	NOUN
ejpam-3860	32	34	m	m	VERB
ejpam-3860	32	35	and	and	CCONJ
ejpam-3860	32	36	n	n	CCONJ
ejpam-3860	32	37	,	,	PUNCT
ejpam-3860	32	38	respectively	respectively	ADV
ejpam-3860	32	39	,	,	PUNCT
ejpam-3860	32	40	called	call	VERB
ejpam-3860	32	41	partite	partite	ADJ
ejpam-3860	32	42	sets	set	NOUN
ejpam-3860	32	43	such	such	ADJ
ejpam-3860	32	44	that	that	SCONJ
ejpam-3860	32	45	every	every	DET
ejpam-3860	32	46	edge	edge	NOUN
ejpam-3860	32	47	of	of	ADP
ejpam-3860	32	48	g	g	PROPN
ejpam-3860	32	49	joins	join	VERB
ejpam-3860	32	50	a	a	DET
ejpam-3860	32	51	vertex	vertex	NOUN
ejpam-3860	32	52	of	of	ADP
ejpam-3860	32	53	vn	vn	PROPN
ejpam-3860	32	54	and	and	CCONJ
ejpam-3860	32	55	a	a	DET
ejpam-3860	32	56	vertex	vertex	NOUN
ejpam-3860	32	57	of	of	ADP
ejpam-3860	32	58	vm	vm	PROPN
ejpam-3860	32	59	.	.	PROPN
ejpam-3860	33	1	if	if	SCONJ
ejpam-3860	33	2	g	g	PROPN
ejpam-3860	33	3	contains	contain	VERB
ejpam-3860	33	4	every	every	DET
ejpam-3860	33	5	edges	edge	NOUN
ejpam-3860	33	6	joining	join	VERB
ejpam-3860	33	7	vn	vn	PROPN
ejpam-3860	33	8	and	and	CCONJ
ejpam-3860	33	9	vm	vm	PROPN
ejpam-3860	33	10	,	,	PUNCT
ejpam-3860	33	11	then	then	ADV
ejpam-3860	33	12	g	g	PROPN
ejpam-3860	33	13	is	be	AUX
ejpam-3860	33	14	called	call	VERB
ejpam-3860	33	15	complete	complete	ADJ
ejpam-3860	33	16	bipartite	bipartite	NOUN
ejpam-3860	33	17	graph	graph	NOUN
ejpam-3860	33	18	.	.	PUNCT
ejpam-3860	34	1	a	a	DET
ejpam-3860	34	2	star	star	NOUN
ejpam-3860	34	3	is	be	AUX
ejpam-3860	34	4	complete	complete	ADJ
ejpam-3860	34	5	bipartite	bipartite	PROPN
ejpam-3860	34	6	k1,n	k1,n	PROPN
ejpam-3860	34	7	,	,	PUNCT
ejpam-3860	34	8	the	the	DET
ejpam-3860	34	9	vertex	vertex	NOUN
ejpam-3860	34	10	in	in	ADP
ejpam-3860	34	11	the	the	DET
ejpam-3860	34	12	singleton	singleton	PROPN
ejpam-3860	34	13	partition	partition	NOUN
ejpam-3860	34	14	class	class	NOUN
ejpam-3860	34	15	is	be	AUX
ejpam-3860	34	16	called	call	VERB
ejpam-3860	34	17	the	the	DET
ejpam-3860	34	18	apex	apex	NOUN
ejpam-3860	34	19	vertex	vertex	NOUN
ejpam-3860	34	20	.	.	PUNCT
ejpam-3860	35	1	a	a	DET
ejpam-3860	35	2	star	star	NOUN
ejpam-3860	35	3	graph	graph	NOUN
ejpam-3860	35	4	k1,n−1	k1,n−1	ADJ
ejpam-3860	35	5	is	be	AUX
ejpam-3860	35	6	also	also	ADV
ejpam-3860	35	7	called	call	VERB
ejpam-3860	35	8	an	an	DET
ejpam-3860	35	9	n	n	CCONJ
ejpam-3860	35	10	-	-	PUNCT
ejpam-3860	35	11	star	star	NOUN
ejpam-3860	35	12	graph	graph	NOUN
ejpam-3860	35	13	.	.	PUNCT
ejpam-3860	36	1	u	u	PROPN
ejpam-3860	36	2	u1	u1	NOUN
ejpam-3860	36	3	u2	u2	PROPN
ejpam-3860	36	4	u3	u3	PROPN
ejpam-3860	36	5	u4	u4	PROPN
ejpam-3860	36	6	figure	figure	NOUN
ejpam-3860	36	7	1	1	NUM
ejpam-3860	36	8	:	:	PUNCT
ejpam-3860	36	9	a	a	DET
ejpam-3860	36	10	star	star	NOUN
ejpam-3860	36	11	graph	graph	NOUN
ejpam-3860	36	12	k1,4	k1,4	PROPN
ejpam-3860	36	13	with	with	ADP
ejpam-3860	36	14	apex	apex	PROPN
ejpam-3860	36	15	vertex	vertex	NOUN
ejpam-3860	36	16	u	u	NOUN
ejpam-3860	36	17	and	and	CCONJ
ejpam-3860	36	18	pendant	pendant	ADJ
ejpam-3860	36	19	vertices	vertex	NOUN
ejpam-3860	36	20	u1	u1	NOUN
ejpam-3860	36	21	,	,	PUNCT
ejpam-3860	36	22	u2	u2	NOUN
ejpam-3860	36	23	,	,	PUNCT
ejpam-3860	36	24	u3	u3	NOUN
ejpam-3860	36	25	,	,	PUNCT
ejpam-3860	36	26	u4	u4	PROPN
ejpam-3860	36	27	*	*	PROPN
ejpam-3860	36	28	n.	n.	PROPN
ejpam-3860	36	29	abdulcarim	abdulcarim	PROPN
ejpam-3860	36	30	,	,	PUNCT
ejpam-3860	36	31	s.	s.	PROPN
ejpam-3860	36	32	dagondon	dagondon	PROPN
ejpam-3860	36	33	,	,	PUNCT
ejpam-3860	36	34	e.	e.	PROPN
ejpam-3860	36	35	chacon	chacon	PROPN
ejpam-3860	36	36	/	/	SYM
ejpam-3860	36	37	eur	eur	PROPN
ejpam-3860	36	38	.	.	PUNCT
ejpam-3860	37	1	j.	j.	PROPN
ejpam-3860	37	2	pure	pure	PROPN
ejpam-3860	37	3	appl	appl	PROPN
ejpam-3860	37	4	.	.	PROPN
ejpam-3860	37	5	math	math	PROPN
ejpam-3860	37	6	,	,	PUNCT
ejpam-3860	37	7	14	14	NUM
ejpam-3860	37	8	(	(	PUNCT
ejpam-3860	37	9	1	1	NUM
ejpam-3860	37	10	)	)	PUNCT
ejpam-3860	37	11	(	(	PUNCT
ejpam-3860	37	12	2021	2021	NUM
ejpam-3860	37	13	)	)	PUNCT
ejpam-3860	37	14	,	,	PUNCT
ejpam-3860	37	15	173	173	NUM
ejpam-3860	37	16	-	-	SYM
ejpam-3860	37	17	191	191	NUM
ejpam-3860	37	18	175	175	NUM
ejpam-3860	37	19	definition	definition	NOUN
ejpam-3860	37	20	2	2	NUM
ejpam-3860	37	21	.	.	PUNCT
ejpam-3860	38	1	[	[	X
ejpam-3860	38	2	6	6	NUM
ejpam-3860	38	3	]	]	PUNCT
ejpam-3860	38	4	the	the	DET
ejpam-3860	38	5	bistar	bistar	PROPN
ejpam-3860	38	6	graph	graph	PROPN
ejpam-3860	38	7	b(m	b(m	PROPN
ejpam-3860	38	8	,	,	PUNCT
ejpam-3860	38	9	n	n	CCONJ
ejpam-3860	38	10	)	)	PUNCT
ejpam-3860	38	11	is	be	AUX
ejpam-3860	38	12	constructed	construct	VERB
ejpam-3860	38	13	by	by	ADP
ejpam-3860	38	14	joining	join	VERB
ejpam-3860	38	15	the	the	DET
ejpam-3860	38	16	apex	apex	NOUN
ejpam-3860	38	17	vertices	vertex	NOUN
ejpam-3860	38	18	of	of	ADP
ejpam-3860	38	19	two	two	NUM
ejpam-3860	38	20	stars	star	NOUN
ejpam-3860	38	21	k1,m	k1,m	PROPN
ejpam-3860	38	22	and	and	CCONJ
ejpam-3860	38	23	k1,n	k1,n	PROPN
ejpam-3860	38	24	for	for	ADP
ejpam-3860	38	25	m	m	PROPN
ejpam-3860	38	26	≥	≥	NOUN
ejpam-3860	38	27	1	1	NUM
ejpam-3860	38	28	and	and	CCONJ
ejpam-3860	38	29	n	n	PRON
ejpam-3860	38	30	≥	≥	NOUN
ejpam-3860	38	31	1	1	NUM
ejpam-3860	38	32	with	with	ADP
ejpam-3860	38	33	disjoint	disjoint	ADJ
ejpam-3860	38	34	vertex	vertex	NOUN
ejpam-3860	38	35	sets	set	NOUN
ejpam-3860	38	36	.	.	PUNCT
ejpam-3860	39	1	u	u	PRON
ejpam-3860	39	2	u1	u1	NOUN
ejpam-3860	39	3	u2	u2	PROPN
ejpam-3860	39	4	u3	u3	PROPN
ejpam-3860	39	5	u4	u4	PROPN
ejpam-3860	39	6	v	v	PROPN
ejpam-3860	39	7	v1	v1	PROPN
ejpam-3860	39	8	v2	v2	PROPN
ejpam-3860	39	9	v3	v3	PROPN
ejpam-3860	39	10	figure	figure	NOUN
ejpam-3860	39	11	2	2	NUM
ejpam-3860	39	12	:	:	PUNCT
ejpam-3860	39	13	a	a	DET
ejpam-3860	39	14	bistar	bistar	PROPN
ejpam-3860	39	15	graph	graph	NOUN
ejpam-3860	39	16	b(4	b(4	PROPN
ejpam-3860	39	17	,	,	PUNCT
ejpam-3860	39	18	3	3	X
ejpam-3860	39	19	)	)	PUNCT
ejpam-3860	39	20	definition	definition	NOUN
ejpam-3860	39	21	3	3	NUM
ejpam-3860	39	22	.	.	PUNCT
ejpam-3860	40	1	[	[	X
ejpam-3860	40	2	4	4	X
ejpam-3860	40	3	]	]	PUNCT
ejpam-3860	40	4	the	the	DET
ejpam-3860	40	5	banana	banana	NOUN
ejpam-3860	40	6	tree	tree	NOUN
ejpam-3860	40	7	graph	graph	NOUN
ejpam-3860	40	8	bm	bm	PROPN
ejpam-3860	40	9	,	,	PUNCT
ejpam-3860	40	10	n	n	PROPN
ejpam-3860	40	11	is	be	AUX
ejpam-3860	40	12	the	the	DET
ejpam-3860	40	13	graph	graph	NOUN
ejpam-3860	40	14	obtained	obtain	VERB
ejpam-3860	40	15	by	by	ADP
ejpam-3860	40	16	connecting	connect	VERB
ejpam-3860	40	17	one	one	NUM
ejpam-3860	40	18	leaf	leaf	NOUN
ejpam-3860	40	19	of	of	ADP
ejpam-3860	40	20	each	each	DET
ejpam-3860	40	21	m	m	NOUN
ejpam-3860	40	22	copies	copy	NOUN
ejpam-3860	40	23	of	of	ADP
ejpam-3860	40	24	an	an	DET
ejpam-3860	40	25	n	n	CCONJ
ejpam-3860	40	26	-	-	PUNCT
ejpam-3860	40	27	star	star	NOUN
ejpam-3860	40	28	graph	graph	NOUN
ejpam-3860	40	29	with	with	ADP
ejpam-3860	40	30	a	a	DET
ejpam-3860	40	31	single	single	ADJ
ejpam-3860	40	32	root	root	NOUN
ejpam-3860	40	33	vertex	vertex	NOUN
ejpam-3860	40	34	that	that	PRON
ejpam-3860	40	35	is	be	AUX
ejpam-3860	40	36	distinct	distinct	ADJ
ejpam-3860	40	37	for	for	ADP
ejpam-3860	40	38	all	all	DET
ejpam-3860	40	39	the	the	DET
ejpam-3860	40	40	stars	star	NOUN
ejpam-3860	40	41	.	.	PUNCT
ejpam-3860	41	1	figure	figure	VERB
ejpam-3860	41	2	3	3	NUM
ejpam-3860	41	3	:	:	PUNCT
ejpam-3860	41	4	the	the	DET
ejpam-3860	41	5	banana	banana	NOUN
ejpam-3860	41	6	tree	tree	NOUN
ejpam-3860	41	7	graph	graph	NOUN
ejpam-3860	41	8	b3,5	b3,5	PROPN
ejpam-3860	41	9	definition	definition	NOUN
ejpam-3860	41	10	4	4	NUM
ejpam-3860	41	11	.	.	PUNCT
ejpam-3860	42	1	[	[	X
ejpam-3860	42	2	4	4	X
ejpam-3860	42	3	]	]	PUNCT
ejpam-3860	42	4	the	the	DET
ejpam-3860	42	5	firecracker	firecracker	NOUN
ejpam-3860	42	6	graph	graph	NOUN
ejpam-3860	42	7	fm	fm	PROPN
ejpam-3860	42	8	,	,	PUNCT
ejpam-3860	42	9	n	n	X
ejpam-3860	42	10	is	be	AUX
ejpam-3860	42	11	the	the	DET
ejpam-3860	42	12	graph	graph	NOUN
ejpam-3860	42	13	obtained	obtain	VERB
ejpam-3860	42	14	by	by	ADP
ejpam-3860	42	15	the	the	DET
ejpam-3860	42	16	concatenation	concatenation	NOUN
ejpam-3860	42	17	of	of	ADP
ejpam-3860	42	18	mn	mn	PROPN
ejpam-3860	42	19	-	-	PUNCT
ejpam-3860	42	20	stars	star	NOUN
ejpam-3860	42	21	by	by	ADP
ejpam-3860	42	22	linking	link	VERB
ejpam-3860	42	23	one	one	NUM
ejpam-3860	42	24	leaf	leaf	NOUN
ejpam-3860	42	25	from	from	ADP
ejpam-3860	42	26	each	each	PRON
ejpam-3860	42	27	.	.	PUNCT
ejpam-3860	43	1	figure	figure	VERB
ejpam-3860	43	2	4	4	NUM
ejpam-3860	43	3	:	:	PUNCT
ejpam-3860	43	4	the	the	DET
ejpam-3860	43	5	firecracker	firecracker	NOUN
ejpam-3860	43	6	graph	graph	NOUN
ejpam-3860	43	7	f3,5	f3,5	NOUN
ejpam-3860	43	8	definition	definition	NOUN
ejpam-3860	43	9	5	5	NUM
ejpam-3860	43	10	.	.	PUNCT
ejpam-3860	44	1	[	[	X
ejpam-3860	44	2	8	8	NUM
ejpam-3860	44	3	]	]	X
ejpam-3860	44	4	the	the	DET
ejpam-3860	44	5	n	n	NOUN
ejpam-3860	44	6	-	-	PUNCT
ejpam-3860	44	7	centipede	centipede	NOUN
ejpam-3860	44	8	graph	graph	NOUN
ejpam-3860	44	9	or	or	CCONJ
ejpam-3860	44	10	simply	simply	ADV
ejpam-3860	44	11	cenn	cenn	NOUN
ejpam-3860	44	12	is	be	AUX
ejpam-3860	44	13	the	the	DET
ejpam-3860	44	14	tree	tree	NOUN
ejpam-3860	44	15	on	on	ADP
ejpam-3860	44	16	2n	2n	NUM
ejpam-3860	44	17	vertices	vertex	NOUN
ejpam-3860	44	18	obtained	obtain	VERB
ejpam-3860	44	19	by	by	ADP
ejpam-3860	44	20	joining	join	VERB
ejpam-3860	44	21	the	the	DET
ejpam-3860	44	22	bottoms	bottom	NOUN
ejpam-3860	44	23	of	of	ADP
ejpam-3860	44	24	n	n	NOUN
ejpam-3860	44	25	copies	copy	NOUN
ejpam-3860	44	26	of	of	ADP
ejpam-3860	44	27	the	the	DET
ejpam-3860	44	28	path	path	NOUN
ejpam-3860	44	29	graph	graph	NOUN
ejpam-3860	44	30	p2	p2	PROPN
ejpam-3860	44	31	laid	lay	VERB
ejpam-3860	44	32	in	in	ADP
ejpam-3860	44	33	a	a	DET
ejpam-3860	44	34	row	row	NOUN
ejpam-3860	44	35	with	with	ADP
ejpam-3860	44	36	edges	edge	NOUN
ejpam-3860	44	37	.	.	PUNCT
ejpam-3860	45	1	n.	n.	PROPN
ejpam-3860	45	2	abdulcarim	abdulcarim	PROPN
ejpam-3860	45	3	,	,	PUNCT
ejpam-3860	45	4	s.	s.	PROPN
ejpam-3860	45	5	dagondon	dagondon	PROPN
ejpam-3860	45	6	,	,	PUNCT
ejpam-3860	45	7	e.	e.	PROPN
ejpam-3860	45	8	chacon	chacon	PROPN
ejpam-3860	45	9	/	/	SYM
ejpam-3860	45	10	eur	eur	PROPN
ejpam-3860	45	11	.	.	PUNCT
ejpam-3860	46	1	j.	j.	PROPN
ejpam-3860	46	2	pure	pure	PROPN
ejpam-3860	46	3	appl	appl	PROPN
ejpam-3860	46	4	.	.	PROPN
ejpam-3860	46	5	math	math	PROPN
ejpam-3860	46	6	,	,	PUNCT
ejpam-3860	46	7	14	14	NUM
ejpam-3860	46	8	(	(	PUNCT
ejpam-3860	46	9	1	1	NUM
ejpam-3860	46	10	)	)	PUNCT
ejpam-3860	46	11	(	(	PUNCT
ejpam-3860	46	12	2021	2021	NUM
ejpam-3860	46	13	)	)	PUNCT
ejpam-3860	46	14	,	,	PUNCT
ejpam-3860	46	15	173	173	NUM
ejpam-3860	46	16	-	-	SYM
ejpam-3860	46	17	191	191	NUM
ejpam-3860	46	18	176	176	NUM
ejpam-3860	46	19	cen4	cen4	NOUN
ejpam-3860	46	20	cen5	cen5	NOUN
ejpam-3860	46	21	figure	figure	NOUN
ejpam-3860	46	22	5	5	NUM
ejpam-3860	46	23	:	:	PUNCT
ejpam-3860	46	24	the	the	DET
ejpam-3860	46	25	centipede	centipede	NOUN
ejpam-3860	46	26	graphs	graph	NOUN
ejpam-3860	46	27	cen4	cen4	VERB
ejpam-3860	46	28	and	and	CCONJ
ejpam-3860	46	29	cen5	cen5	ADJ
ejpam-3860	46	30	definition	definition	NOUN
ejpam-3860	46	31	6	6	NUM
ejpam-3860	46	32	.	.	PUNCT
ejpam-3860	47	1	[	[	X
ejpam-3860	47	2	5	5	X
ejpam-3860	47	3	]	]	PUNCT
ejpam-3860	47	4	the	the	DET
ejpam-3860	47	5	cartesian	cartesian	ADJ
ejpam-3860	47	6	product	product	NOUN
ejpam-3860	47	7	of	of	ADP
ejpam-3860	47	8	two	two	NUM
ejpam-3860	47	9	graphs	graph	NOUN
ejpam-3860	47	10	g	g	NOUN
ejpam-3860	47	11	and	and	CCONJ
ejpam-3860	47	12	h	h	NOUN
ejpam-3860	47	13	,	,	PUNCT
ejpam-3860	47	14	denoted	denote	VERB
ejpam-3860	47	15	g	g	PROPN
ejpam-3860	47	16	�	�	PROPN
ejpam-3860	47	17	h	h	NOUN
ejpam-3860	47	18	,	,	PUNCT
ejpam-3860	47	19	is	be	AUX
ejpam-3860	47	20	the	the	DET
ejpam-3860	47	21	graph	graph	NOUN
ejpam-3860	47	22	where	where	SCONJ
ejpam-3860	47	23	v	v	X
ejpam-3860	47	24	(	(	PUNCT
ejpam-3860	47	25	g	g	PROPN
ejpam-3860	47	26	�	�	NOUN
ejpam-3860	47	27	h	h	NOUN
ejpam-3860	47	28	)	)	PUNCT
ejpam-3860	48	1	=	=	NOUN
ejpam-3860	48	2	v	v	X
ejpam-3860	48	3	(	(	PUNCT
ejpam-3860	48	4	g)×v	g)×v	PROPN
ejpam-3860	48	5	(	(	PUNCT
ejpam-3860	48	6	h	h	NOUN
ejpam-3860	48	7	)	)	PUNCT
ejpam-3860	48	8	and	and	CCONJ
ejpam-3860	48	9	(	(	PUNCT
ejpam-3860	48	10	g1	g1	PROPN
ejpam-3860	48	11	,	,	PUNCT
ejpam-3860	48	12	h1)(g2	h1)(g2	PROPN
ejpam-3860	48	13	,	,	PUNCT
ejpam-3860	48	14	h2	h2	PROPN
ejpam-3860	48	15	)	)	PUNCT
ejpam-3860	48	16	∈	∈	PROPN
ejpam-3860	48	17	e(g	e(g	PROPN
ejpam-3860	48	18	�	�	PROPN
ejpam-3860	48	19	h	h	PROPN
ejpam-3860	48	20	)	)	PUNCT
ejpam-3860	48	21	if	if	SCONJ
ejpam-3860	49	1	and	and	CCONJ
ejpam-3860	49	2	only	only	ADV
ejpam-3860	49	3	if	if	SCONJ
ejpam-3860	49	4	either	either	DET
ejpam-3860	49	5	(	(	PUNCT
ejpam-3860	49	6	i.	i.	NOUN
ejpam-3860	49	7	)	)	PUNCT
ejpam-3860	49	8	g1	g1	PROPN
ejpam-3860	49	9	=	=	SYM
ejpam-3860	49	10	g2	g2	PROPN
ejpam-3860	49	11	and	and	CCONJ
ejpam-3860	49	12	h1h2	h1h2	NUM
ejpam-3860	49	13	∈	∈	PROPN
ejpam-3860	49	14	e(h	e(h	PROPN
ejpam-3860	49	15	)	)	PUNCT
ejpam-3860	49	16	or	or	CCONJ
ejpam-3860	49	17	(	(	PUNCT
ejpam-3860	49	18	ii	ii	NOUN
ejpam-3860	49	19	.	.	PUNCT
ejpam-3860	49	20	)	)	PUNCT
ejpam-3860	50	1	h1	h1	PROPN
ejpam-3860	50	2	=	=	SYM
ejpam-3860	50	3	h2	h2	PROPN
ejpam-3860	50	4	and	and	CCONJ
ejpam-3860	50	5	g1g2	g1g2	PROPN
ejpam-3860	50	6	∈	∈	PROPN
ejpam-3860	50	7	e(g	e(g	PROPN
ejpam-3860	50	8	)	)	PUNCT
ejpam-3860	50	9	.	.	PUNCT
ejpam-3860	51	1	g	g	PROPN
ejpam-3860	51	2	h	h	NOUN
ejpam-3860	51	3	g	g	NOUN
ejpam-3860	51	4	�	�	PROPN
ejpam-3860	51	5	h	h	NOUN
ejpam-3860	51	6	figure	figure	NOUN
ejpam-3860	51	7	6	6	NUM
ejpam-3860	51	8	:	:	PUNCT
ejpam-3860	51	9	cartesian	cartesian	ADJ
ejpam-3860	51	10	product	product	NOUN
ejpam-3860	51	11	of	of	ADP
ejpam-3860	51	12	g	g	PROPN
ejpam-3860	51	13	and	and	CCONJ
ejpam-3860	51	14	h	h	NOUN
ejpam-3860	51	15	definition	definition	NOUN
ejpam-3860	51	16	7	7	NUM
ejpam-3860	51	17	.	.	PUNCT
ejpam-3860	52	1	[	[	X
ejpam-3860	52	2	11	11	NUM
ejpam-3860	52	3	]	]	PUNCT
ejpam-3860	52	4	a	a	DET
ejpam-3860	52	5	set	set	NOUN
ejpam-3860	52	6	s	s	NOUN
ejpam-3860	52	7	⊆	⊆	NUM
ejpam-3860	52	8	v	v	NOUN
ejpam-3860	52	9	(	(	PUNCT
ejpam-3860	52	10	g	g	NOUN
ejpam-3860	52	11	)	)	PUNCT
ejpam-3860	52	12	is	be	AUX
ejpam-3860	52	13	an	an	DET
ejpam-3860	52	14	independent	independent	ADJ
ejpam-3860	52	15	neighborhood	neighborhood	NOUN
ejpam-3860	52	16	set	set	NOUN
ejpam-3860	52	17	of	of	ADP
ejpam-3860	52	18	g	g	NOUN
ejpam-3860	52	19	,	,	PUNCT
ejpam-3860	52	20	if	if	SCONJ
ejpam-3860	52	21	s	s	VERB
ejpam-3860	52	22	is	be	AUX
ejpam-3860	52	23	a	a	DET
ejpam-3860	52	24	neighborhood	neighborhood	NOUN
ejpam-3860	52	25	set	set	VERB
ejpam-3860	52	26	and	and	CCONJ
ejpam-3860	52	27	no	no	DET
ejpam-3860	52	28	two	two	NUM
ejpam-3860	52	29	vertices	vertex	NOUN
ejpam-3860	52	30	in	in	ADP
ejpam-3860	52	31	s	s	NOUN
ejpam-3860	52	32	are	be	AUX
ejpam-3860	52	33	adjacent	adjacent	ADJ
ejpam-3860	52	34	.	.	PUNCT
ejpam-3860	53	1	definition	definition	NOUN
ejpam-3860	53	2	8	8	NUM
ejpam-3860	53	3	.	.	PUNCT
ejpam-3860	54	1	[	[	X
ejpam-3860	54	2	11	11	NUM
ejpam-3860	54	3	]	]	PUNCT
ejpam-3860	54	4	let	let	VERB
ejpam-3860	54	5	g	g	PROPN
ejpam-3860	54	6	=	=	SYM
ejpam-3860	54	7	(	(	PUNCT
ejpam-3860	54	8	v	v	NOUN
ejpam-3860	54	9	,	,	PUNCT
ejpam-3860	54	10	e	e	NOUN
ejpam-3860	54	11	)	)	PUNCT
ejpam-3860	54	12	be	be	AUX
ejpam-3860	54	13	a	a	DET
ejpam-3860	54	14	graph	graph	NOUN
ejpam-3860	54	15	with	with	ADP
ejpam-3860	54	16	m	m	PROPN
ejpam-3860	54	17	vertices	vertex	NOUN
ejpam-3860	54	18	.	.	PUNCT
ejpam-3860	55	1	then	then	ADV
ejpam-3860	55	2	the	the	DET
ejpam-3860	55	3	independent	independent	ADJ
ejpam-3860	55	4	neighborhood	neighborhood	NOUN
ejpam-3860	55	5	polynomial	polynomial	NOUN
ejpam-3860	55	6	of	of	ADP
ejpam-3860	55	7	g	g	NOUN
ejpam-3860	55	8	of	of	ADP
ejpam-3860	55	9	order	order	NOUN
ejpam-3860	55	10	m	m	NOUN
ejpam-3860	55	11	is	be	AUX
ejpam-3860	55	12	ni(g	ni(g	NOUN
ejpam-3860	55	13	,	,	PUNCT
ejpam-3860	55	14	x	x	X
ejpam-3860	55	15	)	)	PUNCT
ejpam-3860	55	16	=	=	PUNCT
ejpam-3860	55	17	m∑	m∑	PRON
ejpam-3860	55	18	j	j	X
ejpam-3860	55	19	=	=	NOUN
ejpam-3860	55	20	ηi(g	ηi(g	NOUN
ejpam-3860	55	21	)	)	PUNCT
ejpam-3860	55	22	ni(g	ni(g	PUNCT
ejpam-3860	55	23	,	,	PUNCT
ejpam-3860	55	24	j)x	j)x	PROPN
ejpam-3860	55	25	j	j	PROPN
ejpam-3860	55	26	,	,	PUNCT
ejpam-3860	55	27	where	where	SCONJ
ejpam-3860	55	28	ni(g	ni(g	NUM
ejpam-3860	55	29	,	,	PUNCT
ejpam-3860	55	30	j	j	NOUN
ejpam-3860	55	31	)	)	PUNCT
ejpam-3860	55	32	is	be	AUX
ejpam-3860	55	33	the	the	DET
ejpam-3860	55	34	number	number	NOUN
ejpam-3860	55	35	of	of	ADP
ejpam-3860	55	36	independent	independent	ADJ
ejpam-3860	55	37	neighborhood	neighborhood	NOUN
ejpam-3860	55	38	set	set	VERB
ejpam-3860	55	39	ofg	ofg	PROPN
ejpam-3860	55	40	of	of	ADP
ejpam-3860	55	41	size	size	NOUN
ejpam-3860	55	42	j	j	PROPN
ejpam-3860	55	43	and	and	CCONJ
ejpam-3860	55	44	ηi(g	ηi(g	NOUN
ejpam-3860	55	45	)	)	PUNCT
ejpam-3860	55	46	is	be	AUX
ejpam-3860	55	47	the	the	DET
ejpam-3860	55	48	minimum	minimum	ADJ
ejpam-3860	55	49	cardinality	cardinality	NOUN
ejpam-3860	55	50	of	of	ADP
ejpam-3860	55	51	an	an	DET
ejpam-3860	55	52	independent	independent	ADJ
ejpam-3860	55	53	neighborhood	neighborhood	NOUN
ejpam-3860	55	54	set	set	NOUN
ejpam-3860	55	55	which	which	PRON
ejpam-3860	55	56	is	be	AUX
ejpam-3860	55	57	called	call	VERB
ejpam-3860	55	58	the	the	DET
ejpam-3860	55	59	independent	independent	ADJ
ejpam-3860	55	60	neighborhood	neighborhood	NOUN
ejpam-3860	55	61	number	number	NOUN
ejpam-3860	55	62	of	of	ADP
ejpam-3860	55	63	g.	g.	PROPN
ejpam-3860	55	64	example	example	NOUN
ejpam-3860	55	65	1	1	X
ejpam-3860	55	66	.	.	X
ejpam-3860	55	67	consider	consider	VERB
ejpam-3860	55	68	the	the	DET
ejpam-3860	55	69	graph	graph	NOUN
ejpam-3860	55	70	h	h	NOUN
ejpam-3860	55	71	below	below	ADP
ejpam-3860	55	72	v1	v1	PROPN
ejpam-3860	55	73	v2	v2	PROPN
ejpam-3860	55	74	v3	v3	PROPN
ejpam-3860	55	75	v4v5	v4v5	NOUN
ejpam-3860	55	76	h	h	NOUN
ejpam-3860	55	77	:	:	PUNCT
ejpam-3860	55	78	the	the	DET
ejpam-3860	55	79	only	only	ADJ
ejpam-3860	55	80	independent	independent	ADJ
ejpam-3860	55	81	neighborhood	neighborhood	NOUN
ejpam-3860	55	82	sets	set	NOUN
ejpam-3860	55	83	of	of	ADP
ejpam-3860	55	84	h	h	NOUN
ejpam-3860	55	85	are	be	AUX
ejpam-3860	55	86	{	{	PUNCT
ejpam-3860	55	87	v2	v2	PROPN
ejpam-3860	55	88	,	,	PUNCT
ejpam-3860	55	89	v4	v4	NOUN
ejpam-3860	55	90	}	}	PUNCT
ejpam-3860	55	91	and	and	CCONJ
ejpam-3860	55	92	{	{	PUNCT
ejpam-3860	55	93	v1	v1	PROPN
ejpam-3860	55	94	,	,	PUNCT
ejpam-3860	55	95	v3	v3	PROPN
ejpam-3860	55	96	,	,	PUNCT
ejpam-3860	55	97	v5	v5	PROPN
ejpam-3860	55	98	}	}	PUNCT
ejpam-3860	55	99	.	.	PUNCT
ejpam-3860	56	1	therefore	therefore	ADV
ejpam-3860	56	2	,	,	PUNCT
ejpam-3860	56	3	the	the	DET
ejpam-3860	56	4	independent	independent	ADJ
ejpam-3860	56	5	neighborhood	neighborhood	NOUN
ejpam-3860	56	6	polynomial	polynomial	NOUN
ejpam-3860	56	7	of	of	ADP
ejpam-3860	56	8	h	h	NOUN
ejpam-3860	56	9	is	be	AUX
ejpam-3860	56	10	ni(h	ni(h	VERB
ejpam-3860	56	11	,	,	PUNCT
ejpam-3860	56	12	x	x	X
ejpam-3860	56	13	)	)	PUNCT
ejpam-3860	57	1	=	=	SYM
ejpam-3860	57	2	x2	x2	PROPN
ejpam-3860	58	1	+	+	CCONJ
ejpam-3860	58	2	x3	x3	ADJ
ejpam-3860	58	3	.	.	PUNCT
ejpam-3860	59	1	n.	n.	PROPN
ejpam-3860	59	2	abdulcarim	abdulcarim	PROPN
ejpam-3860	59	3	,	,	PUNCT
ejpam-3860	59	4	s.	s.	PROPN
ejpam-3860	59	5	dagondon	dagondon	PROPN
ejpam-3860	59	6	,	,	PUNCT
ejpam-3860	59	7	e.	e.	PROPN
ejpam-3860	59	8	chacon	chacon	PROPN
ejpam-3860	59	9	/	/	SYM
ejpam-3860	59	10	eur	eur	PROPN
ejpam-3860	59	11	.	.	PUNCT
ejpam-3860	60	1	j.	j.	PROPN
ejpam-3860	60	2	pure	pure	PROPN
ejpam-3860	60	3	appl	appl	PROPN
ejpam-3860	60	4	.	.	PROPN
ejpam-3860	60	5	math	math	PROPN
ejpam-3860	60	6	,	,	PUNCT
ejpam-3860	60	7	14	14	NUM
ejpam-3860	60	8	(	(	PUNCT
ejpam-3860	60	9	1	1	NUM
ejpam-3860	60	10	)	)	PUNCT
ejpam-3860	60	11	(	(	PUNCT
ejpam-3860	60	12	2021	2021	NUM
ejpam-3860	60	13	)	)	PUNCT
ejpam-3860	60	14	,	,	PUNCT
ejpam-3860	60	15	173	173	NUM
ejpam-3860	60	16	-	-	SYM
ejpam-3860	60	17	191	191	NUM
ejpam-3860	60	18	177	177	NUM
ejpam-3860	60	19	3	3	NUM
ejpam-3860	60	20	.	.	PUNCT
ejpam-3860	61	1	independent	independent	ADJ
ejpam-3860	61	2	neighborhood	neighborhood	NOUN
ejpam-3860	61	3	polynomial	polynomial	NOUN
ejpam-3860	61	4	of	of	ADP
ejpam-3860	61	5	the	the	DET
ejpam-3860	61	6	cartesian	cartesian	ADJ
ejpam-3860	61	7	product	product	NOUN
ejpam-3860	61	8	of	of	ADP
ejpam-3860	61	9	some	some	DET
ejpam-3860	61	10	special	special	ADJ
ejpam-3860	61	11	graphs	graph	NOUN
ejpam-3860	61	12	with	with	ADP
ejpam-3860	61	13	path	path	NOUN
ejpam-3860	61	14	graph	graph	NOUN
ejpam-3860	61	15	in	in	ADP
ejpam-3860	61	16	this	this	DET
ejpam-3860	61	17	section	section	NOUN
ejpam-3860	61	18	,	,	PUNCT
ejpam-3860	61	19	the	the	DET
ejpam-3860	61	20	independent	independent	ADJ
ejpam-3860	61	21	neighborhood	neighborhood	NOUN
ejpam-3860	61	22	sets	set	NOUN
ejpam-3860	61	23	of	of	ADP
ejpam-3860	61	24	the	the	DET
ejpam-3860	61	25	cartesian	cartesian	ADJ
ejpam-3860	61	26	product	product	NOUN
ejpam-3860	61	27	of	of	ADP
ejpam-3860	61	28	some	some	DET
ejpam-3860	61	29	special	special	ADJ
ejpam-3860	61	30	graphs	graph	NOUN
ejpam-3860	61	31	with	with	ADP
ejpam-3860	61	32	path	path	NOUN
ejpam-3860	61	33	are	be	AUX
ejpam-3860	61	34	determined	determine	VERB
ejpam-3860	61	35	and	and	CCONJ
ejpam-3860	61	36	represented	represent	VERB
ejpam-3860	61	37	in	in	ADP
ejpam-3860	61	38	an	an	DET
ejpam-3860	61	39	independent	independent	ADJ
ejpam-3860	61	40	neighborhood	neighborhood	NOUN
ejpam-3860	61	41	polynomial	polynomial	NOUN
ejpam-3860	61	42	.	.	PUNCT
ejpam-3860	62	1	theorem	theorem	NOUN
ejpam-3860	62	2	1	1	NUM
ejpam-3860	62	3	.	.	X
ejpam-3860	63	1	for	for	ADP
ejpam-3860	63	2	any	any	DET
ejpam-3860	63	3	path	path	NOUN
ejpam-3860	63	4	pk	pk	NOUN
ejpam-3860	63	5	and	and	CCONJ
ejpam-3860	63	6	star	star	PROPN
ejpam-3860	63	7	k1,n	k1,n	PROPN
ejpam-3860	63	8	,	,	PUNCT
ejpam-3860	63	9	ni(pk	ni(pk	PROPN
ejpam-3860	63	10	�	�	NOUN
ejpam-3860	63	11	k1,n	k1,n	PROPN
ejpam-3860	63	12	,	,	PUNCT
ejpam-3860	63	13	x	x	NOUN
ejpam-3860	63	14	)	)	PUNCT
ejpam-3860	63	15	=	=	SYM
ejpam-3860	63	16	{	{	PUNCT
ejpam-3860	63	17	xb	xb	PROPN
ejpam-3860	63	18	k	k	PROPN
ejpam-3860	63	19	2cn+d	2cn+d	PROPN
ejpam-3860	64	1	k2e	k2e	PROPN
ejpam-3860	65	1	+	+	CCONJ
ejpam-3860	65	2	xd	xd	INTJ
ejpam-3860	65	3	k	k	PROPN
ejpam-3860	65	4	2en+b	2en+b	NUM
ejpam-3860	65	5	k2c	k2c	PROPN
ejpam-3860	65	6	,	,	PUNCT
ejpam-3860	65	7	k	k	PROPN
ejpam-3860	65	8	is	be	AUX
ejpam-3860	65	9	odd	odd	ADJ
ejpam-3860	65	10	2x	2x	NUM
ejpam-3860	65	11	(	(	PUNCT
ejpam-3860	65	12	k	k	PROPN
ejpam-3860	65	13	2	2	NUM
ejpam-3860	65	14	)	)	PUNCT
ejpam-3860	65	15	n+	n+	PROPN
ejpam-3860	65	16	(	(	PUNCT
ejpam-3860	65	17	k	k	NOUN
ejpam-3860	65	18	2	2	NUM
ejpam-3860	65	19	)	)	PUNCT
ejpam-3860	65	20	,	,	PUNCT
ejpam-3860	65	21	k	k	PROPN
ejpam-3860	65	22	is	be	AUX
ejpam-3860	65	23	even	even	ADV
ejpam-3860	65	24	for	for	ADP
ejpam-3860	65	25	any	any	DET
ejpam-3860	65	26	k	k	NOUN
ejpam-3860	65	27	,	,	PUNCT
ejpam-3860	65	28	n	n	PROPN
ejpam-3860	65	29	∈	∈	PROPN
ejpam-3860	65	30	z+	z+	PUNCT
ejpam-3860	65	31	.	.	PUNCT
ejpam-3860	66	1	proof	proof	NOUN
ejpam-3860	66	2	:	:	PUNCT
ejpam-3860	66	3	label	label	NOUN
ejpam-3860	66	4	v	v	NOUN
ejpam-3860	66	5	(	(	PUNCT
ejpam-3860	66	6	pk	pk	NOUN
ejpam-3860	66	7	)	)	PUNCT
ejpam-3860	66	8	=	=	NOUN
ejpam-3860	66	9	{	{	PUNCT
ejpam-3860	66	10	1	1	NUM
ejpam-3860	66	11	,	,	PUNCT
ejpam-3860	66	12	2	2	NUM
ejpam-3860	66	13	,	,	PUNCT
ejpam-3860	66	14	·	·	PUNCT
ejpam-3860	66	15	·	·	PUNCT
ejpam-3860	66	16	·	·	PUNCT
ejpam-3860	66	17	,	,	PUNCT
ejpam-3860	66	18	k	k	X
ejpam-3860	66	19	}	}	PUNCT
ejpam-3860	66	20	and	and	CCONJ
ejpam-3860	66	21	v	v	X
ejpam-3860	66	22	(	(	PUNCT
ejpam-3860	66	23	k1,n	k1,n	PROPN
ejpam-3860	66	24	)	)	PUNCT
ejpam-3860	66	25	=	=	PRON
ejpam-3860	66	26	{	{	PUNCT
ejpam-3860	66	27	1	1	NUM
ejpam-3860	66	28	,	,	PUNCT
ejpam-3860	66	29	apex	apex	VERB
ejpam-3860	66	30	vertex	vertex	NOUN
ejpam-3860	66	31	2n	2n	NUM
ejpam-3860	66	32	pendant	pendant	ADJ
ejpam-3860	66	33	vertices	vertex	NOUN
ejpam-3860	66	34	.	.	PUNCT
ejpam-3860	67	1	(	(	PUNCT
ejpam-3860	67	2	1,1	1,1	NUM
ejpam-3860	67	3	)	)	PUNCT
ejpam-3860	67	4	(	(	PUNCT
ejpam-3860	67	5	1,2	1,2	NUM
ejpam-3860	67	6	)	)	PUNCT
ejpam-3860	67	7	(	(	PUNCT
ejpam-3860	67	8	1,4	1,4	NUM
ejpam-3860	67	9	)	)	PUNCT
ejpam-3860	67	10	(	(	PUNCT
ejpam-3860	67	11	1,6	1,6	NUM
ejpam-3860	67	12	)	)	PUNCT
ejpam-3860	67	13	(	(	PUNCT
ejpam-3860	67	14	1,8	1,8	NOUN
ejpam-3860	67	15	)	)	PUNCT
ejpam-3860	67	16	·	·	PUNCT
ejpam-3860	67	17	·	·	PUNCT
ejpam-3860	67	18	·	·	PUNCT
ejpam-3860	67	19	(	(	PUNCT
ejpam-3860	67	20	1,2n	1,2n	NUM
ejpam-3860	67	21	)	)	PUNCT
ejpam-3860	67	22	(	(	PUNCT
ejpam-3860	67	23	2,1	2,1	NUM
ejpam-3860	67	24	)	)	PUNCT
ejpam-3860	67	25	(	(	PUNCT
ejpam-3860	67	26	2,2	2,2	NUM
ejpam-3860	67	27	)	)	PUNCT
ejpam-3860	67	28	(	(	PUNCT
ejpam-3860	67	29	2,4	2,4	NUM
ejpam-3860	67	30	)	)	PUNCT
ejpam-3860	67	31	(	(	PUNCT
ejpam-3860	67	32	2,6	2,6	NUM
ejpam-3860	67	33	)	)	PUNCT
ejpam-3860	67	34	(	(	PUNCT
ejpam-3860	67	35	2,8	2,8	NUM
ejpam-3860	67	36	)	)	PUNCT
ejpam-3860	67	37	·	·	PUNCT
ejpam-3860	67	38	·	·	PUNCT
ejpam-3860	67	39	·	·	PUNCT
ejpam-3860	67	40	(	(	PUNCT
ejpam-3860	67	41	2,2n	2,2n	NUM
ejpam-3860	67	42	)	)	PUNCT
ejpam-3860	67	43	(	(	PUNCT
ejpam-3860	67	44	k,1	k,1	PROPN
ejpam-3860	67	45	)	)	PUNCT
ejpam-3860	67	46	(	(	PUNCT
ejpam-3860	67	47	k,2	k,2	PROPN
ejpam-3860	67	48	)	)	PUNCT
ejpam-3860	67	49	(	(	PUNCT
ejpam-3860	67	50	k,4	k,4	NOUN
ejpam-3860	67	51	)	)	PUNCT
ejpam-3860	67	52	(	(	PUNCT
ejpam-3860	67	53	k,6	k,6	PROPN
ejpam-3860	67	54	)	)	PUNCT
ejpam-3860	67	55	(	(	PUNCT
ejpam-3860	67	56	k,8	k,8	PROPN
ejpam-3860	67	57	)	)	PUNCT
ejpam-3860	67	58	·	·	PUNCT
ejpam-3860	67	59	·	·	PUNCT
ejpam-3860	67	60	·	·	PUNCT
ejpam-3860	67	61	(	(	PUNCT
ejpam-3860	67	62	k,2n	k,2n	NOUN
ejpam-3860	67	63	)	)	PUNCT
ejpam-3860	67	64	then	then	ADV
ejpam-3860	67	65	v	v	X
ejpam-3860	67	66	(	(	PUNCT
ejpam-3860	67	67	pk	pk	NOUN
ejpam-3860	67	68	�	�	PROPN
ejpam-3860	67	69	k1,n	k1,n	PROPN
ejpam-3860	67	70	)	)	PUNCT
ejpam-3860	67	71	=	=	PRON
ejpam-3860	67	72	{	{	PUNCT
ejpam-3860	67	73	(	(	PUNCT
ejpam-3860	67	74	x	x	NOUN
ejpam-3860	67	75	,	,	PUNCT
ejpam-3860	67	76	y	y	PROPN
ejpam-3860	67	77	)	)	PUNCT
ejpam-3860	67	78	:	:	PUNCT
ejpam-3860	68	1	x	x	X
ejpam-3860	68	2	=	=	SYM
ejpam-3860	68	3	1	1	NUM
ejpam-3860	68	4	,	,	PUNCT
ejpam-3860	68	5	2	2	NUM
ejpam-3860	68	6	·	·	PUNCT
ejpam-3860	68	7	·	·	PUNCT
ejpam-3860	68	8	·	·	PUNCT
ejpam-3860	68	9	,	,	PUNCT
ejpam-3860	68	10	k	k	X
ejpam-3860	68	11	,	,	PUNCT
ejpam-3860	68	12	y	y	PROPN
ejpam-3860	68	13	=	=	SYM
ejpam-3860	68	14	1	1	NUM
ejpam-3860	68	15	,	,	PUNCT
ejpam-3860	68	16	2	2	NUM
ejpam-3860	68	17	,	,	PUNCT
ejpam-3860	68	18	4	4	NUM
ejpam-3860	68	19	,	,	PUNCT
ejpam-3860	68	20	6	6	NUM
ejpam-3860	68	21	,	,	PUNCT
ejpam-3860	68	22	·	·	PUNCT
ejpam-3860	68	23	·	·	PUNCT
ejpam-3860	68	24	·	·	PUNCT
ejpam-3860	68	25	,	,	PUNCT
ejpam-3860	68	26	2n	2n	NUM
ejpam-3860	68	27	}	}	PUNCT
ejpam-3860	68	28	and	and	CCONJ
ejpam-3860	68	29	e(pk	e(pk	NOUN
ejpam-3860	68	30	�	�	NOUN
ejpam-3860	68	31	k1,n	k1,n	NOUN
ejpam-3860	68	32	)	)	PUNCT
ejpam-3860	68	33	=	=	PRON
ejpam-3860	68	34	{	{	PUNCT
ejpam-3860	68	35	(	(	PUNCT
ejpam-3860	68	36	x	x	NOUN
ejpam-3860	68	37	,	,	PUNCT
ejpam-3860	68	38	y)(w	y)(w	PROPN
ejpam-3860	68	39	,	,	PUNCT
ejpam-3860	68	40	z	z	NOUN
ejpam-3860	68	41	)	)	PUNCT
ejpam-3860	68	42	:	:	PUNCT
ejpam-3860	69	1	x	x	X
ejpam-3860	69	2	=	=	SYM
ejpam-3860	69	3	w	w	PROPN
ejpam-3860	69	4	and	and	CCONJ
ejpam-3860	69	5	yz	yz	PROPN
ejpam-3860	69	6	∈	∈	PROPN
ejpam-3860	69	7	e(k1,n	e(k1,n	NOUN
ejpam-3860	69	8	)	)	PUNCT
ejpam-3860	69	9	or	or	CCONJ
ejpam-3860	69	10	xw	xw	PROPN
ejpam-3860	69	11	∈	∈	PROPN
ejpam-3860	69	12	e(pk	e(pk	PROPN
ejpam-3860	69	13	)	)	PUNCT
ejpam-3860	69	14	and	and	CCONJ
ejpam-3860	69	15	y	y	PROPN
ejpam-3860	69	16	=	=	SYM
ejpam-3860	69	17	z	z	NOUN
ejpam-3860	69	18	}	}	PUNCT
ejpam-3860	69	19	.	.	PUNCT
ejpam-3860	70	1	observe	observe	VERB
ejpam-3860	70	2	that	that	SCONJ
ejpam-3860	70	3	for	for	ADP
ejpam-3860	70	4	any	any	DET
ejpam-3860	70	5	(	(	PUNCT
ejpam-3860	70	6	x	x	NOUN
ejpam-3860	70	7	,	,	PUNCT
ejpam-3860	70	8	y)(w	y)(w	PROPN
ejpam-3860	70	9	,	,	PUNCT
ejpam-3860	70	10	z	z	NOUN
ejpam-3860	70	11	)	)	PUNCT
ejpam-3860	70	12	∈	∈	PROPN
ejpam-3860	70	13	e(pk	e(pk	PROPN
ejpam-3860	70	14	�	�	NOUN
ejpam-3860	70	15	k1,n	k1,n	NOUN
ejpam-3860	70	16	)	)	PUNCT
ejpam-3860	70	17	,	,	PUNCT
ejpam-3860	70	18	we	we	PRON
ejpam-3860	70	19	have	have	VERB
ejpam-3860	70	20	the	the	DET
ejpam-3860	70	21	following	follow	VERB
ejpam-3860	70	22	cases	case	NOUN
ejpam-3860	70	23	:	:	PUNCT
ejpam-3860	70	24	case	case	NOUN
ejpam-3860	70	25	1	1	NUM
ejpam-3860	70	26	:	:	PUNCT
ejpam-3860	70	27	{	{	PUNCT
ejpam-3860	70	28	(	(	PUNCT
ejpam-3860	70	29	x	x	NOUN
ejpam-3860	70	30	,	,	PUNCT
ejpam-3860	70	31	y	y	PROPN
ejpam-3860	70	32	)	)	PUNCT
ejpam-3860	70	33	,	,	PUNCT
ejpam-3860	70	34	(	(	PUNCT
ejpam-3860	70	35	w	w	PROPN
ejpam-3860	70	36	,	,	PUNCT
ejpam-3860	70	37	z	z	NOUN
ejpam-3860	70	38	)	)	PUNCT
ejpam-3860	70	39	:	:	PUNCT
ejpam-3860	71	1	x	x	X
ejpam-3860	71	2	=	=	SYM
ejpam-3860	71	3	w	w	NOUN
ejpam-3860	71	4	is	be	AUX
ejpam-3860	71	5	odd	odd	ADJ
ejpam-3860	71	6	while	while	SCONJ
ejpam-3860	71	7	y	y	PROPN
ejpam-3860	71	8	is	be	AUX
ejpam-3860	71	9	even	even	ADV
ejpam-3860	71	10	and	and	CCONJ
ejpam-3860	71	11	z	z	NOUN
ejpam-3860	71	12	=	=	NOUN
ejpam-3860	71	13	1	1	NUM
ejpam-3860	71	14	}	}	PUNCT
ejpam-3860	71	15	.	.	PUNCT
ejpam-3860	72	1	case	case	NOUN
ejpam-3860	72	2	2	2	NUM
ejpam-3860	72	3	:	:	PUNCT
ejpam-3860	72	4	{	{	PUNCT
ejpam-3860	72	5	(	(	PUNCT
ejpam-3860	72	6	x	x	NOUN
ejpam-3860	72	7	,	,	PUNCT
ejpam-3860	72	8	y	y	PROPN
ejpam-3860	72	9	)	)	PUNCT
ejpam-3860	72	10	,	,	PUNCT
ejpam-3860	72	11	(	(	PUNCT
ejpam-3860	72	12	w	w	PROPN
ejpam-3860	72	13	,	,	PUNCT
ejpam-3860	72	14	z	z	NOUN
ejpam-3860	72	15	)	)	PUNCT
ejpam-3860	72	16	:	:	PUNCT
ejpam-3860	73	1	x	x	X
ejpam-3860	73	2	=	=	PUNCT
ejpam-3860	73	3	w	w	NOUN
ejpam-3860	73	4	is	be	AUX
ejpam-3860	73	5	even	even	ADV
ejpam-3860	73	6	while	while	SCONJ
ejpam-3860	73	7	y	y	PROPN
ejpam-3860	73	8	is	be	AUX
ejpam-3860	73	9	even	even	ADV
ejpam-3860	73	10	and	and	CCONJ
ejpam-3860	73	11	z	z	NOUN
ejpam-3860	73	12	=	=	NOUN
ejpam-3860	73	13	1	1	NUM
ejpam-3860	73	14	}	}	PUNCT
ejpam-3860	73	15	.	.	PUNCT
ejpam-3860	74	1	case	case	NOUN
ejpam-3860	74	2	3	3	NUM
ejpam-3860	74	3	:	:	PUNCT
ejpam-3860	74	4	{	{	PUNCT
ejpam-3860	74	5	(	(	PUNCT
ejpam-3860	74	6	x	x	NOUN
ejpam-3860	74	7	,	,	PUNCT
ejpam-3860	74	8	y	y	PROPN
ejpam-3860	74	9	)	)	PUNCT
ejpam-3860	74	10	,	,	PUNCT
ejpam-3860	74	11	(	(	PUNCT
ejpam-3860	74	12	w	w	PROPN
ejpam-3860	74	13	,	,	PUNCT
ejpam-3860	74	14	z	z	NOUN
ejpam-3860	74	15	)	)	PUNCT
ejpam-3860	74	16	:	:	PUNCT
ejpam-3860	75	1	y	y	NOUN
ejpam-3860	75	2	=	=	PUNCT
ejpam-3860	75	3	z	z	NOUN
ejpam-3860	75	4	=	=	SYM
ejpam-3860	75	5	1	1	NUM
ejpam-3860	75	6	while	while	SCONJ
ejpam-3860	75	7	x	x	PRON
ejpam-3860	75	8	is	be	AUX
ejpam-3860	75	9	even	even	ADV
ejpam-3860	75	10	and	and	CCONJ
ejpam-3860	75	11	w	w	PROPN
ejpam-3860	75	12	is	be	AUX
ejpam-3860	75	13	odd	odd	ADJ
ejpam-3860	75	14	}	}	PUNCT
ejpam-3860	75	15	.	.	PUNCT
ejpam-3860	76	1	case	case	NOUN
ejpam-3860	76	2	4	4	NUM
ejpam-3860	76	3	:	:	PUNCT
ejpam-3860	76	4	{	{	PUNCT
ejpam-3860	76	5	(	(	PUNCT
ejpam-3860	76	6	x	x	NOUN
ejpam-3860	76	7	,	,	PUNCT
ejpam-3860	76	8	y	y	PROPN
ejpam-3860	76	9	)	)	PUNCT
ejpam-3860	76	10	,	,	PUNCT
ejpam-3860	76	11	(	(	PUNCT
ejpam-3860	76	12	w	w	PROPN
ejpam-3860	76	13	,	,	PUNCT
ejpam-3860	76	14	z	z	NOUN
ejpam-3860	76	15	)	)	PUNCT
ejpam-3860	76	16	:	:	PUNCT
ejpam-3860	77	1	y	y	X
ejpam-3860	77	2	=	=	PUNCT
ejpam-3860	77	3	z	z	NOUN
ejpam-3860	77	4	is	be	AUX
ejpam-3860	77	5	even	even	ADV
ejpam-3860	77	6	while	while	SCONJ
ejpam-3860	77	7	x	x	PRON
ejpam-3860	77	8	is	be	AUX
ejpam-3860	77	9	even	even	ADV
ejpam-3860	77	10	and	and	CCONJ
ejpam-3860	77	11	w	w	PROPN
ejpam-3860	77	12	is	be	AUX
ejpam-3860	77	13	odd	odd	ADJ
ejpam-3860	77	14	}	}	PUNCT
ejpam-3860	77	15	.	.	PUNCT
ejpam-3860	78	1	now	now	ADV
ejpam-3860	78	2	,	,	PUNCT
ejpam-3860	78	3	let	let	VERB
ejpam-3860	78	4	s	s	PRON
ejpam-3860	78	5	=	=	VERB
ejpam-3860	78	6	{	{	PUNCT
ejpam-3860	78	7	(	(	PUNCT
ejpam-3860	78	8	p	p	X
ejpam-3860	78	9	,	,	PUNCT
ejpam-3860	78	10	q	q	NOUN
ejpam-3860	78	11	)	)	PUNCT
ejpam-3860	78	12	∈	∈	NOUN
ejpam-3860	78	13	v	v	NOUN
ejpam-3860	78	14	(	(	PUNCT
ejpam-3860	78	15	pk	pk	NOUN
ejpam-3860	78	16	�	�	PROPN
ejpam-3860	78	17	k1,n	k1,n	PROPN
ejpam-3860	78	18	)	)	PUNCT
ejpam-3860	78	19	:	:	PUNCT
ejpam-3860	79	1	p	p	X
ejpam-3860	79	2	and	and	CCONJ
ejpam-3860	79	3	q	q	NOUN
ejpam-3860	79	4	are	be	AUX
ejpam-3860	79	5	both	both	PRON
ejpam-3860	79	6	even	even	ADV
ejpam-3860	79	7	or	or	CCONJ
ejpam-3860	79	8	p	p	NOUN
ejpam-3860	79	9	and	and	CCONJ
ejpam-3860	79	10	q	q	NOUN
ejpam-3860	79	11	are	be	AUX
ejpam-3860	79	12	both	both	PRON
ejpam-3860	79	13	odd	odd	ADJ
ejpam-3860	79	14	}	}	PUNCT
ejpam-3860	79	15	and	and	CCONJ
ejpam-3860	79	16	t	t	PROPN
ejpam-3860	79	17	=	=	SYM
ejpam-3860	79	18	{	{	PUNCT
ejpam-3860	79	19	(	(	PUNCT
ejpam-3860	79	20	r	r	NOUN
ejpam-3860	79	21	,	,	PUNCT
ejpam-3860	79	22	s	s	PART
ejpam-3860	79	23	)	)	PUNCT
ejpam-3860	79	24	∈	∈	NOUN
ejpam-3860	79	25	v	v	NOUN
ejpam-3860	79	26	(	(	PUNCT
ejpam-3860	79	27	pk	pk	NOUN
ejpam-3860	79	28	�	�	PROPN
ejpam-3860	79	29	k1,n	k1,n	PROPN
ejpam-3860	79	30	)	)	PUNCT
ejpam-3860	79	31	:	:	PUNCT
ejpam-3860	80	1	r	r	NOUN
ejpam-3860	80	2	is	be	AUX
ejpam-3860	80	3	odd	odd	ADJ
ejpam-3860	80	4	and	and	CCONJ
ejpam-3860	80	5	s	s	VERB
ejpam-3860	80	6	is	be	AUX
ejpam-3860	80	7	even	even	ADV
ejpam-3860	80	8	or	or	CCONJ
ejpam-3860	80	9	r	r	NOUN
ejpam-3860	80	10	is	be	AUX
ejpam-3860	80	11	even	even	ADV
ejpam-3860	80	12	and	and	CCONJ
ejpam-3860	80	13	s	s	VERB
ejpam-3860	80	14	is	be	AUX
ejpam-3860	80	15	odd	odd	ADJ
ejpam-3860	80	16	}	}	PUNCT
ejpam-3860	80	17	.	.	PUNCT
ejpam-3860	81	1	we	we	PRON
ejpam-3860	81	2	claim	claim	VERB
ejpam-3860	81	3	that	that	SCONJ
ejpam-3860	81	4	s	s	VERB
ejpam-3860	81	5	and	and	CCONJ
ejpam-3860	81	6	t	t	PROPN
ejpam-3860	81	7	are	be	AUX
ejpam-3860	81	8	the	the	DET
ejpam-3860	81	9	independent	independent	ADJ
ejpam-3860	81	10	neighborhood	neighborhood	NOUN
ejpam-3860	81	11	sets	set	NOUN
ejpam-3860	81	12	of	of	ADP
ejpam-3860	81	13	pk	pk	NOUN
ejpam-3860	81	14	�	�	PROPN
ejpam-3860	81	15	k1,n	k1,n	PROPN
ejpam-3860	81	16	that	that	PRON
ejpam-3860	81	17	is	be	AUX
ejpam-3860	81	18	,	,	PUNCT
ejpam-3860	81	19	we	we	PRON
ejpam-3860	81	20	show	show	VERB
ejpam-3860	81	21	that	that	SCONJ
ejpam-3860	81	22	n.	n.	PROPN
ejpam-3860	81	23	abdulcarim	abdulcarim	PROPN
ejpam-3860	81	24	,	,	PUNCT
ejpam-3860	81	25	s.	s.	PROPN
ejpam-3860	81	26	dagondon	dagondon	PROPN
ejpam-3860	81	27	,	,	PUNCT
ejpam-3860	81	28	e.	e.	PROPN
ejpam-3860	81	29	chacon	chacon	PROPN
ejpam-3860	81	30	/	/	SYM
ejpam-3860	81	31	eur	eur	PROPN
ejpam-3860	81	32	.	.	PUNCT
ejpam-3860	82	1	j.	j.	PROPN
ejpam-3860	82	2	pure	pure	PROPN
ejpam-3860	82	3	appl	appl	PROPN
ejpam-3860	82	4	.	.	PROPN
ejpam-3860	82	5	math	math	PROPN
ejpam-3860	82	6	,	,	PUNCT
ejpam-3860	82	7	14	14	NUM
ejpam-3860	82	8	(	(	PUNCT
ejpam-3860	82	9	1	1	NUM
ejpam-3860	82	10	)	)	PUNCT
ejpam-3860	82	11	(	(	PUNCT
ejpam-3860	82	12	2021	2021	NUM
ejpam-3860	82	13	)	)	PUNCT
ejpam-3860	82	14	,	,	PUNCT
ejpam-3860	82	15	173	173	NUM
ejpam-3860	82	16	-	-	SYM
ejpam-3860	82	17	191	191	NUM
ejpam-3860	82	18	178	178	NUM
ejpam-3860	82	19	a.	a.	NOUN
ejpam-3860	82	20	no	no	DET
ejpam-3860	82	21	two	two	NUM
ejpam-3860	82	22	vertices	vertex	NOUN
ejpam-3860	82	23	in	in	ADP
ejpam-3860	82	24	s	s	NOUN
ejpam-3860	82	25	are	be	AUX
ejpam-3860	82	26	adjacent	adjacent	ADJ
ejpam-3860	82	27	and	and	CCONJ
ejpam-3860	82	28	⋃	⋃	ADJ
ejpam-3860	82	29	u∈s	u∈s	ADJ
ejpam-3860	82	30	〈	〈	PROPN
ejpam-3860	82	31	n	n	PRON
ejpam-3860	82	32	[	[	X
ejpam-3860	82	33	u	u	X
ejpam-3860	82	34	]	]	X
ejpam-3860	82	35	〉	〉	NOUN
ejpam-3860	82	36	=	=	SYM
ejpam-3860	82	37	pk	pk	PROPN
ejpam-3860	82	38	�	�	PROPN
ejpam-3860	82	39	k1,n	k1,n	PROPN
ejpam-3860	82	40	;	;	PUNCT
ejpam-3860	82	41	and	and	CCONJ
ejpam-3860	82	42	b.	b.	X
ejpam-3860	83	1	no	no	DET
ejpam-3860	83	2	two	two	NUM
ejpam-3860	83	3	vertices	vertex	NOUN
ejpam-3860	83	4	in	in	ADP
ejpam-3860	83	5	t	t	PROPN
ejpam-3860	83	6	are	be	AUX
ejpam-3860	83	7	adjacent	adjacent	ADJ
ejpam-3860	83	8	and	and	CCONJ
ejpam-3860	83	9	⋃	⋃	NOUN
ejpam-3860	83	10	v∈t	v∈t	NOUN
ejpam-3860	83	11	〈	〈	PROPN
ejpam-3860	83	12	n	n	PRON
ejpam-3860	83	13	[	[	X
ejpam-3860	83	14	v	v	NOUN
ejpam-3860	83	15	]	]	X
ejpam-3860	83	16	〉	〉	NOUN
ejpam-3860	83	17	=	=	SYM
ejpam-3860	83	18	pk	pk	PROPN
ejpam-3860	83	19	�	�	PROPN
ejpam-3860	83	20	k1,n	k1,n	PROPN
ejpam-3860	83	21	.	.	PUNCT
ejpam-3860	84	1	a.	a.	PROPN
ejpam-3860	84	2	let	let	VERB
ejpam-3860	84	3	(	(	PUNCT
ejpam-3860	84	4	x	x	NOUN
ejpam-3860	84	5	,	,	PUNCT
ejpam-3860	84	6	y	y	PROPN
ejpam-3860	84	7	)	)	PUNCT
ejpam-3860	84	8	,	,	PUNCT
ejpam-3860	85	1	(	(	PUNCT
ejpam-3860	85	2	w	w	PROPN
ejpam-3860	85	3	,	,	PUNCT
ejpam-3860	85	4	z	z	NOUN
ejpam-3860	85	5	)	)	PUNCT
ejpam-3860	85	6	∈	∈	PROPN
ejpam-3860	85	7	s.	s.	PROPN
ejpam-3860	85	8	we	we	PRON
ejpam-3860	85	9	consider	consider	VERB
ejpam-3860	85	10	the	the	DET
ejpam-3860	85	11	following	follow	VERB
ejpam-3860	85	12	cases	case	NOUN
ejpam-3860	85	13	:	:	PUNCT
ejpam-3860	85	14	case	case	NOUN
ejpam-3860	85	15	1	1	NUM
ejpam-3860	85	16	:	:	PUNCT
ejpam-3860	85	17	if	if	SCONJ
ejpam-3860	85	18	x	x	X
ejpam-3860	85	19	,	,	PUNCT
ejpam-3860	85	20	y	y	PROPN
ejpam-3860	85	21	,	,	PUNCT
ejpam-3860	85	22	w	w	PROPN
ejpam-3860	85	23	,	,	PUNCT
ejpam-3860	85	24	z	z	PROPN
ejpam-3860	85	25	are	be	AUX
ejpam-3860	85	26	all	all	PRON
ejpam-3860	85	27	odd	odd	ADJ
ejpam-3860	85	28	,	,	PUNCT
ejpam-3860	85	29	then	then	ADV
ejpam-3860	85	30	(	(	PUNCT
ejpam-3860	85	31	x	x	X
ejpam-3860	85	32	,	,	PUNCT
ejpam-3860	85	33	y)(w	y)(w	PROPN
ejpam-3860	85	34	,	,	PUNCT
ejpam-3860	85	35	z	z	NOUN
ejpam-3860	85	36	)	)	PUNCT
ejpam-3860	85	37	/∈	/∈	PUNCT
ejpam-3860	86	1	e(pk	e(pk	NOUN
ejpam-3860	86	2	�	�	NOUN
ejpam-3860	86	3	k1,n	k1,n	NOUN
ejpam-3860	86	4	)	)	PUNCT
ejpam-3860	86	5	.	.	PUNCT
ejpam-3860	87	1	thus	thus	ADV
ejpam-3860	87	2	,	,	PUNCT
ejpam-3860	87	3	(	(	PUNCT
ejpam-3860	87	4	x	x	X
ejpam-3860	87	5	,	,	PUNCT
ejpam-3860	87	6	y	y	PROPN
ejpam-3860	87	7	)	)	PUNCT
ejpam-3860	87	8	,	,	PUNCT
ejpam-3860	87	9	(	(	PUNCT
ejpam-3860	87	10	w	w	PROPN
ejpam-3860	87	11	,	,	PUNCT
ejpam-3860	87	12	z	z	NOUN
ejpam-3860	87	13	)	)	PUNCT
ejpam-3860	87	14	are	be	AUX
ejpam-3860	87	15	not	not	PART
ejpam-3860	87	16	adjacent	adjacent	ADJ
ejpam-3860	87	17	.	.	PUNCT
ejpam-3860	88	1	case	case	NOUN
ejpam-3860	88	2	2	2	NUM
ejpam-3860	88	3	:	:	PUNCT
ejpam-3860	88	4	if	if	SCONJ
ejpam-3860	88	5	x	x	X
ejpam-3860	88	6	,	,	PUNCT
ejpam-3860	88	7	y	y	PROPN
ejpam-3860	88	8	,	,	PUNCT
ejpam-3860	88	9	w	w	PROPN
ejpam-3860	88	10	,	,	PUNCT
ejpam-3860	88	11	z	z	NOUN
ejpam-3860	88	12	are	be	AUX
ejpam-3860	88	13	all	all	ADV
ejpam-3860	88	14	even	even	ADV
ejpam-3860	88	15	,	,	PUNCT
ejpam-3860	88	16	then	then	ADV
ejpam-3860	88	17	(	(	PUNCT
ejpam-3860	88	18	x	x	X
ejpam-3860	88	19	,	,	PUNCT
ejpam-3860	88	20	y)(w	y)(w	PROPN
ejpam-3860	88	21	,	,	PUNCT
ejpam-3860	88	22	z	z	NOUN
ejpam-3860	88	23	)	)	PUNCT
ejpam-3860	88	24	/∈	/∈	PUNCT
ejpam-3860	89	1	e(pk	e(pk	NOUN
ejpam-3860	89	2	�	�	NOUN
ejpam-3860	89	3	k1,n	k1,n	NOUN
ejpam-3860	89	4	)	)	PUNCT
ejpam-3860	89	5	.	.	PUNCT
ejpam-3860	90	1	thus	thus	ADV
ejpam-3860	90	2	,	,	PUNCT
ejpam-3860	90	3	(	(	PUNCT
ejpam-3860	90	4	x	x	X
ejpam-3860	90	5	,	,	PUNCT
ejpam-3860	90	6	y	y	PROPN
ejpam-3860	90	7	)	)	PUNCT
ejpam-3860	90	8	,	,	PUNCT
ejpam-3860	90	9	(	(	PUNCT
ejpam-3860	90	10	w	w	PROPN
ejpam-3860	90	11	,	,	PUNCT
ejpam-3860	90	12	z	z	NOUN
ejpam-3860	90	13	)	)	PUNCT
ejpam-3860	90	14	are	be	AUX
ejpam-3860	90	15	not	not	PART
ejpam-3860	90	16	adjacent	adjacent	ADJ
ejpam-3860	90	17	.	.	PUNCT
ejpam-3860	91	1	case	case	NOUN
ejpam-3860	91	2	3	3	NUM
ejpam-3860	91	3	:	:	PUNCT
ejpam-3860	91	4	if	if	SCONJ
ejpam-3860	91	5	x	x	X
ejpam-3860	91	6	,	,	PUNCT
ejpam-3860	91	7	y	y	PROPN
ejpam-3860	91	8	are	be	AUX
ejpam-3860	91	9	even	even	ADV
ejpam-3860	91	10	and	and	CCONJ
ejpam-3860	91	11	w	w	PROPN
ejpam-3860	91	12	,	,	PUNCT
ejpam-3860	91	13	z	z	PROPN
ejpam-3860	91	14	are	be	AUX
ejpam-3860	91	15	odd	odd	ADJ
ejpam-3860	91	16	,	,	PUNCT
ejpam-3860	91	17	then	then	ADV
ejpam-3860	91	18	(	(	PUNCT
ejpam-3860	91	19	x	x	X
ejpam-3860	91	20	,	,	PUNCT
ejpam-3860	91	21	y)(w	y)(w	PROPN
ejpam-3860	91	22	,	,	PUNCT
ejpam-3860	91	23	z	z	NOUN
ejpam-3860	91	24	)	)	PUNCT
ejpam-3860	91	25	/∈	/∈	PUNCT
ejpam-3860	92	1	e(pk	e(pk	NOUN
ejpam-3860	92	2	�	�	NOUN
ejpam-3860	92	3	k1,n	k1,n	NOUN
ejpam-3860	92	4	)	)	PUNCT
ejpam-3860	92	5	.	.	PUNCT
ejpam-3860	93	1	thus	thus	ADV
ejpam-3860	93	2	,	,	PUNCT
ejpam-3860	93	3	(	(	PUNCT
ejpam-3860	93	4	x	x	X
ejpam-3860	93	5	,	,	PUNCT
ejpam-3860	93	6	y	y	PROPN
ejpam-3860	93	7	)	)	PUNCT
ejpam-3860	93	8	,	,	PUNCT
ejpam-3860	93	9	(	(	PUNCT
ejpam-3860	93	10	w	w	PROPN
ejpam-3860	93	11	,	,	PUNCT
ejpam-3860	93	12	z	z	NOUN
ejpam-3860	93	13	)	)	PUNCT
ejpam-3860	93	14	are	be	AUX
ejpam-3860	93	15	not	not	PART
ejpam-3860	93	16	adjacent	adjacent	ADJ
ejpam-3860	93	17	.	.	PUNCT
ejpam-3860	94	1	case	case	NOUN
ejpam-3860	94	2	4	4	NUM
ejpam-3860	94	3	:	:	PUNCT
ejpam-3860	94	4	if	if	SCONJ
ejpam-3860	94	5	x	x	X
ejpam-3860	94	6	,	,	PUNCT
ejpam-3860	94	7	y	y	PROPN
ejpam-3860	94	8	are	be	AUX
ejpam-3860	94	9	odd	odd	ADJ
ejpam-3860	94	10	and	and	CCONJ
ejpam-3860	94	11	w	w	PROPN
ejpam-3860	94	12	,	,	PUNCT
ejpam-3860	94	13	z	z	PROPN
ejpam-3860	94	14	are	be	AUX
ejpam-3860	94	15	even	even	ADV
ejpam-3860	94	16	,	,	PUNCT
ejpam-3860	94	17	then	then	ADV
ejpam-3860	94	18	(	(	PUNCT
ejpam-3860	94	19	x	x	X
ejpam-3860	94	20	,	,	PUNCT
ejpam-3860	94	21	y)(w	y)(w	PROPN
ejpam-3860	94	22	,	,	PUNCT
ejpam-3860	94	23	z	z	NOUN
ejpam-3860	94	24	)	)	PUNCT
ejpam-3860	94	25	/∈	/∈	PUNCT
ejpam-3860	95	1	e(pk	e(pk	NOUN
ejpam-3860	95	2	�	�	NOUN
ejpam-3860	95	3	k1,n	k1,n	NOUN
ejpam-3860	95	4	)	)	PUNCT
ejpam-3860	95	5	.	.	PUNCT
ejpam-3860	96	1	thus	thus	ADV
ejpam-3860	96	2	,	,	PUNCT
ejpam-3860	96	3	(	(	PUNCT
ejpam-3860	96	4	x	x	X
ejpam-3860	96	5	,	,	PUNCT
ejpam-3860	96	6	y	y	PROPN
ejpam-3860	96	7	)	)	PUNCT
ejpam-3860	96	8	,	,	PUNCT
ejpam-3860	96	9	(	(	PUNCT
ejpam-3860	96	10	w	w	PROPN
ejpam-3860	96	11	,	,	PUNCT
ejpam-3860	96	12	z	z	NOUN
ejpam-3860	96	13	)	)	PUNCT
ejpam-3860	96	14	are	be	AUX
ejpam-3860	96	15	not	not	PART
ejpam-3860	96	16	adjacent	adjacent	ADJ
ejpam-3860	96	17	.	.	PUNCT
ejpam-3860	97	1	hence	hence	ADV
ejpam-3860	97	2	,	,	PUNCT
ejpam-3860	97	3	in	in	ADP
ejpam-3860	97	4	all	all	PRON
ejpam-3860	97	5	above	above	ADP
ejpam-3860	97	6	cases	case	NOUN
ejpam-3860	97	7	,	,	PUNCT
ejpam-3860	97	8	none	none	NOUN
ejpam-3860	97	9	of	of	ADP
ejpam-3860	97	10	the	the	DET
ejpam-3860	97	11	vertices	vertex	NOUN
ejpam-3860	97	12	of	of	ADP
ejpam-3860	97	13	s	s	NOUN
ejpam-3860	97	14	are	be	AUX
ejpam-3860	97	15	adjacent	adjacent	ADJ
ejpam-3860	97	16	.	.	PUNCT
ejpam-3860	98	1	next	next	ADV
ejpam-3860	98	2	,	,	PUNCT
ejpam-3860	98	3	we	we	PRON
ejpam-3860	98	4	will	will	AUX
ejpam-3860	98	5	show	show	VERB
ejpam-3860	98	6	that	that	SCONJ
ejpam-3860	98	7	⋃	⋃	ADJ
ejpam-3860	98	8	u∈s	u∈s	ADJ
ejpam-3860	98	9	〈	〈	PROPN
ejpam-3860	98	10	n	n	PRON
ejpam-3860	98	11	[	[	X
ejpam-3860	98	12	u	u	X
ejpam-3860	98	13	]	]	X
ejpam-3860	98	14	〉	〉	NOUN
ejpam-3860	98	15	=	=	SYM
ejpam-3860	98	16	pk	pk	PROPN
ejpam-3860	98	17	�	�	PROPN
ejpam-3860	98	18	k1,n	k1,n	PROPN
ejpam-3860	98	19	.	.	PUNCT
ejpam-3860	98	20	assume	assume	VERB
ejpam-3860	98	21	to	to	ADP
ejpam-3860	98	22	the	the	DET
ejpam-3860	98	23	contrary	contrary	NOUN
ejpam-3860	98	24	that	that	SCONJ
ejpam-3860	98	25	⋃	⋃	ADV
ejpam-3860	98	26	u∈s	u∈s	ADJ
ejpam-3860	98	27	〈	〈	PROPN
ejpam-3860	98	28	n	n	PRON
ejpam-3860	98	29	[	[	X
ejpam-3860	98	30	u	u	X
ejpam-3860	98	31	]	]	X
ejpam-3860	98	32	〉	〉	PROPN
ejpam-3860	98	33	6=	6=	SYM
ejpam-3860	98	34	pk	pk	PROPN
ejpam-3860	98	35	�	�	PROPN
ejpam-3860	98	36	k1,n	k1,n	PROPN
ejpam-3860	98	37	.	.	PUNCT
ejpam-3860	99	1	then	then	ADV
ejpam-3860	99	2	there	there	PRON
ejpam-3860	99	3	exists	exist	VERB
ejpam-3860	99	4	(	(	PUNCT
ejpam-3860	99	5	x	x	X
ejpam-3860	99	6	,	,	PUNCT
ejpam-3860	99	7	y)(w	y)(w	PROPN
ejpam-3860	99	8	,	,	PUNCT
ejpam-3860	99	9	z	z	NOUN
ejpam-3860	99	10	)	)	PUNCT
ejpam-3860	99	11	∈	∈	PROPN
ejpam-3860	99	12	e(pk	e(pk	PROPN
ejpam-3860	99	13	�	�	NOUN
ejpam-3860	99	14	k1,n	k1,n	NOUN
ejpam-3860	99	15	)	)	PUNCT
ejpam-3860	99	16	such	such	ADJ
ejpam-3860	99	17	that	that	SCONJ
ejpam-3860	99	18	(	(	PUNCT
ejpam-3860	99	19	x	x	NOUN
ejpam-3860	99	20	,	,	PUNCT
ejpam-3860	99	21	y)(w	y)(w	PROPN
ejpam-3860	99	22	,	,	PUNCT
ejpam-3860	99	23	z	z	NOUN
ejpam-3860	99	24	)	)	PUNCT
ejpam-3860	99	25	/∈	/∈	PUNCT
ejpam-3860	100	1	e	e	NOUN
ejpam-3860	100	2	(	(	PUNCT
ejpam-3860	100	3	⋃	⋃	NOUN
ejpam-3860	100	4	u∈s	u∈s	ADJ
ejpam-3860	100	5	〈	〈	PROPN
ejpam-3860	100	6	n	n	PRON
ejpam-3860	100	7	[	[	X
ejpam-3860	100	8	u	u	X
ejpam-3860	100	9	]	]	X
ejpam-3860	100	10	〉	〉	NUM
ejpam-3860	100	11	)	)	PUNCT
ejpam-3860	100	12	,	,	PUNCT
ejpam-3860	100	13	particularly	particularly	ADV
ejpam-3860	100	14	,	,	PUNCT
ejpam-3860	100	15	both	both	PRON
ejpam-3860	100	16	(	(	PUNCT
ejpam-3860	100	17	x	x	NOUN
ejpam-3860	100	18	,	,	PUNCT
ejpam-3860	100	19	y	y	PROPN
ejpam-3860	100	20	)	)	PUNCT
ejpam-3860	100	21	and	and	CCONJ
ejpam-3860	100	22	(	(	PUNCT
ejpam-3860	100	23	w	w	PROPN
ejpam-3860	100	24	,	,	PUNCT
ejpam-3860	100	25	z	z	NOUN
ejpam-3860	100	26	)	)	PUNCT
ejpam-3860	100	27	are	be	AUX
ejpam-3860	100	28	not	not	PART
ejpam-3860	100	29	in	in	ADP
ejpam-3860	100	30	s.	s.	PROPN
ejpam-3860	100	31	it	it	PRON
ejpam-3860	100	32	follows	follow	VERB
ejpam-3860	100	33	that	that	SCONJ
ejpam-3860	100	34	both	both	CCONJ
ejpam-3860	100	35	x	x	SYM
ejpam-3860	100	36	and	and	CCONJ
ejpam-3860	100	37	y	y	PROPN
ejpam-3860	100	38	are	be	AUX
ejpam-3860	100	39	not	not	PART
ejpam-3860	100	40	odd	odd	ADJ
ejpam-3860	100	41	or	or	CCONJ
ejpam-3860	100	42	both	both	PRON
ejpam-3860	100	43	x	x	X
ejpam-3860	100	44	and	and	CCONJ
ejpam-3860	100	45	y	y	PROPN
ejpam-3860	100	46	are	be	AUX
ejpam-3860	100	47	not	not	PART
ejpam-3860	100	48	even	even	ADV
ejpam-3860	100	49	.	.	PUNCT
ejpam-3860	101	1	similar	similar	ADJ
ejpam-3860	101	2	case	case	NOUN
ejpam-3860	101	3	for	for	ADP
ejpam-3860	101	4	w	w	PROPN
ejpam-3860	101	5	and	and	CCONJ
ejpam-3860	101	6	z.	z.	PROPN
ejpam-3860	101	7	now	now	ADV
ejpam-3860	101	8	,	,	PUNCT
ejpam-3860	101	9	if	if	SCONJ
ejpam-3860	101	10	x	x	PRON
ejpam-3860	101	11	is	be	AUX
ejpam-3860	101	12	odd	odd	ADJ
ejpam-3860	101	13	,	,	PUNCT
ejpam-3860	101	14	y	y	PROPN
ejpam-3860	101	15	is	be	AUX
ejpam-3860	101	16	even	even	ADV
ejpam-3860	101	17	,	,	PUNCT
ejpam-3860	101	18	w	w	NOUN
ejpam-3860	101	19	is	be	AUX
ejpam-3860	101	20	odd	odd	ADJ
ejpam-3860	101	21	and	and	CCONJ
ejpam-3860	101	22	z	z	NOUN
ejpam-3860	101	23	is	be	AUX
ejpam-3860	101	24	even	even	ADV
ejpam-3860	101	25	,	,	PUNCT
ejpam-3860	101	26	then	then	ADV
ejpam-3860	101	27	(	(	PUNCT
ejpam-3860	101	28	x	x	X
ejpam-3860	101	29	,	,	PUNCT
ejpam-3860	101	30	y)(w	y)(w	PROPN
ejpam-3860	101	31	,	,	PUNCT
ejpam-3860	101	32	z	z	NOUN
ejpam-3860	101	33	)	)	PUNCT
ejpam-3860	101	34	/∈	/∈	PUNCT
ejpam-3860	102	1	e(pk	e(pk	NOUN
ejpam-3860	102	2	�	�	NOUN
ejpam-3860	102	3	k1,n	k1,n	NOUN
ejpam-3860	102	4	)	)	PUNCT
ejpam-3860	102	5	.	.	PUNCT
ejpam-3860	103	1	this	this	PRON
ejpam-3860	103	2	is	be	AUX
ejpam-3860	103	3	a	a	DET
ejpam-3860	103	4	contradiction	contradiction	NOUN
ejpam-3860	103	5	.	.	PUNCT
ejpam-3860	104	1	if	if	SCONJ
ejpam-3860	104	2	we	we	PRON
ejpam-3860	104	3	consider	consider	VERB
ejpam-3860	104	4	x	x	PRON
ejpam-3860	104	5	is	be	AUX
ejpam-3860	104	6	odd	odd	ADJ
ejpam-3860	104	7	,	,	PUNCT
ejpam-3860	104	8	y	y	PROPN
ejpam-3860	104	9	is	be	AUX
ejpam-3860	104	10	even	even	ADV
ejpam-3860	104	11	,	,	PUNCT
ejpam-3860	104	12	w	w	NOUN
ejpam-3860	104	13	is	be	AUX
ejpam-3860	104	14	even	even	ADV
ejpam-3860	104	15	and	and	CCONJ
ejpam-3860	104	16	z	z	NOUN
ejpam-3860	104	17	is	be	AUX
ejpam-3860	104	18	odd	odd	ADJ
ejpam-3860	104	19	,	,	PUNCT
ejpam-3860	104	20	then	then	ADV
ejpam-3860	104	21	(	(	PUNCT
ejpam-3860	104	22	x	x	X
ejpam-3860	104	23	,	,	PUNCT
ejpam-3860	104	24	y)(w	y)(w	PROPN
ejpam-3860	104	25	,	,	PUNCT
ejpam-3860	104	26	z	z	NOUN
ejpam-3860	104	27	)	)	PUNCT
ejpam-3860	104	28	/∈	/∈	PUNCT
ejpam-3860	105	1	e(pk	e(pk	NOUN
ejpam-3860	105	2	�	�	NOUN
ejpam-3860	105	3	k1,n	k1,n	NOUN
ejpam-3860	105	4	)	)	PUNCT
ejpam-3860	105	5	.	.	PUNCT
ejpam-3860	106	1	similar	similar	ADJ
ejpam-3860	106	2	case	case	NOUN
ejpam-3860	106	3	when	when	SCONJ
ejpam-3860	106	4	x	x	PRON
ejpam-3860	106	5	is	be	AUX
ejpam-3860	106	6	even	even	ADV
ejpam-3860	106	7	,	,	PUNCT
ejpam-3860	106	8	y	y	PROPN
ejpam-3860	106	9	is	be	AUX
ejpam-3860	106	10	odd	odd	ADJ
ejpam-3860	106	11	,	,	PUNCT
ejpam-3860	106	12	w	w	PROPN
ejpam-3860	106	13	is	be	AUX
ejpam-3860	106	14	odd	odd	ADJ
ejpam-3860	106	15	,	,	PUNCT
ejpam-3860	106	16	z	z	NOUN
ejpam-3860	106	17	is	be	AUX
ejpam-3860	106	18	even	even	ADV
ejpam-3860	106	19	and	and	CCONJ
ejpam-3860	106	20	for	for	ADP
ejpam-3860	106	21	x	x	SYM
ejpam-3860	106	22	is	be	AUX
ejpam-3860	106	23	even	even	ADV
ejpam-3860	106	24	,	,	PUNCT
ejpam-3860	106	25	y	y	PROPN
ejpam-3860	106	26	is	be	AUX
ejpam-3860	106	27	odd	odd	ADJ
ejpam-3860	106	28	,	,	PUNCT
ejpam-3860	106	29	w	w	NOUN
ejpam-3860	106	30	is	be	AUX
ejpam-3860	106	31	even	even	ADV
ejpam-3860	106	32	,	,	PUNCT
ejpam-3860	106	33	z	z	PROPN
ejpam-3860	106	34	is	be	AUX
ejpam-3860	106	35	odd	odd	ADJ
ejpam-3860	106	36	.	.	PUNCT
ejpam-3860	107	1	hence	hence	ADV
ejpam-3860	107	2	,	,	PUNCT
ejpam-3860	107	3	in	in	ADP
ejpam-3860	107	4	either	either	DET
ejpam-3860	107	5	cases	case	NOUN
ejpam-3860	107	6	,	,	PUNCT
ejpam-3860	107	7	(	(	PUNCT
ejpam-3860	107	8	x	x	NOUN
ejpam-3860	107	9	,	,	PUNCT
ejpam-3860	107	10	y)(w	y)(w	PROPN
ejpam-3860	107	11	,	,	PUNCT
ejpam-3860	107	12	z	z	NOUN
ejpam-3860	107	13	)	)	PUNCT
ejpam-3860	107	14	/∈	/∈	PUNCT
ejpam-3860	108	1	e(pk	e(pk	NOUN
ejpam-3860	108	2	�	�	NOUN
ejpam-3860	108	3	k1,n	k1,n	NOUN
ejpam-3860	108	4	)	)	PUNCT
ejpam-3860	108	5	which	which	PRON
ejpam-3860	108	6	is	be	AUX
ejpam-3860	108	7	a	a	DET
ejpam-3860	108	8	contradiction	contradiction	NOUN
ejpam-3860	108	9	to	to	ADP
ejpam-3860	108	10	the	the	DET
ejpam-3860	108	11	assumption	assumption	NOUN
ejpam-3860	108	12	.	.	PUNCT
ejpam-3860	109	1	therefore	therefore	ADV
ejpam-3860	109	2	,	,	PUNCT
ejpam-3860	109	3	⋃	⋃	ADV
ejpam-3860	109	4	u∈s	u∈s	ADJ
ejpam-3860	109	5	〈	〈	PROPN
ejpam-3860	109	6	n	n	PRON
ejpam-3860	109	7	[	[	X
ejpam-3860	109	8	u	u	X
ejpam-3860	109	9	]	]	X
ejpam-3860	109	10	〉	〉	NOUN
ejpam-3860	109	11	=	=	SYM
ejpam-3860	109	12	pk	pk	PROPN
ejpam-3860	109	13	�	�	PROPN
ejpam-3860	109	14	k1,n	k1,n	PROPN
ejpam-3860	109	15	.	.	PUNCT
ejpam-3860	110	1	consequently	consequently	ADV
ejpam-3860	110	2	,	,	PUNCT
ejpam-3860	110	3	s	s	VERB
ejpam-3860	110	4	is	be	AUX
ejpam-3860	110	5	an	an	DET
ejpam-3860	110	6	independent	independent	ADJ
ejpam-3860	110	7	neighborhood	neighborhood	NOUN
ejpam-3860	110	8	set	set	NOUN
ejpam-3860	110	9	of	of	ADP
ejpam-3860	110	10	pk	pk	NOUN
ejpam-3860	110	11	�	�	PROPN
ejpam-3860	110	12	k1,n	k1,n	PROPN
ejpam-3860	110	13	.	.	PUNCT
ejpam-3860	111	1	following	follow	VERB
ejpam-3860	111	2	the	the	DET
ejpam-3860	111	3	same	same	ADJ
ejpam-3860	111	4	argument	argument	NOUN
ejpam-3860	111	5	in	in	ADP
ejpam-3860	111	6	(	(	PUNCT
ejpam-3860	111	7	a	a	NOUN
ejpam-3860	111	8	)	)	PUNCT
ejpam-3860	111	9	for	for	ADP
ejpam-3860	111	10	(	(	PUNCT
ejpam-3860	111	11	b	b	NOUN
ejpam-3860	111	12	)	)	PUNCT
ejpam-3860	111	13	,	,	PUNCT
ejpam-3860	111	14	we	we	PRON
ejpam-3860	111	15	can	can	AUX
ejpam-3860	111	16	show	show	VERB
ejpam-3860	111	17	that	that	SCONJ
ejpam-3860	111	18	t	t	PROPN
ejpam-3860	111	19	is	be	AUX
ejpam-3860	111	20	also	also	ADV
ejpam-3860	111	21	an	an	DET
ejpam-3860	111	22	independent	independent	ADJ
ejpam-3860	111	23	neighborhood	neighborhood	NOUN
ejpam-3860	111	24	set	set	NOUN
ejpam-3860	111	25	of	of	ADP
ejpam-3860	111	26	pk	pk	NOUN
ejpam-3860	111	27	�	�	PROPN
ejpam-3860	111	28	k1,n	k1,n	PROPN
ejpam-3860	111	29	.	.	PUNCT
ejpam-3860	112	1	now	now	ADV
ejpam-3860	112	2	,	,	PUNCT
ejpam-3860	112	3	if	if	SCONJ
ejpam-3860	112	4	we	we	PRON
ejpam-3860	112	5	let	let	VERB
ejpam-3860	112	6	s1	s1	PROPN
ejpam-3860	112	7	=	=	PUNCT
ejpam-3860	112	8	{	{	PUNCT
ejpam-3860	112	9	(	(	PUNCT
ejpam-3860	112	10	x	x	NOUN
ejpam-3860	112	11	,	,	PUNCT
ejpam-3860	112	12	y	y	PROPN
ejpam-3860	112	13	)	)	PUNCT
ejpam-3860	112	14	:	:	PUNCT
ejpam-3860	113	1	x	x	X
ejpam-3860	113	2	and	and	CCONJ
ejpam-3860	113	3	y	y	PROPN
ejpam-3860	113	4	are	be	AUX
ejpam-3860	113	5	odd	odd	ADJ
ejpam-3860	113	6	}	}	PUNCT
ejpam-3860	113	7	,	,	PUNCT
ejpam-3860	113	8	s2	s2	PROPN
ejpam-3860	113	9	=	=	SYM
ejpam-3860	113	10	{	{	PUNCT
ejpam-3860	113	11	(	(	PUNCT
ejpam-3860	113	12	x	x	NOUN
ejpam-3860	113	13	,	,	PUNCT
ejpam-3860	113	14	y	y	PROPN
ejpam-3860	113	15	)	)	PUNCT
ejpam-3860	113	16	:	:	PUNCT
ejpam-3860	114	1	x	x	X
ejpam-3860	114	2	and	and	CCONJ
ejpam-3860	114	3	y	y	PROPN
ejpam-3860	114	4	are	be	AUX
ejpam-3860	114	5	even	even	ADV
ejpam-3860	114	6	}	}	PUNCT
ejpam-3860	114	7	,	,	PUNCT
ejpam-3860	114	8	t1	t1	NOUN
ejpam-3860	114	9	=	=	SYM
ejpam-3860	114	10	{	{	PUNCT
ejpam-3860	114	11	(	(	PUNCT
ejpam-3860	114	12	x	x	NOUN
ejpam-3860	114	13	,	,	PUNCT
ejpam-3860	114	14	y	y	PROPN
ejpam-3860	114	15	)	)	PUNCT
ejpam-3860	114	16	:	:	PUNCT
ejpam-3860	114	17	x	x	X
ejpam-3860	114	18	is	be	AUX
ejpam-3860	114	19	odd	odd	ADJ
ejpam-3860	114	20	and	and	CCONJ
ejpam-3860	114	21	y	y	PROPN
ejpam-3860	114	22	is	be	AUX
ejpam-3860	114	23	even	even	ADV
ejpam-3860	114	24	}	}	PUNCT
ejpam-3860	114	25	and	and	CCONJ
ejpam-3860	114	26	t2	t2	PROPN
ejpam-3860	114	27	=	=	SYM
ejpam-3860	114	28	{	{	PUNCT
ejpam-3860	114	29	(	(	PUNCT
ejpam-3860	114	30	x	x	NOUN
ejpam-3860	114	31	,	,	PUNCT
ejpam-3860	114	32	y	y	PROPN
ejpam-3860	114	33	)	)	PUNCT
ejpam-3860	114	34	:	:	PUNCT
ejpam-3860	114	35	x	x	X
ejpam-3860	114	36	is	be	AUX
ejpam-3860	114	37	even	even	ADV
ejpam-3860	114	38	and	and	CCONJ
ejpam-3860	114	39	y	y	PROPN
ejpam-3860	114	40	is	be	AUX
ejpam-3860	114	41	odd	odd	ADJ
ejpam-3860	114	42	}	}	PUNCT
ejpam-3860	114	43	,	,	PUNCT
ejpam-3860	114	44	then	then	ADV
ejpam-3860	114	45	s1	s1	PROPN
ejpam-3860	114	46	∪s2	∪s2	VERB
ejpam-3860	114	47	∪	∪	VERB
ejpam-3860	114	48	t1	t1	NOUN
ejpam-3860	114	49	∪	∪	NOUN
ejpam-3860	114	50	t2	t2	NOUN
ejpam-3860	114	51	=	=	SYM
ejpam-3860	114	52	v	v	NOUN
ejpam-3860	114	53	(	(	PUNCT
ejpam-3860	114	54	pk	pk	NOUN
ejpam-3860	114	55	�	�	PROPN
ejpam-3860	114	56	k1,n	k1,n	PROPN
ejpam-3860	114	57	)	)	PUNCT
ejpam-3860	114	58	and	and	CCONJ
ejpam-3860	114	59	that	that	SCONJ
ejpam-3860	114	60	s1	s1	NOUN
ejpam-3860	114	61	∪s2	∪s2	VERB
ejpam-3860	114	62	=	=	SYM
ejpam-3860	114	63	s	s	NOUN
ejpam-3860	114	64	and	and	CCONJ
ejpam-3860	114	65	t	t	PROPN
ejpam-3860	114	66	=	=	SYM
ejpam-3860	114	67	t1	t1	PROPN
ejpam-3860	114	68	∪	∪	PROPN
ejpam-3860	114	69	t2	t2	PROPN
ejpam-3860	114	70	.	.	PUNCT
ejpam-3860	115	1	notice	notice	VERB
ejpam-3860	115	2	that	that	SCONJ
ejpam-3860	115	3	when	when	SCONJ
ejpam-3860	115	4	k	k	PROPN
ejpam-3860	115	5	is	be	AUX
ejpam-3860	115	6	odd	odd	ADJ
ejpam-3860	115	7	,	,	PUNCT
ejpam-3860	115	8	|s1|	|s1|	NOUN
ejpam-3860	115	9	=	=	SYM
ejpam-3860	115	10	⌈	⌈	SYM
ejpam-3860	115	11	k	k	X
ejpam-3860	115	12	2	2	NUM
ejpam-3860	115	13	⌉	⌉	NOUN
ejpam-3860	115	14	,	,	PUNCT
ejpam-3860	115	15	|s2|	|s2|	NOUN
ejpam-3860	115	16	=	=	SYM
ejpam-3860	115	17	⌊	⌊	VERB
ejpam-3860	115	18	k	k	X
ejpam-3860	115	19	2	2	NUM
ejpam-3860	115	20	⌋	⌋	NUM
ejpam-3860	115	21	n	n	CCONJ
ejpam-3860	115	22	,	,	PUNCT
ejpam-3860	115	23	|t1|	|t1|	NOUN
ejpam-3860	115	24	=	=	SYM
ejpam-3860	115	25	⌈	⌈	NOUN
ejpam-3860	115	26	k	k	X
ejpam-3860	115	27	2	2	NUM
ejpam-3860	115	28	⌉	⌉	X
ejpam-3860	115	29	n	n	CCONJ
ejpam-3860	115	30	,	,	PUNCT
ejpam-3860	115	31	|t2|	|t2|	NOUN
ejpam-3860	115	32	=	=	PUNCT
ejpam-3860	115	33	⌊	⌊	VERB
ejpam-3860	115	34	k	k	NOUN
ejpam-3860	115	35	2	2	NUM
ejpam-3860	115	36	⌋	⌋	NOUN
ejpam-3860	115	37	.	.	PUNCT
ejpam-3860	116	1	hence	hence	ADV
ejpam-3860	116	2	,	,	PUNCT
ejpam-3860	116	3	|s|	|s|	PROPN
ejpam-3860	116	4	=	=	SYM
ejpam-3860	116	5	⌊	⌊	PROPN
ejpam-3860	116	6	k	k	X
ejpam-3860	116	7	2	2	NUM
ejpam-3860	116	8	⌋	⌋	NUM
ejpam-3860	116	9	n+	n+	PUNCT
ejpam-3860	116	10	⌈	⌈	NOUN
ejpam-3860	116	11	k	k	X
ejpam-3860	116	12	2	2	NUM
ejpam-3860	116	13	⌉	⌉	PUNCT
ejpam-3860	116	14	and	and	CCONJ
ejpam-3860	116	15	|t	|t	VERB
ejpam-3860	116	16	|	|	ADV
ejpam-3860	116	17	=	=	SYM
ejpam-3860	117	1	⌈	⌈	NOUN
ejpam-3860	117	2	k	k	X
ejpam-3860	117	3	2	2	NUM
ejpam-3860	117	4	⌉	⌉	X
ejpam-3860	117	5	n+	n+	PUNCT
ejpam-3860	117	6	⌊	⌊	VERB
ejpam-3860	117	7	k	k	X
ejpam-3860	117	8	2	2	NUM
ejpam-3860	117	9	⌋	⌋	NOUN
ejpam-3860	117	10	.	.	PUNCT
ejpam-3860	118	1	thus	thus	ADV
ejpam-3860	118	2	,	,	PUNCT
ejpam-3860	118	3	ni(pk	ni(pk	PROPN
ejpam-3860	118	4	�	�	NOUN
ejpam-3860	118	5	k1,n	k1,n	PROPN
ejpam-3860	118	6	,	,	PUNCT
ejpam-3860	118	7	x	x	NOUN
ejpam-3860	118	8	)	)	PUNCT
ejpam-3860	118	9	=	=	SYM
ejpam-3860	119	1	xb	xb	PROPN
ejpam-3860	120	1	k	k	PROPN
ejpam-3860	120	2	2cn+d	2cn+d	PROPN
ejpam-3860	120	3	k2e	k2e	PROPN
ejpam-3860	121	1	+	+	CCONJ
ejpam-3860	121	2	xd	xd	INTJ
ejpam-3860	121	3	k	k	PROPN
ejpam-3860	121	4	2en+b	2en+b	NUM
ejpam-3860	121	5	k2c	k2c	NOUN
ejpam-3860	121	6	when	when	SCONJ
ejpam-3860	121	7	k	k	PROPN
ejpam-3860	121	8	is	be	AUX
ejpam-3860	121	9	odd	odd	ADJ
ejpam-3860	121	10	.	.	PUNCT
ejpam-3860	122	1	for	for	SCONJ
ejpam-3860	122	2	k	k	PROPN
ejpam-3860	122	3	is	be	AUX
ejpam-3860	122	4	even	even	ADV
ejpam-3860	122	5	,	,	PUNCT
ejpam-3860	122	6	observe	observe	VERB
ejpam-3860	122	7	that	that	SCONJ
ejpam-3860	122	8	⌊	⌊	PROPN
ejpam-3860	122	9	k	k	NOUN
ejpam-3860	122	10	2	2	NUM
ejpam-3860	122	11	⌋	⌋	NOUN
ejpam-3860	122	12	=	=	PUNCT
ejpam-3860	122	13	(	(	PUNCT
ejpam-3860	122	14	k	k	NOUN
ejpam-3860	122	15	2	2	X
ejpam-3860	122	16	)	)	PUNCT
ejpam-3860	122	17	=	=	PUNCT
ejpam-3860	123	1	⌈	⌈	SYM
ejpam-3860	123	2	k	k	X
ejpam-3860	123	3	2	2	NUM
ejpam-3860	123	4	⌉	⌉	X
ejpam-3860	123	5	.	.	PUNCT
ejpam-3860	124	1	it	it	PRON
ejpam-3860	124	2	follows	follow	VERB
ejpam-3860	124	3	that	that	SCONJ
ejpam-3860	124	4	|s|	|s|	PROPN
ejpam-3860	124	5	=	=	SYM
ejpam-3860	124	6	|t	|t	NOUN
ejpam-3860	125	1	|	|	INTJ
ejpam-3860	125	2	and	and	CCONJ
ejpam-3860	125	3	so	so	ADV
ejpam-3860	125	4	,	,	PUNCT
ejpam-3860	125	5	ni(pk	ni(pk	PROPN
ejpam-3860	125	6	�	�	NOUN
ejpam-3860	125	7	k1,n	k1,n	PROPN
ejpam-3860	125	8	,	,	PUNCT
ejpam-3860	125	9	x	x	NOUN
ejpam-3860	125	10	)	)	PUNCT
ejpam-3860	125	11	=	=	SYM
ejpam-3860	125	12	2x	2x	NOUN
ejpam-3860	125	13	(	(	PUNCT
ejpam-3860	125	14	k	k	NOUN
ejpam-3860	125	15	2	2	NUM
ejpam-3860	125	16	)	)	PUNCT
ejpam-3860	125	17	n+	n+	PROPN
ejpam-3860	125	18	(	(	PUNCT
ejpam-3860	125	19	k	k	NOUN
ejpam-3860	125	20	2	2	NUM
ejpam-3860	125	21	)	)	PUNCT
ejpam-3860	125	22	.	.	PUNCT
ejpam-3860	126	1	n.	n.	PROPN
ejpam-3860	126	2	abdulcarim	abdulcarim	PROPN
ejpam-3860	126	3	,	,	PUNCT
ejpam-3860	126	4	s.	s.	PROPN
ejpam-3860	126	5	dagondon	dagondon	PROPN
ejpam-3860	126	6	,	,	PUNCT
ejpam-3860	126	7	e.	e.	PROPN
ejpam-3860	126	8	chacon	chacon	PROPN
ejpam-3860	126	9	/	/	SYM
ejpam-3860	126	10	eur	eur	PROPN
ejpam-3860	126	11	.	.	PUNCT
ejpam-3860	127	1	j.	j.	PROPN
ejpam-3860	127	2	pure	pure	PROPN
ejpam-3860	127	3	appl	appl	PROPN
ejpam-3860	127	4	.	.	PROPN
ejpam-3860	127	5	math	math	PROPN
ejpam-3860	127	6	,	,	PUNCT
ejpam-3860	127	7	14	14	NUM
ejpam-3860	127	8	(	(	PUNCT
ejpam-3860	127	9	1	1	NUM
ejpam-3860	127	10	)	)	PUNCT
ejpam-3860	127	11	(	(	PUNCT
ejpam-3860	127	12	2021	2021	NUM
ejpam-3860	127	13	)	)	PUNCT
ejpam-3860	127	14	,	,	PUNCT
ejpam-3860	127	15	173	173	NUM
ejpam-3860	127	16	-	-	SYM
ejpam-3860	127	17	191	191	NUM
ejpam-3860	127	18	179	179	NUM
ejpam-3860	127	19	consequently	consequently	ADV
ejpam-3860	127	20	,	,	PUNCT
ejpam-3860	127	21	ni(pk	ni(pk	PROPN
ejpam-3860	127	22	�	�	NOUN
ejpam-3860	127	23	k1,n	k1,n	PROPN
ejpam-3860	127	24	,	,	PUNCT
ejpam-3860	127	25	x	x	NOUN
ejpam-3860	127	26	)	)	PUNCT
ejpam-3860	127	27	=	=	SYM
ejpam-3860	127	28	{	{	PUNCT
ejpam-3860	127	29	xb	xb	PROPN
ejpam-3860	127	30	k	k	PROPN
ejpam-3860	127	31	2cn+d	2cn+d	PROPN
ejpam-3860	128	1	k2e	k2e	PROPN
ejpam-3860	129	1	+	+	CCONJ
ejpam-3860	129	2	xd	xd	INTJ
ejpam-3860	129	3	k	k	PROPN
ejpam-3860	129	4	2en+b	2en+b	NUM
ejpam-3860	129	5	k2c	k2c	PROPN
ejpam-3860	129	6	,	,	PUNCT
ejpam-3860	129	7	k	k	PROPN
ejpam-3860	129	8	is	be	AUX
ejpam-3860	129	9	odd	odd	ADJ
ejpam-3860	129	10	2x	2x	NUM
ejpam-3860	129	11	(	(	PUNCT
ejpam-3860	129	12	k	k	PROPN
ejpam-3860	129	13	2	2	NUM
ejpam-3860	129	14	)	)	PUNCT
ejpam-3860	129	15	n+	n+	PROPN
ejpam-3860	129	16	(	(	PUNCT
ejpam-3860	129	17	k	k	NOUN
ejpam-3860	129	18	2	2	NUM
ejpam-3860	129	19	)	)	PUNCT
ejpam-3860	129	20	,	,	PUNCT
ejpam-3860	129	21	k	k	PROPN
ejpam-3860	129	22	is	be	AUX
ejpam-3860	129	23	even	even	ADV
ejpam-3860	129	24	.	.	PUNCT
ejpam-3860	130	1	theorem	theorem	NOUN
ejpam-3860	130	2	2	2	NUM
ejpam-3860	130	3	.	.	X
ejpam-3860	130	4	for	for	ADP
ejpam-3860	130	5	any	any	DET
ejpam-3860	130	6	path	path	NOUN
ejpam-3860	130	7	pk	pk	NOUN
ejpam-3860	130	8	and	and	CCONJ
ejpam-3860	130	9	bistar	bistar	PROPN
ejpam-3860	130	10	graph	graph	NOUN
ejpam-3860	130	11	b(m	b(m	PROPN
ejpam-3860	130	12	,	,	PUNCT
ejpam-3860	130	13	n	n	CCONJ
ejpam-3860	130	14	)	)	PUNCT
ejpam-3860	130	15	,	,	PUNCT
ejpam-3860	130	16	ni(pk	ni(pk	PROPN
ejpam-3860	130	17	�	�	PROPN
ejpam-3860	130	18	bm	bm	PROPN
ejpam-3860	130	19	,	,	PUNCT
ejpam-3860	130	20	n	n	CCONJ
ejpam-3860	130	21	,	,	PUNCT
ejpam-3860	130	22	x	x	NOUN
ejpam-3860	130	23	)	)	PUNCT
ejpam-3860	130	24	=	=	PUNCT
ejpam-3860	131	1	xd	xd	NUM
ejpam-3860	131	2	k	k	PROPN
ejpam-3860	131	3	2e(m+1)+b	2e(m+1)+b	PROPN
ejpam-3860	131	4	k2c(n+1	k2c(n+1	PROPN
ejpam-3860	131	5	)	)	PUNCT
ejpam-3860	132	1	+	+	CCONJ
ejpam-3860	132	2	xb	xb	PROPN
ejpam-3860	132	3	k	k	PROPN
ejpam-3860	132	4	2c(m+1)+d	2c(m+1)+d	PROPN
ejpam-3860	132	5	k2e(n+1	k2e(n+1	PROPN
ejpam-3860	132	6	)	)	PUNCT
ejpam-3860	132	7	for	for	ADP
ejpam-3860	132	8	any	any	DET
ejpam-3860	132	9	k	k	PROPN
ejpam-3860	132	10	,	,	PUNCT
ejpam-3860	132	11	m	m	PROPN
ejpam-3860	132	12	,	,	PUNCT
ejpam-3860	132	13	n	n	PRON
ejpam-3860	132	14	∈	∈	PROPN
ejpam-3860	132	15	z+	z+	PUNCT
ejpam-3860	132	16	.	.	PUNCT
ejpam-3860	133	1	proof	proof	NOUN
ejpam-3860	133	2	:	:	PUNCT
ejpam-3860	133	3	label	label	VERB
ejpam-3860	133	4	the	the	DET
ejpam-3860	133	5	vertices	vertex	NOUN
ejpam-3860	133	6	of	of	ADP
ejpam-3860	133	7	b(m	b(m	PROPN
ejpam-3860	133	8	,	,	PUNCT
ejpam-3860	133	9	n	n	CCONJ
ejpam-3860	133	10	)	)	PUNCT
ejpam-3860	133	11	as	as	ADP
ejpam-3860	133	12	iu	iu	ADP
ejpam-3860	133	13	,	,	PUNCT
ejpam-3860	133	14	jv	jv	NOUN
ejpam-3860	133	15	,	,	PUNCT
ejpam-3860	133	16	0u	0u	ADJ
ejpam-3860	133	17	,	,	PUNCT
ejpam-3860	133	18	0v	0v	NOUN
ejpam-3860	133	19	,	,	PUNCT
ejpam-3860	133	20	i	i	NOUN
ejpam-3860	133	21	=	=	NOUN
ejpam-3860	133	22	1	1	NUM
ejpam-3860	133	23	,	,	PUNCT
ejpam-3860	133	24	·	·	PUNCT
ejpam-3860	133	25	·	·	PUNCT
ejpam-3860	133	26	·	·	PUNCT
ejpam-3860	133	27	,	,	PUNCT
ejpam-3860	133	28	m	m	PROPN
ejpam-3860	133	29	,	,	PUNCT
ejpam-3860	133	30	j	j	PROPN
ejpam-3860	133	31	=	=	SYM
ejpam-3860	133	32	1	1	NUM
ejpam-3860	133	33	,	,	PUNCT
ejpam-3860	133	34	·	·	PUNCT
ejpam-3860	133	35	·	·	PUNCT
ejpam-3860	133	36	·	·	PUNCT
ejpam-3860	133	37	,	,	PUNCT
ejpam-3860	133	38	n	n	CCONJ
ejpam-3860	133	39	where	where	SCONJ
ejpam-3860	133	40	0u	0u	ADJ
ejpam-3860	133	41	and	and	CCONJ
ejpam-3860	133	42	0v	0v	NOUN
ejpam-3860	133	43	are	be	AUX
ejpam-3860	133	44	the	the	DET
ejpam-3860	133	45	apex	apex	NOUN
ejpam-3860	133	46	vertices	vertex	NOUN
ejpam-3860	133	47	.	.	PUNCT
ejpam-3860	134	1	0u	0u	ADJ
ejpam-3860	134	2	1u	1u	NUM
ejpam-3860	134	3	2u	2u	NOUN
ejpam-3860	134	4	...	...	PUNCT
ejpam-3860	135	1	mu	mu	PROPN
ejpam-3860	135	2	0v	0v	PROPN
ejpam-3860	135	3	1v	1v	NUM
ejpam-3860	135	4	2v	2v	PROPN
ejpam-3860	135	5	...	...	PUNCT
ejpam-3860	136	1	nv	nv	PROPN
ejpam-3860	136	2	then	then	ADV
ejpam-3860	136	3	v	v	X
ejpam-3860	136	4	(	(	PUNCT
ejpam-3860	136	5	pk	pk	NOUN
ejpam-3860	136	6	�	�	PROPN
ejpam-3860	136	7	b(m	b(m	PROPN
ejpam-3860	136	8	,	,	PUNCT
ejpam-3860	136	9	n	n	CCONJ
ejpam-3860	136	10	)	)	PUNCT
ejpam-3860	136	11	)	)	PUNCT
ejpam-3860	137	1	=	=	PRON
ejpam-3860	137	2	{	{	PUNCT
ejpam-3860	137	3	(	(	PUNCT
ejpam-3860	137	4	r	r	NOUN
ejpam-3860	137	5	,	,	PUNCT
ejpam-3860	137	6	ia	ia	PROPN
ejpam-3860	137	7	)	)	PUNCT
ejpam-3860	137	8	,	,	PUNCT
ejpam-3860	137	9	(	(	PUNCT
ejpam-3860	137	10	r	r	NOUN
ejpam-3860	137	11	,	,	PUNCT
ejpam-3860	137	12	jv	jv	NOUN
ejpam-3860	137	13	)	)	PUNCT
ejpam-3860	137	14	,	,	PUNCT
ejpam-3860	137	15	(	(	PUNCT
ejpam-3860	137	16	r	r	NOUN
ejpam-3860	137	17	,	,	PUNCT
ejpam-3860	137	18	0u	0u	ADJ
ejpam-3860	137	19	)	)	PUNCT
ejpam-3860	137	20	,	,	PUNCT
ejpam-3860	137	21	(	(	PUNCT
ejpam-3860	137	22	r	r	NOUN
ejpam-3860	137	23	,	,	PUNCT
ejpam-3860	137	24	0v	0v	NOUN
ejpam-3860	137	25	)	)	PUNCT
ejpam-3860	137	26	:	:	PUNCT
ejpam-3860	138	1	r	r	NOUN
ejpam-3860	138	2	=	=	SYM
ejpam-3860	138	3	1	1	NUM
ejpam-3860	138	4	,	,	PUNCT
ejpam-3860	138	5	·	·	PUNCT
ejpam-3860	138	6	·	·	PUNCT
ejpam-3860	138	7	·	·	PUNCT
ejpam-3860	138	8	,	,	PUNCT
ejpam-3860	138	9	k	k	X
ejpam-3860	138	10	,	,	PUNCT
ejpam-3860	138	11	i	i	NOUN
ejpam-3860	138	12	=	=	NOUN
ejpam-3860	138	13	1	1	NUM
ejpam-3860	138	14	,	,	PUNCT
ejpam-3860	138	15	·	·	PUNCT
ejpam-3860	138	16	·	·	PUNCT
ejpam-3860	138	17	·	·	PUNCT
ejpam-3860	138	18	,	,	PUNCT
ejpam-3860	138	19	m	m	PROPN
ejpam-3860	138	20	,	,	PUNCT
ejpam-3860	138	21	j	j	PROPN
ejpam-3860	138	22	=	=	SYM
ejpam-3860	138	23	1	1	NUM
ejpam-3860	138	24	,	,	PUNCT
ejpam-3860	138	25	·	·	PUNCT
ejpam-3860	138	26	·	·	PUNCT
ejpam-3860	138	27	·	·	PUNCT
ejpam-3860	138	28	,	,	PUNCT
ejpam-3860	138	29	n	n	PROPN
ejpam-3860	138	30	and	and	CCONJ
ejpam-3860	138	31	e(pk	e(pk	NOUN
ejpam-3860	138	32	�	�	PROPN
ejpam-3860	138	33	b(m	b(m	PROPN
ejpam-3860	138	34	,	,	PUNCT
ejpam-3860	138	35	n	n	CCONJ
ejpam-3860	138	36	)	)	PUNCT
ejpam-3860	138	37	)	)	PUNCT
ejpam-3860	139	1	=	=	PRON
ejpam-3860	139	2	{	{	PUNCT
ejpam-3860	139	3	(	(	PUNCT
ejpam-3860	139	4	w	w	PROPN
ejpam-3860	139	5	,	,	PUNCT
ejpam-3860	139	6	xa)(y	xa)(y	PROPN
ejpam-3860	139	7	,	,	PUNCT
ejpam-3860	139	8	zb	zb	PROPN
ejpam-3860	139	9	)	)	PUNCT
ejpam-3860	139	10	:	:	PUNCT
ejpam-3860	139	11	w	w	X
ejpam-3860	139	12	=	=	SYM
ejpam-3860	139	13	y	y	PROPN
ejpam-3860	139	14	,	,	PUNCT
ejpam-3860	139	15	a	a	DET
ejpam-3860	139	16	=	=	SYM
ejpam-3860	139	17	b	b	NOUN
ejpam-3860	139	18	and	and	CCONJ
ejpam-3860	139	19	either	either	CCONJ
ejpam-3860	139	20	x	x	PUNCT
ejpam-3860	139	21	=	=	SYM
ejpam-3860	139	22	0	0	NUM
ejpam-3860	139	23	or	or	CCONJ
ejpam-3860	139	24	z	z	NOUN
ejpam-3860	139	25	=	=	SYM
ejpam-3860	139	26	0	0	NUM
ejpam-3860	139	27	,	,	PUNCT
ejpam-3860	139	28	w	w	PROPN
ejpam-3860	139	29	=	=	SYM
ejpam-3860	139	30	y	y	PROPN
ejpam-3860	139	31	+	+	NOUN
ejpam-3860	139	32	1	1	NUM
ejpam-3860	139	33	,	,	PUNCT
ejpam-3860	139	34	a	a	DET
ejpam-3860	139	35	=	=	SYM
ejpam-3860	139	36	b	b	PROPN
ejpam-3860	139	37	and	and	CCONJ
ejpam-3860	139	38	x	x	X
ejpam-3860	139	39	=	=	SYM
ejpam-3860	139	40	z	z	NOUN
ejpam-3860	139	41	,	,	PUNCT
ejpam-3860	139	42	and	and	CCONJ
ejpam-3860	139	43	w	w	PROPN
ejpam-3860	139	44	=	=	SYM
ejpam-3860	139	45	y	y	PROPN
ejpam-3860	139	46	,	,	PUNCT
ejpam-3860	139	47	a	a	DET
ejpam-3860	139	48	=	=	SYM
ejpam-3860	139	49	u	u	NOUN
ejpam-3860	139	50	,	,	PUNCT
ejpam-3860	139	51	b	b	PROPN
ejpam-3860	139	52	=	=	SYM
ejpam-3860	139	53	v	v	PROPN
ejpam-3860	139	54	and	and	CCONJ
ejpam-3860	139	55	x	x	PUNCT
ejpam-3860	139	56	=	=	SYM
ejpam-3860	139	57	0	0	PUNCT
ejpam-3860	139	58	=	=	SYM
ejpam-3860	139	59	z	z	NOUN
ejpam-3860	139	60	}	}	PUNCT
ejpam-3860	139	61	.	.	PUNCT
ejpam-3860	140	1	consider	consider	VERB
ejpam-3860	140	2	the	the	DET
ejpam-3860	140	3	following	follow	VERB
ejpam-3860	140	4	sets	set	NOUN
ejpam-3860	140	5	of	of	ADP
ejpam-3860	140	6	vertices	vertex	NOUN
ejpam-3860	140	7	.	.	PUNCT
ejpam-3860	141	1	ar	ar	PROPN
ejpam-3860	141	2	=	=	PRON
ejpam-3860	141	3	{	{	PUNCT
ejpam-3860	141	4	(	(	PUNCT
ejpam-3860	141	5	r	r	NOUN
ejpam-3860	141	6	,	,	PUNCT
ejpam-3860	141	7	iu	iu	ADP
ejpam-3860	141	8	)	)	PUNCT
ejpam-3860	141	9	:	:	PUNCT
ejpam-3860	142	1	r	r	NOUN
ejpam-3860	142	2	=	=	SYM
ejpam-3860	142	3	1	1	NUM
ejpam-3860	142	4	,	,	PUNCT
ejpam-3860	142	5	·	·	PUNCT
ejpam-3860	142	6	·	·	PUNCT
ejpam-3860	142	7	·	·	PUNCT
ejpam-3860	142	8	,	,	PUNCT
ejpam-3860	142	9	k	k	X
ejpam-3860	142	10	,	,	PUNCT
ejpam-3860	142	11	i	i	PRON
ejpam-3860	142	12	=	=	NOUN
ejpam-3860	142	13	1	1	NUM
ejpam-3860	142	14	·	·	PUNCT
ejpam-3860	142	15	·	·	PUNCT
ejpam-3860	142	16	·	·	PUNCT
ejpam-3860	142	17	,	,	PUNCT
ejpam-3860	142	18	m	m	VERB
ejpam-3860	142	19	}	}	PUNCT
ejpam-3860	142	20	∪	∪	ADJ
ejpam-3860	142	21	{	{	PUNCT
ejpam-3860	142	22	{	{	PUNCT
ejpam-3860	142	23	(	(	PUNCT
ejpam-3860	142	24	r	r	NOUN
ejpam-3860	142	25	,	,	PUNCT
ejpam-3860	142	26	0v	0v	NOUN
ejpam-3860	142	27	)	)	PUNCT
ejpam-3860	142	28	}	}	PUNCT
ejpam-3860	142	29	bs	bs	NOUN
ejpam-3860	142	30	=	=	PRON
ejpam-3860	142	31	{	{	PUNCT
ejpam-3860	142	32	(	(	PUNCT
ejpam-3860	142	33	s	s	PROPN
ejpam-3860	142	34	,	,	PUNCT
ejpam-3860	142	35	jv	jv	PROPN
ejpam-3860	142	36	)	)	PUNCT
ejpam-3860	142	37	:	:	PUNCT
ejpam-3860	142	38	s	s	X
ejpam-3860	142	39	=	=	SYM
ejpam-3860	142	40	1	1	NUM
ejpam-3860	142	41	,	,	PUNCT
ejpam-3860	142	42	·	·	PUNCT
ejpam-3860	142	43	·	·	PUNCT
ejpam-3860	142	44	·	·	PUNCT
ejpam-3860	142	45	,	,	PUNCT
ejpam-3860	142	46	k	k	X
ejpam-3860	142	47	,	,	PUNCT
ejpam-3860	142	48	j	j	PROPN
ejpam-3860	142	49	=	=	SYM
ejpam-3860	142	50	1	1	NUM
ejpam-3860	142	51	·	·	PUNCT
ejpam-3860	142	52	·	·	PUNCT
ejpam-3860	142	53	·	·	PUNCT
ejpam-3860	142	54	,	,	PUNCT
ejpam-3860	142	55	n	n	CCONJ
ejpam-3860	142	56	}	}	PUNCT
ejpam-3860	142	57	∪	∪	VERB
ejpam-3860	142	58	{	{	PUNCT
ejpam-3860	142	59	{	{	PUNCT
ejpam-3860	142	60	(	(	PUNCT
ejpam-3860	142	61	s	s	X
ejpam-3860	142	62	,	,	PUNCT
ejpam-3860	142	63	0u	0u	ADJ
ejpam-3860	142	64	)	)	PUNCT
ejpam-3860	142	65	}	}	PUNCT
ejpam-3860	142	66	.	.	PUNCT
ejpam-3860	143	1	let	let	VERB
ejpam-3860	143	2	s	s	PRON
ejpam-3860	143	3	=	=	VERB
ejpam-3860	143	4	ar	ar	VERB
ejpam-3860	143	5	∪bs	∪bs	ADV
ejpam-3860	143	6	such	such	ADJ
ejpam-3860	143	7	that	that	SCONJ
ejpam-3860	143	8	r	r	NOUN
ejpam-3860	143	9	is	be	AUX
ejpam-3860	143	10	odd	odd	ADJ
ejpam-3860	143	11	and	and	CCONJ
ejpam-3860	143	12	s	s	VERB
ejpam-3860	143	13	is	be	AUX
ejpam-3860	143	14	even	even	ADV
ejpam-3860	143	15	and	and	CCONJ
ejpam-3860	143	16	t	t	NOUN
ejpam-3860	143	17	=	=	PUNCT
ejpam-3860	143	18	ar	ar	VERB
ejpam-3860	143	19	∪bs	∪bs	ADV
ejpam-3860	143	20	such	such	ADJ
ejpam-3860	143	21	that	that	SCONJ
ejpam-3860	143	22	r	r	NOUN
ejpam-3860	143	23	is	be	AUX
ejpam-3860	143	24	even	even	ADV
ejpam-3860	143	25	and	and	CCONJ
ejpam-3860	143	26	s	s	VERB
ejpam-3860	143	27	is	be	AUX
ejpam-3860	143	28	odd	odd	ADJ
ejpam-3860	143	29	.	.	PUNCT
ejpam-3860	144	1	then	then	ADV
ejpam-3860	144	2	s	s	VERB
ejpam-3860	144	3	=	=	PUNCT
ejpam-3860	144	4			X
ejpam-3860	144	5	(	(	PUNCT
ejpam-3860	144	6	r	r	NOUN
ejpam-3860	144	7	,	,	PUNCT
ejpam-3860	144	8	iu	iu	ADP
ejpam-3860	144	9	)	)	PUNCT
ejpam-3860	144	10	:	:	PUNCT
ejpam-3860	144	11	r	r	NOUN
ejpam-3860	144	12	is	be	AUX
ejpam-3860	144	13	odd	odd	ADJ
ejpam-3860	144	14	,	,	PUNCT
ejpam-3860	144	15	i	i	PRON
ejpam-3860	144	16	=	=	NOUN
ejpam-3860	144	17	1	1	NUM
ejpam-3860	144	18	,	,	PUNCT
ejpam-3860	144	19	·	·	PUNCT
ejpam-3860	144	20	·	·	PUNCT
ejpam-3860	144	21	·	·	PUNCT
ejpam-3860	144	22	,	,	PUNCT
ejpam-3860	144	23	m	m	PROPN
ejpam-3860	144	24	(	(	PUNCT
ejpam-3860	144	25	s	s	PROPN
ejpam-3860	144	26	,	,	PUNCT
ejpam-3860	144	27	jv	jv	PROPN
ejpam-3860	144	28	)	)	PUNCT
ejpam-3860	144	29	:	:	PUNCT
ejpam-3860	145	1	s	s	VERB
ejpam-3860	145	2	is	be	AUX
ejpam-3860	145	3	even	even	ADV
ejpam-3860	145	4	,	,	PUNCT
ejpam-3860	145	5	j	j	PROPN
ejpam-3860	145	6	=	=	SYM
ejpam-3860	145	7	1	1	NUM
ejpam-3860	145	8	,	,	PUNCT
ejpam-3860	145	9	·	·	PUNCT
ejpam-3860	145	10	·	·	PUNCT
ejpam-3860	145	11	·	·	PUNCT
ejpam-3860	145	12	,	,	PUNCT
ejpam-3860	145	13	n	n	X
ejpam-3860	145	14	(	(	PUNCT
ejpam-3860	145	15	r	r	NOUN
ejpam-3860	145	16	,	,	PUNCT
ejpam-3860	145	17	0v	0v	NOUN
ejpam-3860	145	18	)	)	PUNCT
ejpam-3860	145	19	:	:	PUNCT
ejpam-3860	146	1	r	r	NOUN
ejpam-3860	146	2	is	be	AUX
ejpam-3860	146	3	odd	odd	ADJ
ejpam-3860	146	4	(	(	PUNCT
ejpam-3860	146	5	s	s	X
ejpam-3860	146	6	,	,	PUNCT
ejpam-3860	146	7	0u	0u	ADJ
ejpam-3860	146	8	)	)	PUNCT
ejpam-3860	146	9	:	:	PUNCT
ejpam-3860	146	10	s	s	VERB
ejpam-3860	146	11	is	be	AUX
ejpam-3860	146	12	even	even	ADV
ejpam-3860	146	13	and	and	CCONJ
ejpam-3860	146	14	t	t	NOUN
ejpam-3860	146	15	=	=	PUNCT
ejpam-3860	146	16			X
ejpam-3860	146	17	(	(	PUNCT
ejpam-3860	146	18	r	r	NOUN
ejpam-3860	146	19	,	,	PUNCT
ejpam-3860	146	20	iu	iu	ADP
ejpam-3860	146	21	)	)	PUNCT
ejpam-3860	146	22	:	:	PUNCT
ejpam-3860	146	23	r	r	NOUN
ejpam-3860	146	24	is	be	AUX
ejpam-3860	146	25	even	even	ADV
ejpam-3860	146	26	,	,	PUNCT
ejpam-3860	146	27	i	i	PRON
ejpam-3860	146	28	=	=	NOUN
ejpam-3860	146	29	1	1	NUM
ejpam-3860	146	30	,	,	PUNCT
ejpam-3860	146	31	·	·	PUNCT
ejpam-3860	146	32	·	·	PUNCT
ejpam-3860	146	33	·	·	PUNCT
ejpam-3860	146	34	,	,	PUNCT
ejpam-3860	146	35	m	m	PROPN
ejpam-3860	146	36	(	(	PUNCT
ejpam-3860	146	37	s	s	PROPN
ejpam-3860	146	38	,	,	PUNCT
ejpam-3860	146	39	jv	jv	PROPN
ejpam-3860	146	40	)	)	PUNCT
ejpam-3860	146	41	:	:	PUNCT
ejpam-3860	147	1	s	s	VERB
ejpam-3860	147	2	is	be	AUX
ejpam-3860	147	3	odd	odd	ADJ
ejpam-3860	147	4	,	,	PUNCT
ejpam-3860	147	5	j	j	PROPN
ejpam-3860	147	6	=	=	SYM
ejpam-3860	147	7	1	1	NUM
ejpam-3860	147	8	,	,	PUNCT
ejpam-3860	147	9	·	·	PUNCT
ejpam-3860	147	10	·	·	PUNCT
ejpam-3860	147	11	·	·	PUNCT
ejpam-3860	147	12	,	,	PUNCT
ejpam-3860	147	13	n	n	X
ejpam-3860	147	14	(	(	PUNCT
ejpam-3860	147	15	r	r	NOUN
ejpam-3860	147	16	,	,	PUNCT
ejpam-3860	147	17	0v	0v	NOUN
ejpam-3860	147	18	)	)	PUNCT
ejpam-3860	147	19	:	:	PUNCT
ejpam-3860	148	1	r	r	NOUN
ejpam-3860	148	2	is	be	AUX
ejpam-3860	148	3	even	even	ADV
ejpam-3860	148	4	(	(	PUNCT
ejpam-3860	148	5	s	s	X
ejpam-3860	148	6	,	,	PUNCT
ejpam-3860	148	7	0u	0u	ADJ
ejpam-3860	148	8	)	)	PUNCT
ejpam-3860	148	9	:	:	PUNCT
ejpam-3860	148	10	s	s	VERB
ejpam-3860	148	11	is	be	AUX
ejpam-3860	148	12	odd	odd	ADJ
ejpam-3860	148	13	we	we	PRON
ejpam-3860	148	14	claim	claim	VERB
ejpam-3860	148	15	that	that	SCONJ
ejpam-3860	148	16	s	s	VERB
ejpam-3860	148	17	and	and	CCONJ
ejpam-3860	148	18	t	t	PROPN
ejpam-3860	148	19	are	be	AUX
ejpam-3860	148	20	the	the	DET
ejpam-3860	148	21	independent	independent	ADJ
ejpam-3860	148	22	neighborhood	neighborhood	NOUN
ejpam-3860	148	23	sets	set	NOUN
ejpam-3860	148	24	of	of	ADP
ejpam-3860	148	25	pk	pk	NOUN
ejpam-3860	148	26	�	�	PROPN
ejpam-3860	148	27	b(m	b(m	PROPN
ejpam-3860	148	28	,	,	PUNCT
ejpam-3860	148	29	n	n	CCONJ
ejpam-3860	148	30	)	)	PUNCT
ejpam-3860	148	31	.	.	PUNCT
ejpam-3860	149	1	first	first	ADV
ejpam-3860	149	2	,	,	PUNCT
ejpam-3860	149	3	we	we	PRON
ejpam-3860	149	4	show	show	VERB
ejpam-3860	149	5	that	that	SCONJ
ejpam-3860	149	6	no	no	DET
ejpam-3860	149	7	two	two	NUM
ejpam-3860	149	8	vertices	vertex	NOUN
ejpam-3860	149	9	in	in	ADP
ejpam-3860	149	10	s	s	NOUN
ejpam-3860	149	11	are	be	AUX
ejpam-3860	149	12	adjacent	adjacent	ADJ
ejpam-3860	149	13	.	.	PUNCT
ejpam-3860	150	1	observe	observe	VERB
ejpam-3860	150	2	that	that	SCONJ
ejpam-3860	150	3	for	for	ADP
ejpam-3860	150	4	any	any	DET
ejpam-3860	150	5	(	(	PUNCT
ejpam-3860	150	6	r	r	NOUN
ejpam-3860	150	7	,	,	PUNCT
ejpam-3860	150	8	iu	iu	ADJ
ejpam-3860	150	9	)	)	PUNCT
ejpam-3860	150	10	,	,	PUNCT
ejpam-3860	150	11	(	(	PUNCT
ejpam-3860	150	12	s	s	X
ejpam-3860	150	13	,	,	PUNCT
ejpam-3860	150	14	0u	0u	ADJ
ejpam-3860	150	15	)	)	PUNCT
ejpam-3860	150	16	∈	∈	PROPN
ejpam-3860	150	17	s	s	PART
ejpam-3860	150	18	,	,	PUNCT
ejpam-3860	150	19	(	(	PUNCT
ejpam-3860	150	20	r	r	NOUN
ejpam-3860	150	21	,	,	PUNCT
ejpam-3860	150	22	iu)(s	iu)(s	PROPN
ejpam-3860	150	23	,	,	PUNCT
ejpam-3860	150	24	0u	0u	ADJ
ejpam-3860	150	25	)	)	PUNCT
ejpam-3860	150	26	/∈	/∈	PUNCT
ejpam-3860	151	1	e	e	X
ejpam-3860	151	2	(	(	PUNCT
ejpam-3860	151	3	pk	pk	NOUN
ejpam-3860	151	4	�	�	PROPN
ejpam-3860	151	5	b(m	b(m	PROPN
ejpam-3860	151	6	,	,	PUNCT
ejpam-3860	151	7	n	n	CCONJ
ejpam-3860	151	8	)	)	PUNCT
ejpam-3860	151	9	)	)	PUNCT
ejpam-3860	151	10	since	since	SCONJ
ejpam-3860	151	11	r	r	NOUN
ejpam-3860	151	12	is	be	AUX
ejpam-3860	151	13	odd	odd	ADJ
ejpam-3860	151	14	in	in	ADP
ejpam-3860	151	15	(	(	PUNCT
ejpam-3860	151	16	r	r	NOUN
ejpam-3860	151	17	,	,	PUNCT
ejpam-3860	151	18	jiu	jiu	NOUN
ejpam-3860	151	19	)	)	PUNCT
ejpam-3860	151	20	and	and	CCONJ
ejpam-3860	151	21	s	s	VERB
ejpam-3860	151	22	is	be	AUX
ejpam-3860	151	23	even	even	ADV
ejpam-3860	151	24	in	in	ADP
ejpam-3860	151	25	(	(	PUNCT
ejpam-3860	151	26	s	s	X
ejpam-3860	151	27	,	,	PUNCT
ejpam-3860	151	28	0u	0u	ADJ
ejpam-3860	151	29	)	)	PUNCT
ejpam-3860	151	30	.	.	PUNCT
ejpam-3860	152	1	similarly	similarly	ADV
ejpam-3860	152	2	,	,	PUNCT
ejpam-3860	152	3	n.	n.	PROPN
ejpam-3860	152	4	abdulcarim	abdulcarim	PROPN
ejpam-3860	152	5	,	,	PUNCT
ejpam-3860	152	6	s.	s.	PROPN
ejpam-3860	152	7	dagondon	dagondon	PROPN
ejpam-3860	152	8	,	,	PUNCT
ejpam-3860	152	9	e.	e.	PROPN
ejpam-3860	152	10	chacon	chacon	PROPN
ejpam-3860	152	11	/	/	SYM
ejpam-3860	152	12	eur	eur	PROPN
ejpam-3860	152	13	.	.	PUNCT
ejpam-3860	153	1	j.	j.	PROPN
ejpam-3860	153	2	pure	pure	PROPN
ejpam-3860	153	3	appl	appl	PROPN
ejpam-3860	153	4	.	.	PROPN
ejpam-3860	153	5	math	math	PROPN
ejpam-3860	153	6	,	,	PUNCT
ejpam-3860	153	7	14	14	NUM
ejpam-3860	153	8	(	(	PUNCT
ejpam-3860	153	9	1	1	NUM
ejpam-3860	153	10	)	)	PUNCT
ejpam-3860	153	11	(	(	PUNCT
ejpam-3860	153	12	2021	2021	NUM
ejpam-3860	153	13	)	)	PUNCT
ejpam-3860	153	14	,	,	PUNCT
ejpam-3860	153	15	173	173	NUM
ejpam-3860	153	16	-	-	SYM
ejpam-3860	153	17	191	191	NUM
ejpam-3860	153	18	180	180	NUM
ejpam-3860	153	19	(	(	PUNCT
ejpam-3860	153	20	1	1	NUM
ejpam-3860	153	21	,	,	PUNCT
ejpam-3860	153	22	1u	1u	NUM
ejpam-3860	153	23	)	)	PUNCT
ejpam-3860	153	24	(	(	PUNCT
ejpam-3860	153	25	1	1	NUM
ejpam-3860	153	26	,	,	PUNCT
ejpam-3860	153	27	2u	2u	NOUN
ejpam-3860	153	28	)	)	PUNCT
ejpam-3860	153	29	...	...	PUNCT
ejpam-3860	153	30	(	(	PUNCT
ejpam-3860	153	31	1,mu	1,mu	NOUN
ejpam-3860	153	32	)	)	PUNCT
ejpam-3860	153	33	(	(	PUNCT
ejpam-3860	153	34	1	1	NUM
ejpam-3860	153	35	,	,	PUNCT
ejpam-3860	153	36	0u	0u	ADJ
ejpam-3860	153	37	)	)	PUNCT
ejpam-3860	153	38	(	(	PUNCT
ejpam-3860	153	39	1	1	NUM
ejpam-3860	153	40	,	,	PUNCT
ejpam-3860	153	41	1v	1v	NUM
ejpam-3860	153	42	)	)	PUNCT
ejpam-3860	153	43	(	(	PUNCT
ejpam-3860	153	44	1	1	NUM
ejpam-3860	153	45	,	,	PUNCT
ejpam-3860	153	46	2v	2v	NUM
ejpam-3860	153	47	)	)	PUNCT
ejpam-3860	153	48	...	...	PUNCT
ejpam-3860	154	1	(	(	PUNCT
ejpam-3860	154	2	1	1	NUM
ejpam-3860	154	3	,	,	PUNCT
ejpam-3860	154	4	nv	nv	PROPN
ejpam-3860	154	5	)	)	PUNCT
ejpam-3860	154	6	(	(	PUNCT
ejpam-3860	154	7	1	1	NUM
ejpam-3860	154	8	,	,	PUNCT
ejpam-3860	154	9	0v	0v	NOUN
ejpam-3860	154	10	)	)	PUNCT
ejpam-3860	154	11	(	(	PUNCT
ejpam-3860	154	12	2	2	NUM
ejpam-3860	154	13	,	,	PUNCT
ejpam-3860	154	14	1u	1u	NUM
ejpam-3860	154	15	)	)	PUNCT
ejpam-3860	154	16	(	(	PUNCT
ejpam-3860	154	17	2	2	NUM
ejpam-3860	154	18	,	,	PUNCT
ejpam-3860	154	19	2u	2u	NOUN
ejpam-3860	154	20	)	)	PUNCT
ejpam-3860	154	21	...	...	PUNCT
ejpam-3860	155	1	(	(	PUNCT
ejpam-3860	155	2	2,mu	2,mu	NUM
ejpam-3860	155	3	)	)	PUNCT
ejpam-3860	155	4	(	(	PUNCT
ejpam-3860	155	5	2	2	NUM
ejpam-3860	155	6	,	,	PUNCT
ejpam-3860	155	7	0u	0u	ADJ
ejpam-3860	155	8	)	)	PUNCT
ejpam-3860	155	9	(	(	PUNCT
ejpam-3860	155	10	2	2	NUM
ejpam-3860	155	11	,	,	PUNCT
ejpam-3860	155	12	1v	1v	NUM
ejpam-3860	155	13	)	)	PUNCT
ejpam-3860	155	14	(	(	PUNCT
ejpam-3860	155	15	2	2	NUM
ejpam-3860	155	16	,	,	PUNCT
ejpam-3860	155	17	2v	2v	NUM
ejpam-3860	155	18	)	)	PUNCT
ejpam-3860	155	19	...	...	PUNCT
ejpam-3860	156	1	(	(	PUNCT
ejpam-3860	156	2	2	2	NUM
ejpam-3860	156	3	,	,	PUNCT
ejpam-3860	156	4	nv	nv	PROPN
ejpam-3860	156	5	)	)	PUNCT
ejpam-3860	156	6	(	(	PUNCT
ejpam-3860	156	7	2	2	NUM
ejpam-3860	156	8	,	,	PUNCT
ejpam-3860	156	9	0v	0v	NOUN
ejpam-3860	156	10	)	)	PUNCT
ejpam-3860	156	11	(	(	PUNCT
ejpam-3860	156	12	k	k	X
ejpam-3860	156	13	,	,	PUNCT
ejpam-3860	156	14	1u	1u	NUM
ejpam-3860	156	15	)	)	PUNCT
ejpam-3860	156	16	(	(	PUNCT
ejpam-3860	156	17	k	k	NOUN
ejpam-3860	156	18	,	,	PUNCT
ejpam-3860	156	19	2u	2u	NOUN
ejpam-3860	156	20	)	)	PUNCT
ejpam-3860	156	21	...	...	PUNCT
ejpam-3860	157	1	(	(	PUNCT
ejpam-3860	157	2	k	k	X
ejpam-3860	157	3	,	,	PUNCT
ejpam-3860	157	4	mu	mu	NOUN
ejpam-3860	157	5	)	)	PUNCT
ejpam-3860	157	6	(	(	PUNCT
ejpam-3860	157	7	k	k	NOUN
ejpam-3860	157	8	,	,	PUNCT
ejpam-3860	157	9	0u	0u	ADJ
ejpam-3860	157	10	)	)	PUNCT
ejpam-3860	157	11	(	(	PUNCT
ejpam-3860	157	12	k	k	NOUN
ejpam-3860	157	13	,	,	PUNCT
ejpam-3860	157	14	1v	1v	NUM
ejpam-3860	157	15	)	)	PUNCT
ejpam-3860	157	16	(	(	PUNCT
ejpam-3860	157	17	k	k	X
ejpam-3860	157	18	,	,	PUNCT
ejpam-3860	157	19	2v	2v	NUM
ejpam-3860	157	20	)	)	PUNCT
ejpam-3860	157	21	...	...	PUNCT
ejpam-3860	158	1	(	(	PUNCT
ejpam-3860	158	2	k	k	X
ejpam-3860	158	3	,	,	PUNCT
ejpam-3860	158	4	nv	nv	PROPN
ejpam-3860	158	5	)	)	PUNCT
ejpam-3860	158	6	(	(	PUNCT
ejpam-3860	158	7	k	k	NOUN
ejpam-3860	158	8	,	,	PUNCT
ejpam-3860	158	9	0v	0v	NOUN
ejpam-3860	158	10	)	)	PUNCT
ejpam-3860	158	11	(	(	PUNCT
ejpam-3860	158	12	s	s	X
ejpam-3860	158	13	,	,	PUNCT
ejpam-3860	158	14	jv)(r	jv)(r	PROPN
ejpam-3860	158	15	,	,	PUNCT
ejpam-3860	158	16	0v	0v	NOUN
ejpam-3860	158	17	)	)	PUNCT
ejpam-3860	158	18	/∈	/∈	PUNCT
ejpam-3860	159	1	e	e	NOUN
ejpam-3860	159	2	(	(	PUNCT
ejpam-3860	159	3	pk	pk	NOUN
ejpam-3860	159	4	�	�	PROPN
ejpam-3860	159	5	b(m	b(m	PROPN
ejpam-3860	159	6	,	,	PUNCT
ejpam-3860	159	7	n	n	CCONJ
ejpam-3860	159	8	)	)	PUNCT
ejpam-3860	159	9	)	)	PUNCT
ejpam-3860	159	10	for	for	ADP
ejpam-3860	159	11	any	any	DET
ejpam-3860	159	12	(	(	PUNCT
ejpam-3860	159	13	s	s	PROPN
ejpam-3860	159	14	,	,	PUNCT
ejpam-3860	159	15	jv	jv	NOUN
ejpam-3860	159	16	)	)	PUNCT
ejpam-3860	159	17	,	,	PUNCT
ejpam-3860	159	18	(	(	PUNCT
ejpam-3860	159	19	r	r	NOUN
ejpam-3860	159	20	,	,	PUNCT
ejpam-3860	159	21	0v	0v	NOUN
ejpam-3860	159	22	)	)	PUNCT
ejpam-3860	159	23	∈	∈	PROPN
ejpam-3860	159	24	s.	s.	PROPN
ejpam-3860	159	25	hence	hence	ADV
ejpam-3860	159	26	,	,	PUNCT
ejpam-3860	159	27	none	none	NOUN
ejpam-3860	159	28	of	of	ADP
ejpam-3860	159	29	the	the	DET
ejpam-3860	159	30	vertices	vertex	NOUN
ejpam-3860	159	31	of	of	ADP
ejpam-3860	159	32	s	s	NOUN
ejpam-3860	159	33	are	be	AUX
ejpam-3860	159	34	adjacent	adjacent	ADJ
ejpam-3860	159	35	.	.	PUNCT
ejpam-3860	160	1	next	next	ADV
ejpam-3860	160	2	,	,	PUNCT
ejpam-3860	160	3	we	we	PRON
ejpam-3860	160	4	show	show	VERB
ejpam-3860	160	5	that	that	SCONJ
ejpam-3860	160	6	⋃	⋃	ADP
ejpam-3860	160	7	v∈s	v∈s	ADJ
ejpam-3860	160	8	〈	〈	PROPN
ejpam-3860	160	9	n	n	PRON
ejpam-3860	160	10	[	[	X
ejpam-3860	160	11	v	v	NOUN
ejpam-3860	160	12	]	]	X
ejpam-3860	160	13	〉	〉	NOUN
ejpam-3860	160	14	=	=	SYM
ejpam-3860	160	15	pk	pk	PROPN
ejpam-3860	160	16	�	�	PROPN
ejpam-3860	160	17	b(m	b(m	PROPN
ejpam-3860	160	18	,	,	PUNCT
ejpam-3860	160	19	n	n	CCONJ
ejpam-3860	160	20	)	)	PUNCT
ejpam-3860	160	21	.	.	PUNCT
ejpam-3860	161	1	assume	assume	VERB
ejpam-3860	161	2	to	to	ADP
ejpam-3860	161	3	the	the	DET
ejpam-3860	161	4	contrary	contrary	NOUN
ejpam-3860	161	5	that	that	SCONJ
ejpam-3860	161	6	⋃	⋃	PUNCT
ejpam-3860	161	7	v∈s	v∈s	ADJ
ejpam-3860	161	8	〈	〈	PROPN
ejpam-3860	161	9	n	n	PRON
ejpam-3860	161	10	[	[	X
ejpam-3860	161	11	v	v	NOUN
ejpam-3860	161	12	]	]	X
ejpam-3860	161	13	〉	〉	PROPN
ejpam-3860	161	14	6=	6=	SYM
ejpam-3860	161	15	pk	pk	PROPN
ejpam-3860	161	16	�	�	PROPN
ejpam-3860	161	17	b(m	b(m	PROPN
ejpam-3860	161	18	,	,	PUNCT
ejpam-3860	161	19	n	n	CCONJ
ejpam-3860	161	20	)	)	PUNCT
ejpam-3860	161	21	.	.	PUNCT
ejpam-3860	162	1	this	this	PRON
ejpam-3860	162	2	implies	imply	VERB
ejpam-3860	162	3	there	there	PRON
ejpam-3860	162	4	exists	exist	VERB
ejpam-3860	162	5	(	(	PUNCT
ejpam-3860	162	6	w	w	PROPN
ejpam-3860	162	7	,	,	PUNCT
ejpam-3860	162	8	xa)(y	xa)(y	PROPN
ejpam-3860	162	9	,	,	PUNCT
ejpam-3860	162	10	zb	zb	X
ejpam-3860	162	11	)	)	PUNCT
ejpam-3860	162	12	∈	∈	PROPN
ejpam-3860	162	13	e(pk	e(pk	PROPN
ejpam-3860	162	14	�	�	NOUN
ejpam-3860	162	15	b(m	b(m	PROPN
ejpam-3860	162	16	,	,	PUNCT
ejpam-3860	162	17	n	n	CCONJ
ejpam-3860	162	18	)	)	PUNCT
ejpam-3860	162	19	)	)	PUNCT
ejpam-3860	162	20	such	such	ADJ
ejpam-3860	162	21	that	that	SCONJ
ejpam-3860	162	22	(	(	PUNCT
ejpam-3860	162	23	w	w	PROPN
ejpam-3860	162	24	,	,	PUNCT
ejpam-3860	162	25	xa)(y	xa)(y	PROPN
ejpam-3860	162	26	,	,	PUNCT
ejpam-3860	162	27	zb	zb	NOUN
ejpam-3860	162	28	)	)	PUNCT
ejpam-3860	162	29	/∈	/∈	PUNCT
ejpam-3860	163	1	e	e	NOUN
ejpam-3860	163	2	(	(	PUNCT
ejpam-3860	163	3	⋃	⋃	ADP
ejpam-3860	163	4	v∈s	v∈s	ADJ
ejpam-3860	163	5	〈	〈	PROPN
ejpam-3860	163	6	n	n	PRON
ejpam-3860	163	7	[	[	X
ejpam-3860	163	8	v	v	NOUN
ejpam-3860	163	9	]	]	X
ejpam-3860	163	10	〉	〉	NUM
ejpam-3860	163	11	)	)	PUNCT
ejpam-3860	163	12	.	.	PUNCT
ejpam-3860	164	1	consider	consider	VERB
ejpam-3860	164	2	the	the	DET
ejpam-3860	164	3	following	follow	VERB
ejpam-3860	164	4	cases	case	NOUN
ejpam-3860	164	5	:	:	PUNCT
ejpam-3860	164	6	case	case	NOUN
ejpam-3860	164	7	i.	i.	NOUN
ejpam-3860	164	8	w	w	PROPN
ejpam-3860	164	9	=	=	PROPN
ejpam-3860	164	10	y	y	PROPN
ejpam-3860	164	11	,	,	PUNCT
ejpam-3860	164	12	a	a	DET
ejpam-3860	164	13	=	=	SYM
ejpam-3860	164	14	b	b	NOUN
ejpam-3860	164	15	and	and	CCONJ
ejpam-3860	164	16	either	either	CCONJ
ejpam-3860	164	17	x	x	PUNCT
ejpam-3860	164	18	=	=	SYM
ejpam-3860	164	19	0	0	NUM
ejpam-3860	164	20	or	or	CCONJ
ejpam-3860	164	21	y	y	PROPN
ejpam-3860	164	22	=	=	SYM
ejpam-3860	164	23	0	0	NUM
ejpam-3860	164	24	wlog	wlog	NOUN
ejpam-3860	164	25	,	,	PUNCT
ejpam-3860	164	26	let	let	VERB
ejpam-3860	164	27	z	z	NOUN
ejpam-3860	164	28	=	=	SYM
ejpam-3860	164	29	0	0	PROPN
ejpam-3860	164	30	.	.	PUNCT
ejpam-3860	165	1	i.	i.	PROPN
ejpam-3860	166	1	if	if	SCONJ
ejpam-3860	166	2	(	(	PUNCT
ejpam-3860	166	3	r1	r1	NOUN
ejpam-3860	166	4	,	,	PUNCT
ejpam-3860	166	5	iu)(r2	iu)(r2	NOUN
ejpam-3860	166	6	,	,	PUNCT
ejpam-3860	166	7	0u	0u	ADJ
ejpam-3860	166	8	)	)	PUNCT
ejpam-3860	166	9	/∈	/∈	PUNCT
ejpam-3860	167	1	e	e	NOUN
ejpam-3860	167	2	(	(	PUNCT
ejpam-3860	167	3	⋃	⋃	ADP
ejpam-3860	167	4	v∈s	v∈s	ADJ
ejpam-3860	167	5	〈	〈	PROPN
ejpam-3860	167	6	n	n	PRON
ejpam-3860	167	7	[	[	X
ejpam-3860	167	8	v	v	NOUN
ejpam-3860	167	9	]	]	X
ejpam-3860	167	10	〉	〉	NOUN
ejpam-3860	167	11	)	)	PUNCT
ejpam-3860	167	12	,	,	PUNCT
ejpam-3860	167	13	then	then	ADV
ejpam-3860	167	14	both	both	DET
ejpam-3860	167	15	(	(	PUNCT
ejpam-3860	167	16	r1	r1	PROPN
ejpam-3860	167	17	,	,	PUNCT
ejpam-3860	167	18	iu	iu	ADP
ejpam-3860	167	19	)	)	PUNCT
ejpam-3860	167	20	,	,	PUNCT
ejpam-3860	167	21	(	(	PUNCT
ejpam-3860	167	22	r2	r2	NOUN
ejpam-3860	167	23	,	,	PUNCT
ejpam-3860	167	24	0u	0u	ADJ
ejpam-3860	167	25	)	)	PUNCT
ejpam-3860	167	26	/∈	/∈	PUNCT
ejpam-3860	168	1	s.	s.	PROPN
ejpam-3860	169	1	it	it	PRON
ejpam-3860	169	2	follows	follow	VERB
ejpam-3860	169	3	that	that	SCONJ
ejpam-3860	169	4	r2	r2	PROPN
ejpam-3860	169	5	is	be	AUX
ejpam-3860	169	6	odd	odd	ADJ
ejpam-3860	169	7	and	and	CCONJ
ejpam-3860	169	8	so	so	ADV
ejpam-3860	169	9	is	be	AUX
ejpam-3860	169	10	r1	r1	VERB
ejpam-3860	169	11	.	.	PUNCT
ejpam-3860	170	1	but	but	CCONJ
ejpam-3860	170	2	(	(	PUNCT
ejpam-3860	170	3	r1	r1	PROPN
ejpam-3860	170	4	,	,	PUNCT
ejpam-3860	170	5	iu	iu	ADJ
ejpam-3860	170	6	)	)	PUNCT
ejpam-3860	170	7	∈	∈	PROPN
ejpam-3860	170	8	s	s	NOUN
ejpam-3860	170	9	for	for	ADP
ejpam-3860	170	10	r1	r1	NOUN
ejpam-3860	170	11	odd	odd	ADJ
ejpam-3860	170	12	.	.	PUNCT
ejpam-3860	171	1	this	this	PRON
ejpam-3860	171	2	is	be	AUX
ejpam-3860	171	3	a	a	DET
ejpam-3860	171	4	contradiction	contradiction	NOUN
ejpam-3860	171	5	.	.	PUNCT
ejpam-3860	172	1	ii	ii	PROPN
ejpam-3860	172	2	.	.	PUNCT
ejpam-3860	173	1	if	if	SCONJ
ejpam-3860	173	2	(	(	PUNCT
ejpam-3860	173	3	s1	s1	NOUN
ejpam-3860	173	4	,	,	PUNCT
ejpam-3860	173	5	jv)(s2	jv)(s2	PROPN
ejpam-3860	173	6	,	,	PUNCT
ejpam-3860	173	7	0v	0v	NOUN
ejpam-3860	173	8	)	)	PUNCT
ejpam-3860	173	9	/∈	/∈	PUNCT
ejpam-3860	174	1	e	e	NOUN
ejpam-3860	174	2	(	(	PUNCT
ejpam-3860	174	3	⋃	⋃	ADP
ejpam-3860	174	4	v∈s	v∈s	ADJ
ejpam-3860	174	5	〈	〈	PROPN
ejpam-3860	174	6	n	n	PRON
ejpam-3860	174	7	[	[	X
ejpam-3860	174	8	v	v	NOUN
ejpam-3860	174	9	]	]	X
ejpam-3860	174	10	〉	〉	NOUN
ejpam-3860	174	11	)	)	PUNCT
ejpam-3860	174	12	,	,	PUNCT
ejpam-3860	174	13	then	then	ADV
ejpam-3860	174	14	both	both	PRON
ejpam-3860	174	15	(	(	PUNCT
ejpam-3860	174	16	s1	s1	NOUN
ejpam-3860	174	17	,	,	PUNCT
ejpam-3860	174	18	jv	jv	NOUN
ejpam-3860	174	19	)	)	PUNCT
ejpam-3860	174	20	,	,	PUNCT
ejpam-3860	174	21	(	(	PUNCT
ejpam-3860	174	22	s2	s2	PROPN
ejpam-3860	174	23	,	,	PUNCT
ejpam-3860	174	24	0v	0v	NOUN
ejpam-3860	174	25	)	)	PUNCT
ejpam-3860	174	26	/∈	/∈	PUNCT
ejpam-3860	174	27	s.	s.	PROPN
ejpam-3860	175	1	it	it	PRON
ejpam-3860	175	2	follows	follow	VERB
ejpam-3860	175	3	that	that	SCONJ
ejpam-3860	175	4	s2	s2	NOUN
ejpam-3860	175	5	is	be	AUX
ejpam-3860	175	6	even	even	ADV
ejpam-3860	175	7	and	and	CCONJ
ejpam-3860	175	8	so	so	ADV
ejpam-3860	175	9	is	be	AUX
ejpam-3860	175	10	s1	s1	NOUN
ejpam-3860	175	11	because	because	SCONJ
ejpam-3860	175	12	(	(	PUNCT
ejpam-3860	175	13	s1	s1	NOUN
ejpam-3860	175	14	,	,	PUNCT
ejpam-3860	175	15	jv)(s2	jv)(s2	PROPN
ejpam-3860	175	16	,	,	PUNCT
ejpam-3860	175	17	0v	0v	NOUN
ejpam-3860	175	18	)	)	PUNCT
ejpam-3860	175	19	∈	∈	PROPN
ejpam-3860	175	20	e	e	X
ejpam-3860	175	21	(	(	PUNCT
ejpam-3860	175	22	pk	pk	NOUN
ejpam-3860	175	23	�	�	PROPN
ejpam-3860	175	24	b(m	b(m	PROPN
ejpam-3860	175	25	,	,	PUNCT
ejpam-3860	175	26	n	n	CCONJ
ejpam-3860	175	27	)	)	PUNCT
ejpam-3860	175	28	)	)	PUNCT
ejpam-3860	175	29	when	when	SCONJ
ejpam-3860	175	30	s1	s1	PROPN
ejpam-3860	175	31	=	=	PROPN
ejpam-3860	175	32	s2	s2	PROPN
ejpam-3860	175	33	.	.	PUNCT
ejpam-3860	176	1	but	but	CCONJ
ejpam-3860	176	2	(	(	PUNCT
ejpam-3860	176	3	s1	s1	NOUN
ejpam-3860	176	4	,	,	PUNCT
ejpam-3860	176	5	jv	jv	NOUN
ejpam-3860	176	6	)	)	PUNCT
ejpam-3860	176	7	∈	∈	PROPN
ejpam-3860	176	8	s	s	PART
ejpam-3860	176	9	for	for	ADP
ejpam-3860	176	10	s1	s1	PROPN
ejpam-3860	176	11	even	even	ADV
ejpam-3860	176	12	which	which	PRON
ejpam-3860	176	13	is	be	AUX
ejpam-3860	176	14	a	a	DET
ejpam-3860	176	15	contradiction	contradiction	NOUN
ejpam-3860	176	16	.	.	PUNCT
ejpam-3860	177	1	case	case	NOUN
ejpam-3860	177	2	ii	ii	PROPN
ejpam-3860	177	3	.	.	PUNCT
ejpam-3860	178	1	w	w	PROPN
ejpam-3860	178	2	=	=	SYM
ejpam-3860	178	3	y	y	PROPN
ejpam-3860	178	4	+	+	NOUN
ejpam-3860	178	5	1	1	NUM
ejpam-3860	178	6	,	,	PUNCT
ejpam-3860	178	7	a	a	DET
ejpam-3860	178	8	=	=	SYM
ejpam-3860	178	9	b	b	PROPN
ejpam-3860	178	10	and	and	CCONJ
ejpam-3860	178	11	x	x	X
ejpam-3860	178	12	=	=	SYM
ejpam-3860	178	13	z	z	NOUN
ejpam-3860	178	14	assume	assume	VERB
ejpam-3860	178	15	that	that	SCONJ
ejpam-3860	178	16	x	x	PRON
ejpam-3860	179	1	=	=	PUNCT
ejpam-3860	179	2	z	z	PROPN
ejpam-3860	179	3	6=	6=	NUM
ejpam-3860	179	4	0	0	NUM
ejpam-3860	179	5	.	.	PUNCT
ejpam-3860	179	6	i.	i.	PROPN
ejpam-3860	179	7	when	when	SCONJ
ejpam-3860	179	8	(	(	PUNCT
ejpam-3860	179	9	r1	r1	PROPN
ejpam-3860	179	10	,	,	PUNCT
ejpam-3860	179	11	i1u)(r2	i1u)(r2	ADV
ejpam-3860	179	12	,	,	PUNCT
ejpam-3860	179	13	i2u	i2u	NOUN
ejpam-3860	179	14	)	)	PUNCT
ejpam-3860	179	15	/∈	/∈	PUNCT
ejpam-3860	180	1	e	e	NOUN
ejpam-3860	180	2	(	(	PUNCT
ejpam-3860	180	3	⋃	⋃	ADP
ejpam-3860	180	4	v∈s	v∈s	ADJ
ejpam-3860	180	5	〈	〈	PROPN
ejpam-3860	180	6	n	n	PRON
ejpam-3860	180	7	[	[	X
ejpam-3860	180	8	v	v	NOUN
ejpam-3860	180	9	]	]	X
ejpam-3860	180	10	〉	〉	NOUN
ejpam-3860	180	11	)	)	PUNCT
ejpam-3860	180	12	,	,	PUNCT
ejpam-3860	180	13	then	then	ADV
ejpam-3860	180	14	both	both	DET
ejpam-3860	180	15	(	(	PUNCT
ejpam-3860	180	16	r1	r1	NOUN
ejpam-3860	180	17	,	,	PUNCT
ejpam-3860	180	18	i1u	i1u	NUM
ejpam-3860	180	19	)	)	PUNCT
ejpam-3860	180	20	,	,	PUNCT
ejpam-3860	180	21	(	(	PUNCT
ejpam-3860	180	22	r2	r2	NOUN
ejpam-3860	180	23	,	,	PUNCT
ejpam-3860	180	24	i2u	i2u	NOUN
ejpam-3860	180	25	)	)	PUNCT
ejpam-3860	180	26	/∈	/∈	PUNCT
ejpam-3860	181	1	s.	s.	PROPN
ejpam-3860	181	2	this	this	PRON
ejpam-3860	181	3	implies	imply	VERB
ejpam-3860	181	4	r1	r1	PROPN
ejpam-3860	181	5	and	and	CCONJ
ejpam-3860	181	6	r2	r2	PROPN
ejpam-3860	181	7	are	be	AUX
ejpam-3860	181	8	odd	odd	ADJ
ejpam-3860	181	9	.	.	PUNCT
ejpam-3860	182	1	but	but	CCONJ
ejpam-3860	182	2	(	(	PUNCT
ejpam-3860	182	3	r1	r1	PROPN
ejpam-3860	182	4	,	,	PUNCT
ejpam-3860	182	5	i1u)(r2	i1u)(r2	ADV
ejpam-3860	182	6	,	,	PUNCT
ejpam-3860	182	7	i2u	i2u	NOUN
ejpam-3860	182	8	)	)	PUNCT
ejpam-3860	182	9	/∈	/∈	PUNCT
ejpam-3860	183	1	e	e	NOUN
ejpam-3860	183	2	(	(	PUNCT
ejpam-3860	183	3	pk	pk	NOUN
ejpam-3860	183	4	�	�	PROPN
ejpam-3860	183	5	b(m	b(m	PROPN
ejpam-3860	183	6	,	,	PUNCT
ejpam-3860	183	7	n	n	CCONJ
ejpam-3860	183	8	)	)	PUNCT
ejpam-3860	183	9	)	)	PUNCT
ejpam-3860	183	10	which	which	PRON
ejpam-3860	183	11	is	be	AUX
ejpam-3860	183	12	a	a	DET
ejpam-3860	183	13	n.	n.	NOUN
ejpam-3860	183	14	abdulcarim	abdulcarim	PROPN
ejpam-3860	183	15	,	,	PUNCT
ejpam-3860	183	16	s.	s.	PROPN
ejpam-3860	183	17	dagondon	dagondon	PROPN
ejpam-3860	183	18	,	,	PUNCT
ejpam-3860	183	19	e.	e.	PROPN
ejpam-3860	183	20	chacon	chacon	PROPN
ejpam-3860	183	21	/	/	SYM
ejpam-3860	183	22	eur	eur	PROPN
ejpam-3860	183	23	.	.	PUNCT
ejpam-3860	184	1	j.	j.	PROPN
ejpam-3860	184	2	pure	pure	PROPN
ejpam-3860	184	3	appl	appl	PROPN
ejpam-3860	184	4	.	.	PROPN
ejpam-3860	184	5	math	math	PROPN
ejpam-3860	184	6	,	,	PUNCT
ejpam-3860	184	7	14	14	NUM
ejpam-3860	184	8	(	(	PUNCT
ejpam-3860	184	9	1	1	NUM
ejpam-3860	184	10	)	)	PUNCT
ejpam-3860	184	11	(	(	PUNCT
ejpam-3860	184	12	2021	2021	NUM
ejpam-3860	184	13	)	)	PUNCT
ejpam-3860	184	14	,	,	PUNCT
ejpam-3860	184	15	173	173	NUM
ejpam-3860	184	16	-	-	SYM
ejpam-3860	184	17	191	191	NUM
ejpam-3860	184	18	181	181	NUM
ejpam-3860	184	19	contradiction	contradiction	NOUN
ejpam-3860	184	20	.	.	PUNCT
ejpam-3860	185	1	ii	ii	PROPN
ejpam-3860	185	2	.	.	PUNCT
ejpam-3860	186	1	when	when	SCONJ
ejpam-3860	186	2	(	(	PUNCT
ejpam-3860	186	3	s1	s1	NOUN
ejpam-3860	186	4	,	,	PUNCT
ejpam-3860	186	5	j1u)(s2	j1u)(s2	ADJ
ejpam-3860	186	6	,	,	PUNCT
ejpam-3860	186	7	j2u	j2u	NOUN
ejpam-3860	186	8	)	)	PUNCT
ejpam-3860	186	9	/∈	/∈	PUNCT
ejpam-3860	187	1	e	e	NOUN
ejpam-3860	187	2	(	(	PUNCT
ejpam-3860	187	3	⋃	⋃	ADP
ejpam-3860	187	4	v∈s	v∈s	ADJ
ejpam-3860	187	5	〈	〈	PROPN
ejpam-3860	187	6	n	n	PRON
ejpam-3860	187	7	[	[	X
ejpam-3860	187	8	v	v	NOUN
ejpam-3860	187	9	]	]	X
ejpam-3860	187	10	〉	〉	NUM
ejpam-3860	187	11	)	)	PUNCT
ejpam-3860	187	12	,	,	PUNCT
ejpam-3860	187	13	we	we	PRON
ejpam-3860	187	14	will	will	AUX
ejpam-3860	187	15	arrive	arrive	VERB
ejpam-3860	187	16	contradiction	contradiction	NOUN
ejpam-3860	187	17	similar	similar	ADJ
ejpam-3860	187	18	to	to	ADP
ejpam-3860	187	19	i.	i.	PROPN
ejpam-3860	187	20	next	next	ADV
ejpam-3860	187	21	,	,	PUNCT
ejpam-3860	187	22	we	we	PRON
ejpam-3860	187	23	assume	assume	VERB
ejpam-3860	187	24	x	x	X
ejpam-3860	187	25	=	=	PUNCT
ejpam-3860	187	26	z	z	NOUN
ejpam-3860	187	27	=	=	SYM
ejpam-3860	188	1	0	0	PROPN
ejpam-3860	188	2	.	.	X
ejpam-3860	188	3	iii	iii	X
ejpam-3860	188	4	.	.	PUNCT
ejpam-3860	189	1	if	if	SCONJ
ejpam-3860	189	2	(	(	PUNCT
ejpam-3860	189	3	r1	r1	PROPN
ejpam-3860	189	4	,	,	PUNCT
ejpam-3860	189	5	0u)(r2	0u)(r2	NOUN
ejpam-3860	189	6	,	,	PUNCT
ejpam-3860	189	7	0u	0u	ADJ
ejpam-3860	189	8	)	)	PUNCT
ejpam-3860	189	9	/∈	/∈	PUNCT
ejpam-3860	190	1	e	e	NOUN
ejpam-3860	190	2	(	(	PUNCT
ejpam-3860	190	3	⋃	⋃	ADP
ejpam-3860	190	4	v∈s	v∈s	ADJ
ejpam-3860	190	5	〈	〈	PROPN
ejpam-3860	190	6	n	n	PRON
ejpam-3860	190	7	[	[	X
ejpam-3860	190	8	v	v	NOUN
ejpam-3860	190	9	]	]	X
ejpam-3860	190	10	〉	〉	NOUN
ejpam-3860	190	11	)	)	PUNCT
ejpam-3860	190	12	,	,	PUNCT
ejpam-3860	190	13	then	then	ADV
ejpam-3860	190	14	both	both	DET
ejpam-3860	190	15	(	(	PUNCT
ejpam-3860	190	16	r1	r1	PROPN
ejpam-3860	190	17	,	,	PUNCT
ejpam-3860	190	18	0u	0u	ADJ
ejpam-3860	190	19	)	)	PUNCT
ejpam-3860	190	20	,	,	PUNCT
ejpam-3860	190	21	(	(	PUNCT
ejpam-3860	190	22	r2	r2	NOUN
ejpam-3860	190	23	,	,	PUNCT
ejpam-3860	190	24	0u	0u	ADJ
ejpam-3860	190	25	)	)	PUNCT
ejpam-3860	190	26	/∈	/∈	PUNCT
ejpam-3860	191	1	s.	s.	PROPN
ejpam-3860	191	2	this	this	PRON
ejpam-3860	191	3	implies	imply	VERB
ejpam-3860	191	4	r1	r1	PROPN
ejpam-3860	191	5	is	be	AUX
ejpam-3860	191	6	odd	odd	ADJ
ejpam-3860	191	7	and	and	CCONJ
ejpam-3860	191	8	r2	r2	PROPN
ejpam-3860	191	9	is	be	AUX
ejpam-3860	191	10	even	even	ADV
ejpam-3860	191	11	.	.	PUNCT
ejpam-3860	192	1	but	but	CCONJ
ejpam-3860	192	2	(	(	PUNCT
ejpam-3860	192	3	r2	r2	PROPN
ejpam-3860	192	4	,	,	PUNCT
ejpam-3860	192	5	0u	0u	ADJ
ejpam-3860	192	6	)	)	PUNCT
ejpam-3860	192	7	∈	∈	PROPN
ejpam-3860	192	8	s	s	PROPN
ejpam-3860	192	9	,	,	PUNCT
ejpam-3860	192	10	a	a	DET
ejpam-3860	192	11	contradiction	contradiction	NOUN
ejpam-3860	192	12	.	.	PUNCT
ejpam-3860	193	1	iv	iv	X
ejpam-3860	193	2	.	.	PUNCT
ejpam-3860	194	1	if	if	SCONJ
ejpam-3860	194	2	(	(	PUNCT
ejpam-3860	194	3	s1	s1	NOUN
ejpam-3860	194	4	,	,	PUNCT
ejpam-3860	194	5	0v)(s2	0v)(s2	NUM
ejpam-3860	194	6	,	,	PUNCT
ejpam-3860	194	7	0v	0v	NOUN
ejpam-3860	194	8	)	)	PUNCT
ejpam-3860	194	9	/∈	/∈	PUNCT
ejpam-3860	195	1	e	e	NOUN
ejpam-3860	195	2	(	(	PUNCT
ejpam-3860	195	3	⋃	⋃	ADP
ejpam-3860	195	4	v∈s	v∈s	ADJ
ejpam-3860	195	5	〈	〈	PROPN
ejpam-3860	195	6	n	n	PRON
ejpam-3860	195	7	[	[	X
ejpam-3860	195	8	v	v	NOUN
ejpam-3860	195	9	]	]	X
ejpam-3860	195	10	〉	〉	NOUN
ejpam-3860	195	11	)	)	PUNCT
ejpam-3860	195	12	,	,	PUNCT
ejpam-3860	195	13	then	then	ADV
ejpam-3860	195	14	both	both	DET
ejpam-3860	195	15	(	(	PUNCT
ejpam-3860	195	16	s1	s1	NOUN
ejpam-3860	195	17	,	,	PUNCT
ejpam-3860	195	18	0v	0v	NOUN
ejpam-3860	195	19	)	)	PUNCT
ejpam-3860	195	20	,	,	PUNCT
ejpam-3860	195	21	(	(	PUNCT
ejpam-3860	195	22	s2	s2	PROPN
ejpam-3860	195	23	,	,	PUNCT
ejpam-3860	195	24	0v	0v	NOUN
ejpam-3860	195	25	)	)	PUNCT
ejpam-3860	195	26	/∈	/∈	PUNCT
ejpam-3860	196	1	s.	s.	PROPN
ejpam-3860	196	2	note	note	VERB
ejpam-3860	196	3	that	that	SCONJ
ejpam-3860	196	4	whenever	whenever	SCONJ
ejpam-3860	196	5	s1	s1	PROPN
ejpam-3860	196	6	is	be	AUX
ejpam-3860	196	7	odd	odd	ADJ
ejpam-3860	196	8	,	,	PUNCT
ejpam-3860	196	9	s2	s2	PROPN
ejpam-3860	196	10	is	be	AUX
ejpam-3860	196	11	even	even	ADV
ejpam-3860	196	12	.	.	PUNCT
ejpam-3860	197	1	but	but	CCONJ
ejpam-3860	197	2	(	(	PUNCT
ejpam-3860	197	3	s	s	X
ejpam-3860	197	4	,	,	PUNCT
ejpam-3860	197	5	0v	0v	NOUN
ejpam-3860	197	6	)	)	PUNCT
ejpam-3860	197	7	∈	∈	PROPN
ejpam-3860	197	8	s	s	PART
ejpam-3860	197	9	for	for	ADP
ejpam-3860	197	10	s	s	PRON
ejpam-3860	197	11	even	even	ADV
ejpam-3860	197	12	.	.	PUNCT
ejpam-3860	198	1	this	this	PRON
ejpam-3860	198	2	is	be	AUX
ejpam-3860	198	3	a	a	DET
ejpam-3860	198	4	contradiction	contradiction	NOUN
ejpam-3860	198	5	.	.	PUNCT
ejpam-3860	199	1	case	case	NOUN
ejpam-3860	199	2	iii	iii	X
ejpam-3860	199	3	.	.	PUNCT
ejpam-3860	200	1	w	w	PROPN
ejpam-3860	200	2	=	=	SYM
ejpam-3860	200	3	y	y	PROPN
ejpam-3860	200	4	,	,	PUNCT
ejpam-3860	200	5	a	a	DET
ejpam-3860	200	6	=	=	SYM
ejpam-3860	200	7	u	u	NOUN
ejpam-3860	200	8	,	,	PUNCT
ejpam-3860	200	9	b	b	PROPN
ejpam-3860	200	10	=	=	SYM
ejpam-3860	200	11	v	v	PROPN
ejpam-3860	200	12	and	and	CCONJ
ejpam-3860	200	13	x	x	PUNCT
ejpam-3860	201	1	=	=	SYM
ejpam-3860	201	2	0	0	X
ejpam-3860	202	1	=	=	SYM
ejpam-3860	202	2	z	z	NOUN
ejpam-3860	202	3	if	if	SCONJ
ejpam-3860	202	4	(	(	PUNCT
ejpam-3860	202	5	r	r	NOUN
ejpam-3860	202	6	,	,	PUNCT
ejpam-3860	202	7	0u)(s	0u)(s	NOUN
ejpam-3860	202	8	,	,	PUNCT
ejpam-3860	202	9	0v	0v	NOUN
ejpam-3860	202	10	)	)	PUNCT
ejpam-3860	202	11	/∈	/∈	PUNCT
ejpam-3860	203	1	e	e	NOUN
ejpam-3860	203	2	(	(	PUNCT
ejpam-3860	203	3	⋃	⋃	ADP
ejpam-3860	203	4	v∈s	v∈s	ADJ
ejpam-3860	203	5	〈	〈	PROPN
ejpam-3860	203	6	n	n	PRON
ejpam-3860	203	7	[	[	X
ejpam-3860	203	8	v	v	NOUN
ejpam-3860	203	9	]	]	X
ejpam-3860	203	10	〉	〉	NUM
ejpam-3860	203	11	)	)	PUNCT
ejpam-3860	203	12	,	,	PUNCT
ejpam-3860	203	13	then	then	ADV
ejpam-3860	203	14	(	(	PUNCT
ejpam-3860	203	15	r	r	NOUN
ejpam-3860	203	16	,	,	PUNCT
ejpam-3860	203	17	0u	0u	ADJ
ejpam-3860	203	18	)	)	PUNCT
ejpam-3860	203	19	,	,	PUNCT
ejpam-3860	203	20	(	(	PUNCT
ejpam-3860	203	21	s	s	X
ejpam-3860	203	22	,	,	PUNCT
ejpam-3860	203	23	ov	ov	PROPN
ejpam-3860	203	24	)	)	PUNCT
ejpam-3860	203	25	/∈	/∈	PUNCT
ejpam-3860	204	1	s.	s.	PROPN
ejpam-3860	204	2	this	this	PRON
ejpam-3860	204	3	implies	imply	VERB
ejpam-3860	204	4	r	r	NOUN
ejpam-3860	204	5	is	be	AUX
ejpam-3860	204	6	odd	odd	ADJ
ejpam-3860	204	7	.	.	PUNCT
ejpam-3860	205	1	but	but	CCONJ
ejpam-3860	205	2	r	r	NOUN
ejpam-3860	205	3	=	=	SYM
ejpam-3860	205	4	s	s	X
ejpam-3860	205	5	and	and	CCONJ
ejpam-3860	205	6	thus	thus	ADV
ejpam-3860	205	7	,	,	PUNCT
ejpam-3860	205	8	s	s	X
ejpam-3860	205	9	is	be	AUX
ejpam-3860	205	10	also	also	ADV
ejpam-3860	205	11	odd	odd	ADJ
ejpam-3860	205	12	.	.	PUNCT
ejpam-3860	206	1	this	this	PRON
ejpam-3860	206	2	is	be	AUX
ejpam-3860	206	3	a	a	DET
ejpam-3860	206	4	contradiction	contradiction	NOUN
ejpam-3860	206	5	.	.	PUNCT
ejpam-3860	207	1	hence	hence	ADV
ejpam-3860	207	2	,	,	PUNCT
ejpam-3860	207	3	in	in	ADP
ejpam-3860	207	4	either	either	PRON
ejpam-3860	207	5	of	of	ADP
ejpam-3860	207	6	the	the	DET
ejpam-3860	207	7	above	above	ADJ
ejpam-3860	207	8	cases	case	NOUN
ejpam-3860	207	9	,	,	PUNCT
ejpam-3860	207	10	we	we	PRON
ejpam-3860	207	11	arrived	arrive	VERB
ejpam-3860	207	12	at	at	ADP
ejpam-3860	207	13	a	a	DET
ejpam-3860	207	14	contradiction	contradiction	NOUN
ejpam-3860	207	15	.	.	PUNCT
ejpam-3860	208	1	thus	thus	ADV
ejpam-3860	208	2	,	,	PUNCT
ejpam-3860	208	3	(	(	PUNCT
ejpam-3860	208	4	w	w	PROPN
ejpam-3860	208	5	,	,	PUNCT
ejpam-3860	208	6	xa)(y	xa)(y	PROPN
ejpam-3860	208	7	,	,	PUNCT
ejpam-3860	208	8	zb	zb	X
ejpam-3860	208	9	)	)	PUNCT
ejpam-3860	208	10	∈	∈	PROPN
ejpam-3860	208	11	e	e	X
ejpam-3860	208	12	(	(	PUNCT
ejpam-3860	208	13	⋃	⋃	ADP
ejpam-3860	208	14	v∈s	v∈s	ADJ
ejpam-3860	208	15	〈	〈	PROPN
ejpam-3860	208	16	n	n	PRON
ejpam-3860	208	17	[	[	X
ejpam-3860	208	18	v	v	NOUN
ejpam-3860	208	19	]	]	X
ejpam-3860	208	20	〉	〉	NUM
ejpam-3860	208	21	)	)	PUNCT
ejpam-3860	208	22	.	.	PUNCT
ejpam-3860	209	1	consequently	consequently	ADV
ejpam-3860	209	2	,	,	PUNCT
ejpam-3860	209	3	⋃	⋃	PUNCT
ejpam-3860	209	4	v∈s	v∈s	ADJ
ejpam-3860	209	5	〈	〈	PROPN
ejpam-3860	209	6	n	n	PRON
ejpam-3860	209	7	[	[	X
ejpam-3860	209	8	v	v	NOUN
ejpam-3860	209	9	]	]	X
ejpam-3860	209	10	〉	〉	NOUN
ejpam-3860	209	11	=	=	SYM
ejpam-3860	209	12	pk	pk	PROPN
ejpam-3860	209	13	�	�	PROPN
ejpam-3860	209	14	b(m	b(m	PROPN
ejpam-3860	209	15	,	,	PUNCT
ejpam-3860	209	16	n	n	CCONJ
ejpam-3860	209	17	)	)	PUNCT
ejpam-3860	209	18	.	.	PUNCT
ejpam-3860	210	1	hence	hence	ADV
ejpam-3860	210	2	,	,	PUNCT
ejpam-3860	210	3	s	s	VERB
ejpam-3860	210	4	is	be	AUX
ejpam-3860	210	5	an	an	DET
ejpam-3860	210	6	independent	independent	ADJ
ejpam-3860	210	7	neighborhood	neighborhood	NOUN
ejpam-3860	210	8	set	set	NOUN
ejpam-3860	210	9	of	of	ADP
ejpam-3860	210	10	pk	pk	NOUN
ejpam-3860	210	11	�	�	PROPN
ejpam-3860	210	12	b(m	b(m	PROPN
ejpam-3860	210	13	,	,	PUNCT
ejpam-3860	210	14	n	n	CCONJ
ejpam-3860	210	15	)	)	PUNCT
ejpam-3860	210	16	.	.	PUNCT
ejpam-3860	211	1	following	follow	VERB
ejpam-3860	211	2	the	the	DET
ejpam-3860	211	3	same	same	ADJ
ejpam-3860	211	4	argument	argument	NOUN
ejpam-3860	211	5	in	in	ADP
ejpam-3860	211	6	s	s	PROPN
ejpam-3860	211	7	,	,	PUNCT
ejpam-3860	211	8	we	we	PRON
ejpam-3860	211	9	can	can	AUX
ejpam-3860	211	10	also	also	ADV
ejpam-3860	211	11	show	show	VERB
ejpam-3860	211	12	that	that	SCONJ
ejpam-3860	211	13	t	t	PROPN
ejpam-3860	211	14	is	be	AUX
ejpam-3860	211	15	an	an	DET
ejpam-3860	211	16	independent	independent	ADJ
ejpam-3860	211	17	neighborhood	neighborhood	NOUN
ejpam-3860	211	18	set	set	NOUN
ejpam-3860	211	19	of	of	ADP
ejpam-3860	211	20	pk	pk	NOUN
ejpam-3860	211	21	�	�	PROPN
ejpam-3860	211	22	b(m	b(m	PROPN
ejpam-3860	211	23	,	,	PUNCT
ejpam-3860	211	24	n	n	CCONJ
ejpam-3860	211	25	)	)	PUNCT
ejpam-3860	211	26	now	now	ADV
ejpam-3860	211	27	,	,	PUNCT
ejpam-3860	211	28	observe	observe	VERB
ejpam-3860	211	29	that	that	SCONJ
ejpam-3860	211	30	for	for	ADP
ejpam-3860	211	31	each	each	DET
ejpam-3860	211	32	ai	ai	NOUN
ejpam-3860	211	33	and	and	CCONJ
ejpam-3860	211	34	br	br	NOUN
ejpam-3860	211	35	,	,	PUNCT
ejpam-3860	211	36	|ai|	|ai|	PROPN
ejpam-3860	211	37	=	=	SYM
ejpam-3860	211	38	m+	m+	NUM
ejpam-3860	211	39	1	1	NUM
ejpam-3860	211	40	and	and	CCONJ
ejpam-3860	211	41	|br|	|br|	ADJ
ejpam-3860	211	42	=	=	SYM
ejpam-3860	211	43	|n+	|n+	PROPN
ejpam-3860	211	44	1|	1|	NUM
ejpam-3860	211	45	.	.	PUNCT
ejpam-3860	212	1	thus	thus	ADV
ejpam-3860	212	2	,	,	PUNCT
ejpam-3860	212	3	|s|	|s|	PROPN
ejpam-3860	212	4	=	=	SYM
ejpam-3860	212	5	∑	∑	PROPN
ejpam-3860	212	6	i	i	PRON
ejpam-3860	212	7	is	be	AUX
ejpam-3860	212	8	odd	odd	ADJ
ejpam-3860	212	9	|ai|+	|ai|+	NOUN
ejpam-3860	212	10	∑	∑	ADP
ejpam-3860	212	11	r	r	NOUN
ejpam-3860	212	12	is	be	AUX
ejpam-3860	212	13	even	even	ADV
ejpam-3860	212	14	|br|	|br|	ADJ
ejpam-3860	212	15	=	=	PUNCT
ejpam-3860	212	16	⌈	⌈	SYM
ejpam-3860	212	17	k	k	X
ejpam-3860	212	18	2	2	NUM
ejpam-3860	212	19	⌉	⌉	X
ejpam-3860	212	20	(	(	PUNCT
ejpam-3860	212	21	m+	m+	NOUN
ejpam-3860	212	22	1	1	NUM
ejpam-3860	212	23	)	)	PUNCT
ejpam-3860	212	24	+	+	CCONJ
ejpam-3860	213	1	⌊	⌊	VERB
ejpam-3860	213	2	k	k	ADJ
ejpam-3860	213	3	2	2	NUM
ejpam-3860	213	4	⌋	⌋	NOUN
ejpam-3860	213	5	(	(	PUNCT
ejpam-3860	213	6	n+	n+	NOUN
ejpam-3860	213	7	1	1	NUM
ejpam-3860	213	8	)	)	PUNCT
ejpam-3860	213	9	and	and	CCONJ
ejpam-3860	213	10	|t	|t	VERB
ejpam-3860	214	1	|	|	ADV
ejpam-3860	214	2	=	=	PUNCT
ejpam-3860	215	1	∑	∑	PUNCT
ejpam-3860	216	1	i	i	PRON
ejpam-3860	216	2	is	be	AUX
ejpam-3860	216	3	even	even	ADV
ejpam-3860	216	4	|ai|+	|ai|+	NOUN
ejpam-3860	216	5	∑	∑	ADP
ejpam-3860	216	6	r	r	NOUN
ejpam-3860	216	7	is	be	AUX
ejpam-3860	216	8	odd	odd	ADJ
ejpam-3860	216	9	|br|	|br|	NOUN
ejpam-3860	216	10	=	=	PUNCT
ejpam-3860	217	1	⌊	⌊	VERB
ejpam-3860	217	2	k	k	X
ejpam-3860	217	3	2	2	NUM
ejpam-3860	217	4	⌋	⌋	NOUN
ejpam-3860	217	5	(	(	PUNCT
ejpam-3860	217	6	m+	m+	NOUN
ejpam-3860	217	7	1	1	NUM
ejpam-3860	217	8	)	)	PUNCT
ejpam-3860	217	9	+	+	CCONJ
ejpam-3860	218	1	⌈	⌈	SYM
ejpam-3860	218	2	k	k	PROPN
ejpam-3860	218	3	2	2	NUM
ejpam-3860	218	4	⌉	⌉	X
ejpam-3860	218	5	(	(	PUNCT
ejpam-3860	218	6	n+	n+	NOUN
ejpam-3860	218	7	1	1	NUM
ejpam-3860	218	8	)	)	PUNCT
ejpam-3860	218	9	.	.	PUNCT
ejpam-3860	219	1	therefore	therefore	ADV
ejpam-3860	219	2	,	,	PUNCT
ejpam-3860	219	3	ni(pk	ni(pk	PROPN
ejpam-3860	219	4	�	�	PROPN
ejpam-3860	219	5	b(m	b(m	PROPN
ejpam-3860	219	6	,	,	PUNCT
ejpam-3860	219	7	n	n	CCONJ
ejpam-3860	219	8	)	)	PUNCT
ejpam-3860	219	9	,	,	PUNCT
ejpam-3860	219	10	x	x	X
ejpam-3860	219	11	)	)	PUNCT
ejpam-3860	219	12	=	=	PUNCT
ejpam-3860	220	1	xd	xd	NUM
ejpam-3860	220	2	k	k	PROPN
ejpam-3860	220	3	2e(m+1)+b	2e(m+1)+b	PROPN
ejpam-3860	220	4	k2c(n+1	k2c(n+1	PROPN
ejpam-3860	220	5	)	)	PUNCT
ejpam-3860	221	1	+	+	CCONJ
ejpam-3860	221	2	xb	xb	PROPN
ejpam-3860	221	3	k	k	PROPN
ejpam-3860	221	4	2c(m+1)+d	2c(m+1)+d	PROPN
ejpam-3860	221	5	k2e(n+1	k2e(n+1	PROPN
ejpam-3860	221	6	)	)	PUNCT
ejpam-3860	221	7	.	.	PUNCT
ejpam-3860	222	1	n.	n.	PROPN
ejpam-3860	222	2	abdulcarim	abdulcarim	PROPN
ejpam-3860	222	3	,	,	PUNCT
ejpam-3860	222	4	s.	s.	PROPN
ejpam-3860	222	5	dagondon	dagondon	PROPN
ejpam-3860	222	6	,	,	PUNCT
ejpam-3860	222	7	e.	e.	PROPN
ejpam-3860	222	8	chacon	chacon	PROPN
ejpam-3860	222	9	/	/	SYM
ejpam-3860	222	10	eur	eur	PROPN
ejpam-3860	222	11	.	.	PUNCT
ejpam-3860	223	1	j.	j.	PROPN
ejpam-3860	223	2	pure	pure	PROPN
ejpam-3860	223	3	appl	appl	PROPN
ejpam-3860	223	4	.	.	PROPN
ejpam-3860	223	5	math	math	PROPN
ejpam-3860	223	6	,	,	PUNCT
ejpam-3860	223	7	14	14	NUM
ejpam-3860	223	8	(	(	PUNCT
ejpam-3860	223	9	1	1	NUM
ejpam-3860	223	10	)	)	PUNCT
ejpam-3860	223	11	(	(	PUNCT
ejpam-3860	223	12	2021	2021	NUM
ejpam-3860	223	13	)	)	PUNCT
ejpam-3860	223	14	,	,	PUNCT
ejpam-3860	223	15	173	173	NUM
ejpam-3860	223	16	-	-	SYM
ejpam-3860	223	17	191	191	NUM
ejpam-3860	223	18	182	182	NUM
ejpam-3860	223	19	theorem	theorem	NOUN
ejpam-3860	223	20	3	3	NUM
ejpam-3860	223	21	.	.	X
ejpam-3860	224	1	for	for	ADP
ejpam-3860	224	2	any	any	DET
ejpam-3860	224	3	path	path	NOUN
ejpam-3860	224	4	pk	pk	NOUN
ejpam-3860	224	5	and	and	CCONJ
ejpam-3860	224	6	banana	banana	NOUN
ejpam-3860	224	7	graph	graph	NOUN
ejpam-3860	224	8	bm	bm	PROPN
ejpam-3860	224	9	,	,	PUNCT
ejpam-3860	224	10	n	n	CCONJ
ejpam-3860	224	11	,	,	PUNCT
ejpam-3860	224	12	ni(pk	ni(pk	PROPN
ejpam-3860	224	13	�	�	PROPN
ejpam-3860	224	14	bm	bm	PROPN
ejpam-3860	224	15	,	,	PUNCT
ejpam-3860	224	16	n	n	CCONJ
ejpam-3860	224	17	,	,	PUNCT
ejpam-3860	224	18	x	x	NOUN
ejpam-3860	224	19	)	)	PUNCT
ejpam-3860	224	20	=	=	SYM
ejpam-3860	224	21	xb	xb	PROPN
ejpam-3860	224	22	k	k	PROPN
ejpam-3860	224	23	2cm(n−1)+d	2cm(n−1)+d	NUM
ejpam-3860	224	24	k2e(m+1	k2e(m+1	PROPN
ejpam-3860	224	25	)	)	PUNCT
ejpam-3860	225	1	+	+	CCONJ
ejpam-3860	225	2	xd	xd	INTJ
ejpam-3860	225	3	k	k	PROPN
ejpam-3860	225	4	2em(n−1)+b	2em(n−1)+b	NUM
ejpam-3860	225	5	k2c(m+1	k2c(m+1	PUNCT
ejpam-3860	225	6	)	)	PUNCT
ejpam-3860	225	7	for	for	ADP
ejpam-3860	225	8	any	any	DET
ejpam-3860	225	9	k	k	PROPN
ejpam-3860	225	10	,	,	PUNCT
ejpam-3860	225	11	m	m	PROPN
ejpam-3860	225	12	,	,	PUNCT
ejpam-3860	225	13	n	n	PRON
ejpam-3860	225	14	∈	∈	PROPN
ejpam-3860	225	15	z+	z+	PUNCT
ejpam-3860	225	16	.	.	PUNCT
ejpam-3860	226	1	proof	proof	NOUN
ejpam-3860	226	2	:	:	PUNCT
ejpam-3860	226	3	label	label	VERB
ejpam-3860	226	4	the	the	DET
ejpam-3860	226	5	vertices	vertex	NOUN
ejpam-3860	226	6	of	of	ADP
ejpam-3860	226	7	each	each	DET
ejpam-3860	226	8	star	star	NOUN
ejpam-3860	226	9	in	in	ADP
ejpam-3860	226	10	bm	bm	PROPN
ejpam-3860	226	11	,	,	PUNCT
ejpam-3860	226	12	n	n	CCONJ
ejpam-3860	226	13	by	by	ADP
ejpam-3860	226	14	ij	ij	NOUN
ejpam-3860	226	15	,	,	PUNCT
ejpam-3860	226	16	i	i	PRON
ejpam-3860	226	17	=	=	NOUN
ejpam-3860	226	18	1	1	NUM
ejpam-3860	226	19	,	,	PUNCT
ejpam-3860	226	20	·	·	PUNCT
ejpam-3860	226	21	·	·	PUNCT
ejpam-3860	226	22	·	·	PUNCT
ejpam-3860	226	23	,	,	PUNCT
ejpam-3860	226	24	m	m	PROPN
ejpam-3860	226	25	,	,	PUNCT
ejpam-3860	226	26	j	j	PROPN
ejpam-3860	226	27	=	=	SYM
ejpam-3860	226	28	1	1	NUM
ejpam-3860	226	29	,	,	PUNCT
ejpam-3860	226	30	·	·	PUNCT
ejpam-3860	226	31	·	·	PUNCT
ejpam-3860	226	32	·	·	PUNCT
ejpam-3860	226	33	,	,	PUNCT
ejpam-3860	226	34	n	n	PROPN
ejpam-3860	226	35	and	and	CCONJ
ejpam-3860	226	36	0	0	NUM
ejpam-3860	226	37	as	as	ADP
ejpam-3860	226	38	the	the	DET
ejpam-3860	226	39	root	root	NOUN
ejpam-3860	226	40	vertex	vertex	NOUN
ejpam-3860	226	41	in	in	ADP
ejpam-3860	226	42	bm	bm	PROPN
ejpam-3860	226	43	,	,	PUNCT
ejpam-3860	226	44	n.	n.	PROPN
ejpam-3860	226	45	1n	1n	PROPN
ejpam-3860	226	46	13	13	NUM
ejpam-3860	226	47	12	12	NUM
ejpam-3860	226	48	11	11	NUM
ejpam-3860	226	49	1n−	1n−	NUM
ejpam-3860	226	50	1	1	NUM
ejpam-3860	226	51	2n	2n	NUM
ejpam-3860	226	52	23	23	NUM
ejpam-3860	226	53	22	22	NUM
ejpam-3860	226	54	21	21	NUM
ejpam-3860	226	55	2n−	2n−	PROPN
ejpam-3860	226	56	1	1	NUM
ejpam-3860	226	57	mn	mn	PROPN
ejpam-3860	226	58	m3	m3	PROPN
ejpam-3860	226	59	m2	m2	PROPN
ejpam-3860	226	60	m1	m1	PROPN
ejpam-3860	226	61	mn−	mn−	PROPN
ejpam-3860	227	1	1	1	NUM
ejpam-3860	227	2	0	0	NUM
ejpam-3860	227	3	·	·	PUNCT
ejpam-3860	227	4	·	·	PUNCT
ejpam-3860	227	5	·	·	PUNCT
ejpam-3860	227	6	then	then	ADV
ejpam-3860	227	7	v	v	X
ejpam-3860	227	8	(	(	PUNCT
ejpam-3860	227	9	pk	pk	PROPN
ejpam-3860	227	10	�	�	PROPN
ejpam-3860	227	11	bm	bm	PROPN
ejpam-3860	227	12	,	,	PUNCT
ejpam-3860	227	13	n	n	CCONJ
ejpam-3860	227	14	)	)	PUNCT
ejpam-3860	227	15	=	=	PRON
ejpam-3860	227	16	{	{	PUNCT
ejpam-3860	227	17	(	(	PUNCT
ejpam-3860	227	18	e	e	NOUN
ejpam-3860	227	19	,	,	PUNCT
ejpam-3860	227	20	ij	ij	NOUN
ejpam-3860	227	21	)	)	PUNCT
ejpam-3860	227	22	,	,	PUNCT
ejpam-3860	227	23	(	(	PUNCT
ejpam-3860	227	24	e	e	NOUN
ejpam-3860	227	25	,	,	PUNCT
ejpam-3860	227	26	0	0	NUM
ejpam-3860	227	27	)	)	PUNCT
ejpam-3860	227	28	:	:	PUNCT
ejpam-3860	228	1	e	e	X
ejpam-3860	228	2	=	=	SYM
ejpam-3860	228	3	1	1	NUM
ejpam-3860	228	4	,	,	PUNCT
ejpam-3860	228	5	·	·	PUNCT
ejpam-3860	228	6	·	·	PUNCT
ejpam-3860	228	7	·	·	PUNCT
ejpam-3860	228	8	,	,	PUNCT
ejpam-3860	228	9	k	k	X
ejpam-3860	228	10	,	,	PUNCT
ejpam-3860	228	11	i	i	NOUN
ejpam-3860	228	12	=	=	NOUN
ejpam-3860	228	13	1	1	NUM
ejpam-3860	228	14	,	,	PUNCT
ejpam-3860	228	15	·	·	PUNCT
ejpam-3860	228	16	·	·	PUNCT
ejpam-3860	228	17	·	·	PUNCT
ejpam-3860	228	18	,	,	PUNCT
ejpam-3860	228	19	m	m	PROPN
ejpam-3860	228	20	,	,	PUNCT
ejpam-3860	228	21	j	j	PROPN
ejpam-3860	228	22	=	=	SYM
ejpam-3860	228	23	1	1	NUM
ejpam-3860	228	24	,	,	PUNCT
ejpam-3860	228	25	·	·	PUNCT
ejpam-3860	228	26	·	·	PUNCT
ejpam-3860	228	27	·	·	PUNCT
ejpam-3860	228	28	,	,	PUNCT
ejpam-3860	228	29	n	n	CCONJ
ejpam-3860	228	30	}	}	PUNCT
ejpam-3860	228	31	as	as	SCONJ
ejpam-3860	228	32	shown	show	VERB
ejpam-3860	228	33	in	in	ADP
ejpam-3860	228	34	the	the	DET
ejpam-3860	228	35	figure	figure	NOUN
ejpam-3860	228	36	below	below	ADV
ejpam-3860	228	37	:	:	PUNCT
ejpam-3860	228	38	observe	observe	VERB
ejpam-3860	228	39	that	that	SCONJ
ejpam-3860	228	40	a.	a.	NOUN
ejpam-3860	228	41	(	(	PUNCT
ejpam-3860	228	42	e1	e1	PROPN
ejpam-3860	228	43	,	,	PUNCT
ejpam-3860	228	44	i1j1)(e2	i1j1)(e2	PROPN
ejpam-3860	228	45	,	,	PUNCT
ejpam-3860	228	46	i2j2	i2j2	PROPN
ejpam-3860	228	47	)	)	PUNCT
ejpam-3860	228	48	∈	∈	PROPN
ejpam-3860	228	49	e(pk	e(pk	PROPN
ejpam-3860	228	50	�	�	NOUN
ejpam-3860	228	51	bm	bm	PROPN
ejpam-3860	228	52	,	,	PUNCT
ejpam-3860	228	53	n	n	CCONJ
ejpam-3860	228	54	)	)	PUNCT
ejpam-3860	228	55	if	if	SCONJ
ejpam-3860	228	56	i.	i.	PROPN
ejpam-3860	228	57	e1	e1	PROPN
ejpam-3860	228	58	=	=	PROPN
ejpam-3860	228	59	e2	e2	PROPN
ejpam-3860	228	60	,	,	PUNCT
ejpam-3860	228	61	i1	i1	PROPN
ejpam-3860	228	62	=	=	PROPN
ejpam-3860	228	63	i2	i2	PROPN
ejpam-3860	228	64	and	and	CCONJ
ejpam-3860	228	65	either	either	CCONJ
ejpam-3860	228	66	j1	j1	PROPN
ejpam-3860	228	67	=	=	SYM
ejpam-3860	228	68	n	n	PROPN
ejpam-3860	228	69	or	or	CCONJ
ejpam-3860	228	70	j2	j2	PROPN
ejpam-3860	228	71	=	=	SYM
ejpam-3860	228	72	n	n	CCONJ
ejpam-3860	228	73	;	;	PUNCT
ejpam-3860	228	74	or	or	CCONJ
ejpam-3860	228	75	ii	ii	PROPN
ejpam-3860	228	76	.	.	PUNCT
ejpam-3860	228	77	e1	e1	PROPN
ejpam-3860	228	78	=	=	PROPN
ejpam-3860	228	79	e2	e2	PROPN
ejpam-3860	228	80	+	+	CCONJ
ejpam-3860	228	81	1	1	NUM
ejpam-3860	228	82	,	,	PUNCT
ejpam-3860	228	83	i1	i1	PROPN
ejpam-3860	228	84	=	=	PROPN
ejpam-3860	228	85	i2	i2	PROPN
ejpam-3860	228	86	and	and	CCONJ
ejpam-3860	228	87	j1	j1	PROPN
ejpam-3860	228	88	=	=	SYM
ejpam-3860	228	89	j2	j2	PROPN
ejpam-3860	228	90	.	.	PROPN
ejpam-3860	228	91	b.	b.	PROPN
ejpam-3860	228	92	(	(	PUNCT
ejpam-3860	228	93	e1	e1	PROPN
ejpam-3860	228	94	,	,	PUNCT
ejpam-3860	228	95	i1)(e2	i1)(e2	NOUN
ejpam-3860	228	96	,	,	PUNCT
ejpam-3860	228	97	0	0	NUM
ejpam-3860	228	98	)	)	PUNCT
ejpam-3860	228	99	∈	∈	PROPN
ejpam-3860	228	100	e(pk	e(pk	PROPN
ejpam-3860	228	101	�	�	NOUN
ejpam-3860	228	102	bm	bm	PROPN
ejpam-3860	228	103	,	,	PUNCT
ejpam-3860	228	104	n	n	CCONJ
ejpam-3860	228	105	)	)	PUNCT
ejpam-3860	228	106	if	if	SCONJ
ejpam-3860	228	107	e1	e1	NOUN
ejpam-3860	228	108	=	=	SYM
ejpam-3860	228	109	e2	e2	PROPN
ejpam-3860	228	110	,	,	PUNCT
ejpam-3860	228	111	and	and	CCONJ
ejpam-3860	228	112	c.	c.	PROPN
ejpam-3860	228	113	(	(	PUNCT
ejpam-3860	228	114	e1	e1	PROPN
ejpam-3860	228	115	,	,	PUNCT
ejpam-3860	228	116	0)(e2	0)(e2	NOUN
ejpam-3860	228	117	,	,	PUNCT
ejpam-3860	228	118	0	0	X
ejpam-3860	228	119	)	)	PUNCT
ejpam-3860	228	120	∈	∈	PROPN
ejpam-3860	228	121	e(pk	e(pk	PROPN
ejpam-3860	228	122	�	�	NOUN
ejpam-3860	228	123	bm	bm	PROPN
ejpam-3860	228	124	,	,	PUNCT
ejpam-3860	228	125	n	n	CCONJ
ejpam-3860	228	126	)	)	PUNCT
ejpam-3860	228	127	if	if	SCONJ
ejpam-3860	228	128	e1	e1	NOUN
ejpam-3860	228	129	=	=	SYM
ejpam-3860	228	130	e2	e2	PROPN
ejpam-3860	228	131	+	+	CCONJ
ejpam-3860	228	132	1	1	X
ejpam-3860	228	133	.	.	X
ejpam-3860	228	134	consider	consider	VERB
ejpam-3860	228	135	the	the	DET
ejpam-3860	228	136	following	follow	VERB
ejpam-3860	228	137	sets	set	NOUN
ejpam-3860	228	138	:	:	PUNCT
ejpam-3860	228	139	ap	ap	PROPN
ejpam-3860	229	1	=	=	PUNCT
ejpam-3860	229	2	{	{	PUNCT
ejpam-3860	229	3	(	(	PUNCT
ejpam-3860	229	4	e	e	NOUN
ejpam-3860	229	5	,	,	PUNCT
ejpam-3860	229	6	ij	ij	NOUN
ejpam-3860	229	7	)	)	PUNCT
ejpam-3860	229	8	:	:	PUNCT
ejpam-3860	230	1	e	e	NOUN
ejpam-3860	230	2	is	be	AUX
ejpam-3860	230	3	odd	odd	ADJ
ejpam-3860	230	4	,	,	PUNCT
ejpam-3860	230	5	i	i	PRON
ejpam-3860	230	6	=	=	NOUN
ejpam-3860	230	7	1	1	NUM
ejpam-3860	230	8	,	,	PUNCT
ejpam-3860	230	9	·	·	PUNCT
ejpam-3860	230	10	·	·	PUNCT
ejpam-3860	230	11	·	·	PUNCT
ejpam-3860	230	12	,	,	PUNCT
ejpam-3860	230	13	m	m	PROPN
ejpam-3860	230	14	,	,	PUNCT
ejpam-3860	230	15	j	j	PROPN
ejpam-3860	230	16	=	=	SYM
ejpam-3860	230	17	1	1	NUM
ejpam-3860	230	18	,	,	PUNCT
ejpam-3860	230	19	·	·	PUNCT
ejpam-3860	230	20	·	·	PUNCT
ejpam-3860	230	21	·	·	PUNCT
ejpam-3860	230	22	,	,	PUNCT
ejpam-3860	230	23	n−	n−	NOUN
ejpam-3860	230	24	1	1	NUM
ejpam-3860	230	25	}	}	PUNCT
ejpam-3860	230	26	,	,	PUNCT
ejpam-3860	230	27	aq	aq	X
ejpam-3860	230	28	=	=	SYM
ejpam-3860	230	29	{	{	PUNCT
ejpam-3860	230	30	(	(	PUNCT
ejpam-3860	230	31	e	e	NOUN
ejpam-3860	230	32	,	,	PUNCT
ejpam-3860	230	33	ij	ij	NOUN
ejpam-3860	230	34	)	)	PUNCT
ejpam-3860	230	35	:	:	PUNCT
ejpam-3860	230	36	e	e	X
ejpam-3860	230	37	is	be	AUX
ejpam-3860	230	38	even	even	ADV
ejpam-3860	230	39	,	,	PUNCT
ejpam-3860	230	40	i	i	PRON
ejpam-3860	230	41	=	=	NOUN
ejpam-3860	230	42	1	1	NUM
ejpam-3860	230	43	,	,	PUNCT
ejpam-3860	230	44	·	·	PUNCT
ejpam-3860	230	45	·	·	PUNCT
ejpam-3860	230	46	·	·	PUNCT
ejpam-3860	230	47	,	,	PUNCT
ejpam-3860	230	48	m	m	PROPN
ejpam-3860	230	49	,	,	PUNCT
ejpam-3860	230	50	j	j	PROPN
ejpam-3860	230	51	=	=	SYM
ejpam-3860	230	52	1	1	NUM
ejpam-3860	230	53	,	,	PUNCT
ejpam-3860	230	54	·	·	PUNCT
ejpam-3860	230	55	·	·	PUNCT
ejpam-3860	230	56	·	·	PUNCT
ejpam-3860	230	57	,	,	PUNCT
ejpam-3860	230	58	n−	n−	NOUN
ejpam-3860	230	59	1	1	NUM
ejpam-3860	230	60	}	}	PUNCT
ejpam-3860	230	61	,	,	PUNCT
ejpam-3860	230	62	bp	bp	PROPN
ejpam-3860	230	63	=	=	PRON
ejpam-3860	230	64	{	{	PUNCT
ejpam-3860	230	65	(	(	PUNCT
ejpam-3860	230	66	e	e	NOUN
ejpam-3860	230	67	,	,	PUNCT
ejpam-3860	230	68	0	0	NUM
ejpam-3860	230	69	)	)	PUNCT
ejpam-3860	230	70	:	:	PUNCT
ejpam-3860	231	1	e	e	NOUN
ejpam-3860	231	2	is	be	AUX
ejpam-3860	231	3	odd	odd	ADJ
ejpam-3860	231	4	}	}	PUNCT
ejpam-3860	231	5	∪	∪	X
ejpam-3860	231	6	{	{	PUNCT
ejpam-3860	231	7	(	(	PUNCT
ejpam-3860	231	8	e	e	NOUN
ejpam-3860	231	9	,	,	PUNCT
ejpam-3860	231	10	in	in	ADP
ejpam-3860	231	11	)	)	PUNCT
ejpam-3860	231	12	:	:	PUNCT
ejpam-3860	232	1	e	e	NOUN
ejpam-3860	232	2	is	be	AUX
ejpam-3860	232	3	odd	odd	ADJ
ejpam-3860	232	4	,	,	PUNCT
ejpam-3860	232	5	i	i	PRON
ejpam-3860	232	6	=	=	NOUN
ejpam-3860	232	7	1	1	NUM
ejpam-3860	232	8	,	,	PUNCT
ejpam-3860	232	9	·	·	PUNCT
ejpam-3860	232	10	·	·	PUNCT
ejpam-3860	232	11	·	·	PUNCT
ejpam-3860	232	12	,	,	PUNCT
ejpam-3860	232	13	m	m	PROPN
ejpam-3860	232	14	}	}	PUNCT
ejpam-3860	232	15	,	,	PUNCT
ejpam-3860	232	16	bq	bq	INTJ
ejpam-3860	232	17	=	=	PRON
ejpam-3860	232	18	{	{	PUNCT
ejpam-3860	232	19	(	(	PUNCT
ejpam-3860	232	20	e	e	NOUN
ejpam-3860	232	21	,	,	PUNCT
ejpam-3860	232	22	0	0	NUM
ejpam-3860	232	23	)	)	PUNCT
ejpam-3860	232	24	:	:	PUNCT
ejpam-3860	233	1	e	e	X
ejpam-3860	233	2	is	be	AUX
ejpam-3860	233	3	even	even	ADV
ejpam-3860	233	4	}	}	PUNCT
ejpam-3860	233	5	∪	∪	X
ejpam-3860	233	6	{	{	PUNCT
ejpam-3860	233	7	(	(	PUNCT
ejpam-3860	233	8	e	e	NOUN
ejpam-3860	233	9	,	,	PUNCT
ejpam-3860	233	10	in	in	ADP
ejpam-3860	233	11	)	)	PUNCT
ejpam-3860	233	12	:	:	PUNCT
ejpam-3860	233	13	e	e	X
ejpam-3860	233	14	is	be	AUX
ejpam-3860	233	15	even	even	ADV
ejpam-3860	233	16	,	,	PUNCT
ejpam-3860	233	17	i	i	PRON
ejpam-3860	233	18	=	=	NOUN
ejpam-3860	233	19	1	1	NUM
ejpam-3860	233	20	,	,	PUNCT
ejpam-3860	233	21	·	·	PUNCT
ejpam-3860	233	22	·	·	PUNCT
ejpam-3860	233	23	·	·	PUNCT
ejpam-3860	233	24	,	,	PUNCT
ejpam-3860	233	25	m	m	NOUN
ejpam-3860	233	26	}	}	PUNCT
ejpam-3860	233	27	.	.	PUNCT
ejpam-3860	234	1	let	let	VERB
ejpam-3860	234	2	s	s	PRON
ejpam-3860	234	3	=	=	VERB
ejpam-3860	234	4	ap	ap	PROPN
ejpam-3860	234	5	∪	∪	NOUN
ejpam-3860	234	6	bq	bq	PROPN
ejpam-3860	234	7	and	and	CCONJ
ejpam-3860	234	8	t	t	PROPN
ejpam-3860	234	9	=	=	SYM
ejpam-3860	234	10	aq	aq	PROPN
ejpam-3860	234	11	∪	∪	PROPN
ejpam-3860	234	12	bp	bp	PROPN
ejpam-3860	234	13	.	.	PUNCT
ejpam-3860	235	1	we	we	PRON
ejpam-3860	235	2	claim	claim	VERB
ejpam-3860	235	3	that	that	SCONJ
ejpam-3860	235	4	s	s	VERB
ejpam-3860	235	5	and	and	CCONJ
ejpam-3860	235	6	t	t	PROPN
ejpam-3860	235	7	are	be	AUX
ejpam-3860	235	8	the	the	DET
ejpam-3860	235	9	independent	independent	ADJ
ejpam-3860	235	10	neighborhood	neighborhood	NOUN
ejpam-3860	235	11	sets	set	NOUN
ejpam-3860	235	12	of	of	ADP
ejpam-3860	235	13	pk	pk	NOUN
ejpam-3860	235	14	�	�	PROPN
ejpam-3860	235	15	bm	bm	PROPN
ejpam-3860	235	16	,	,	PUNCT
ejpam-3860	235	17	n.	n.	PROPN
ejpam-3860	235	18	first	first	ADV
ejpam-3860	235	19	,	,	PUNCT
ejpam-3860	235	20	we	we	PRON
ejpam-3860	235	21	show	show	VERB
ejpam-3860	235	22	that	that	SCONJ
ejpam-3860	235	23	no	no	DET
ejpam-3860	235	24	two	two	NUM
ejpam-3860	235	25	vertices	vertex	NOUN
ejpam-3860	235	26	in	in	ADP
ejpam-3860	235	27	s	s	NOUN
ejpam-3860	235	28	are	be	AUX
ejpam-3860	235	29	adjacent	adjacent	ADJ
ejpam-3860	235	30	.	.	PUNCT
ejpam-3860	236	1	observe	observe	VERB
ejpam-3860	236	2	that	that	SCONJ
ejpam-3860	236	3	for	for	ADP
ejpam-3860	236	4	any	any	DET
ejpam-3860	236	5	(	(	PUNCT
ejpam-3860	236	6	e1	e1	PROPN
ejpam-3860	236	7	,	,	PUNCT
ejpam-3860	236	8	i1j1	i1j1	NOUN
ejpam-3860	236	9	)	)	PUNCT
ejpam-3860	236	10	,	,	PUNCT
ejpam-3860	236	11	(	(	PUNCT
ejpam-3860	236	12	e2	e2	PROPN
ejpam-3860	236	13	,	,	PUNCT
ejpam-3860	236	14	i2j2	i2j2	PROPN
ejpam-3860	236	15	)	)	PUNCT
ejpam-3860	236	16	∈	∈	PROPN
ejpam-3860	236	17	s	s	VERB
ejpam-3860	236	18	such	such	ADJ
ejpam-3860	236	19	that	that	DET
ejpam-3860	236	20	e1	e1	PROPN
ejpam-3860	236	21	=	=	SYM
ejpam-3860	236	22	e2	e2	PROPN
ejpam-3860	236	23	and	and	CCONJ
ejpam-3860	236	24	i1	i1	PROPN
ejpam-3860	236	25	=	=	PROPN
ejpam-3860	236	26	i2	i2	PROPN
ejpam-3860	236	27	,	,	PUNCT
ejpam-3860	236	28	we	we	PRON
ejpam-3860	236	29	have	have	VERB
ejpam-3860	236	30	j1	j1	PROPN
ejpam-3860	236	31	6=	6=	NUM
ejpam-3860	236	32	n	n	PROPN
ejpam-3860	236	33	and	and	CCONJ
ejpam-3860	236	34	j2	j2	PROPN
ejpam-3860	236	35	6=	6=	PROPN
ejpam-3860	236	36	n.	n.	PROPN
ejpam-3860	236	37	for	for	ADP
ejpam-3860	236	38	the	the	DET
ejpam-3860	236	39	case	case	NOUN
ejpam-3860	236	40	when	when	SCONJ
ejpam-3860	236	41	either	either	CCONJ
ejpam-3860	236	42	j1	j1	PROPN
ejpam-3860	236	43	=	=	SYM
ejpam-3860	236	44	n	n	PROPN
ejpam-3860	236	45	or	or	CCONJ
ejpam-3860	236	46	j2	j2	PROPN
ejpam-3860	236	47	=	=	SYM
ejpam-3860	236	48	n	n	CCONJ
ejpam-3860	236	49	,	,	PUNCT
ejpam-3860	236	50	e1	e1	PROPN
ejpam-3860	236	51	6=	6=	PROPN
ejpam-3860	236	52	e2	e2	PROPN
ejpam-3860	236	53	.	.	PUNCT
ejpam-3860	237	1	also	also	ADV
ejpam-3860	237	2	,	,	PUNCT
ejpam-3860	237	3	for	for	ADP
ejpam-3860	237	4	(	(	PUNCT
ejpam-3860	237	5	e1	e1	NOUN
ejpam-3860	237	6	,	,	PUNCT
ejpam-3860	237	7	i1j1	i1j1	NOUN
ejpam-3860	237	8	)	)	PUNCT
ejpam-3860	237	9	,	,	PUNCT
ejpam-3860	237	10	(	(	PUNCT
ejpam-3860	237	11	e2	e2	PROPN
ejpam-3860	237	12	,	,	PUNCT
ejpam-3860	237	13	i2j2	i2j2	PROPN
ejpam-3860	237	14	)	)	PUNCT
ejpam-3860	237	15	∈	∈	PROPN
ejpam-3860	237	16	s	s	VERB
ejpam-3860	237	17	such	such	ADJ
ejpam-3860	237	18	that	that	DET
ejpam-3860	237	19	e1	e1	PROPN
ejpam-3860	237	20	=	=	PROPN
ejpam-3860	237	21	e2	e2	PROPN
ejpam-3860	237	22	+	+	CCONJ
ejpam-3860	237	23	1	1	NUM
ejpam-3860	237	24	and	and	CCONJ
ejpam-3860	237	25	i1	i1	PROPN
ejpam-3860	237	26	=	=	PROPN
ejpam-3860	237	27	i2	i2	PROPN
ejpam-3860	237	28	,	,	PUNCT
ejpam-3860	237	29	j1	j1	PROPN
ejpam-3860	237	30	6=	6=	NUM
ejpam-3860	237	31	j2	j2	PROPN
ejpam-3860	237	32	.	.	PUNCT
ejpam-3860	238	1	this	this	PRON
ejpam-3860	238	2	implies	imply	VERB
ejpam-3860	238	3	(	(	PUNCT
ejpam-3860	238	4	e1	e1	NOUN
ejpam-3860	238	5	,	,	PUNCT
ejpam-3860	238	6	i1j1	i1j1	NOUN
ejpam-3860	238	7	)	)	PUNCT
ejpam-3860	238	8	and	and	CCONJ
ejpam-3860	238	9	(	(	PUNCT
ejpam-3860	238	10	e2	e2	PROPN
ejpam-3860	238	11	,	,	PUNCT
ejpam-3860	238	12	i2j2	i2j2	X
ejpam-3860	238	13	)	)	PUNCT
ejpam-3860	238	14	are	be	AUX
ejpam-3860	238	15	non	non	ADJ
ejpam-3860	238	16	-	-	NOUN
ejpam-3860	238	17	adjacents	adjacent	NOUN
ejpam-3860	238	18	.	.	PUNCT
ejpam-3860	239	1	note	note	VERB
ejpam-3860	239	2	that	that	SCONJ
ejpam-3860	239	3	for	for	ADP
ejpam-3860	239	4	any	any	DET
ejpam-3860	239	5	(	(	PUNCT
ejpam-3860	239	6	e1	e1	PROPN
ejpam-3860	239	7	,	,	PUNCT
ejpam-3860	239	8	i1	i1	PROPN
ejpam-3860	239	9	)	)	PUNCT
ejpam-3860	239	10	,	,	PUNCT
ejpam-3860	239	11	(	(	PUNCT
ejpam-3860	239	12	e2	e2	PROPN
ejpam-3860	239	13	,	,	PUNCT
ejpam-3860	239	14	0	0	NUM
ejpam-3860	239	15	)	)	PUNCT
ejpam-3860	239	16	∈	∈	PROPN
ejpam-3860	239	17	s	s	PROPN
ejpam-3860	239	18	,	,	PUNCT
ejpam-3860	239	19	e1	e1	PROPN
ejpam-3860	239	20	is	be	AUX
ejpam-3860	239	21	odd	odd	ADJ
ejpam-3860	239	22	while	while	SCONJ
ejpam-3860	239	23	e2	e2	PROPN
ejpam-3860	239	24	is	be	AUX
ejpam-3860	239	25	even	even	ADV
ejpam-3860	239	26	and	and	CCONJ
ejpam-3860	239	27	so	so	ADV
ejpam-3860	239	28	,	,	PUNCT
ejpam-3860	239	29	(	(	PUNCT
ejpam-3860	239	30	e1	e1	PROPN
ejpam-3860	239	31	,	,	PUNCT
ejpam-3860	239	32	i1	i1	PROPN
ejpam-3860	239	33	)	)	PUNCT
ejpam-3860	239	34	,	,	PUNCT
ejpam-3860	239	35	(	(	PUNCT
ejpam-3860	239	36	e2	e2	PROPN
ejpam-3860	239	37	,	,	PUNCT
ejpam-3860	239	38	0	0	NUM
ejpam-3860	239	39	)	)	PUNCT
ejpam-3860	239	40	are	be	AUX
ejpam-3860	239	41	non	non	ADJ
ejpam-3860	239	42	-	-	NOUN
ejpam-3860	239	43	adjacents	adjacent	NOUN
ejpam-3860	239	44	.	.	PUNCT
ejpam-3860	240	1	hence	hence	ADV
ejpam-3860	240	2	,	,	PUNCT
ejpam-3860	240	3	none	none	NOUN
ejpam-3860	240	4	of	of	ADP
ejpam-3860	240	5	the	the	DET
ejpam-3860	240	6	vertices	vertex	NOUN
ejpam-3860	240	7	in	in	ADP
ejpam-3860	240	8	s	s	NOUN
ejpam-3860	240	9	are	be	AUX
ejpam-3860	240	10	adjacent	adjacent	ADJ
ejpam-3860	240	11	.	.	PUNCT
ejpam-3860	241	1	n.	n.	PROPN
ejpam-3860	241	2	abdulcarim	abdulcarim	PROPN
ejpam-3860	241	3	,	,	PUNCT
ejpam-3860	241	4	s.	s.	PROPN
ejpam-3860	241	5	dagondon	dagondon	PROPN
ejpam-3860	241	6	,	,	PUNCT
ejpam-3860	241	7	e.	e.	PROPN
ejpam-3860	241	8	chacon	chacon	PROPN
ejpam-3860	241	9	/	/	SYM
ejpam-3860	241	10	eur	eur	PROPN
ejpam-3860	241	11	.	.	PUNCT
ejpam-3860	242	1	j.	j.	PROPN
ejpam-3860	242	2	pure	pure	PROPN
ejpam-3860	242	3	appl	appl	PROPN
ejpam-3860	242	4	.	.	PROPN
ejpam-3860	242	5	math	math	PROPN
ejpam-3860	242	6	,	,	PUNCT
ejpam-3860	242	7	14	14	NUM
ejpam-3860	242	8	(	(	PUNCT
ejpam-3860	242	9	1	1	NUM
ejpam-3860	242	10	)	)	PUNCT
ejpam-3860	242	11	(	(	PUNCT
ejpam-3860	242	12	2021	2021	NUM
ejpam-3860	242	13	)	)	PUNCT
ejpam-3860	242	14	,	,	PUNCT
ejpam-3860	242	15	173	173	NUM
ejpam-3860	242	16	-	-	SYM
ejpam-3860	242	17	191	191	NUM
ejpam-3860	242	18	183	183	NUM
ejpam-3860	242	19	(	(	PUNCT
ejpam-3860	242	20	1	1	NUM
ejpam-3860	242	21	,	,	PUNCT
ejpam-3860	242	22	13	13	NUM
ejpam-3860	242	23	)	)	PUNCT
ejpam-3860	242	24	(	(	PUNCT
ejpam-3860	242	25	1	1	NUM
ejpam-3860	242	26	,	,	PUNCT
ejpam-3860	242	27	12	12	NUM
ejpam-3860	242	28	)	)	PUNCT
ejpam-3860	242	29	(	(	PUNCT
ejpam-3860	242	30	1	1	NUM
ejpam-3860	242	31	,	,	PUNCT
ejpam-3860	242	32	11	11	NUM
ejpam-3860	242	33	)	)	PUNCT
ejpam-3860	242	34	(	(	PUNCT
ejpam-3860	242	35	1	1	NUM
ejpam-3860	242	36	,	,	PUNCT
ejpam-3860	242	37	1n	1n	NUM
ejpam-3860	242	38	−	−	PROPN
ejpam-3860	242	39	1	1	NUM
ejpam-3860	242	40	)	)	PUNCT
ejpam-3860	242	41	(	(	PUNCT
ejpam-3860	242	42	1	1	NUM
ejpam-3860	242	43	,	,	PUNCT
ejpam-3860	242	44	1n	1n	NUM
ejpam-3860	242	45	)	)	PUNCT
ejpam-3860	242	46	(	(	PUNCT
ejpam-3860	242	47	1	1	NUM
ejpam-3860	242	48	,	,	PUNCT
ejpam-3860	242	49	23	23	NUM
ejpam-3860	242	50	)	)	PUNCT
ejpam-3860	242	51	(	(	PUNCT
ejpam-3860	242	52	1	1	NUM
ejpam-3860	242	53	,	,	PUNCT
ejpam-3860	242	54	22	22	NUM
ejpam-3860	242	55	)	)	PUNCT
ejpam-3860	242	56	(	(	PUNCT
ejpam-3860	242	57	1	1	NUM
ejpam-3860	242	58	,	,	PUNCT
ejpam-3860	242	59	21	21	NUM
ejpam-3860	242	60	)	)	PUNCT
ejpam-3860	242	61	(	(	PUNCT
ejpam-3860	242	62	1	1	NUM
ejpam-3860	242	63	,	,	PUNCT
ejpam-3860	242	64	2n	2n	NUM
ejpam-3860	242	65	−	−	ADP
ejpam-3860	242	66	1	1	NUM
ejpam-3860	242	67	)	)	PUNCT
ejpam-3860	242	68	(	(	PUNCT
ejpam-3860	242	69	1	1	NUM
ejpam-3860	242	70	,	,	PUNCT
ejpam-3860	242	71	2n	2n	NUM
ejpam-3860	242	72	)	)	PUNCT
ejpam-3860	242	73	(	(	PUNCT
ejpam-3860	242	74	1,m3	1,m3	NUM
ejpam-3860	242	75	)	)	PUNCT
ejpam-3860	242	76	(	(	PUNCT
ejpam-3860	242	77	1,m2	1,m2	NUM
ejpam-3860	242	78	)	)	PUNCT
ejpam-3860	242	79	(	(	PUNCT
ejpam-3860	242	80	1,m1	1,m1	NUM
ejpam-3860	242	81	)	)	PUNCT
ejpam-3860	242	82	(	(	PUNCT
ejpam-3860	242	83	1,mn	1,mn	NUM
ejpam-3860	242	84	−	−	NOUN
ejpam-3860	242	85	1	1	NUM
ejpam-3860	242	86	)	)	PUNCT
ejpam-3860	242	87	(	(	PUNCT
ejpam-3860	242	88	1,mn	1,mn	NUM
ejpam-3860	242	89	)	)	PUNCT
ejpam-3860	242	90	(	(	PUNCT
ejpam-3860	242	91	1	1	NUM
ejpam-3860	242	92	,	,	PUNCT
ejpam-3860	242	93	0	0	NUM
ejpam-3860	242	94	)	)	PUNCT
ejpam-3860	242	95	·	·	PUNCT
ejpam-3860	242	96	·	·	PUNCT
ejpam-3860	242	97	·	·	PUNCT
ejpam-3860	243	1	(	(	PUNCT
ejpam-3860	243	2	2	2	NUM
ejpam-3860	243	3	,	,	PUNCT
ejpam-3860	243	4	13	13	NUM
ejpam-3860	243	5	)	)	PUNCT
ejpam-3860	243	6	(	(	PUNCT
ejpam-3860	243	7	2	2	NUM
ejpam-3860	243	8	,	,	PUNCT
ejpam-3860	243	9	12	12	NUM
ejpam-3860	243	10	)	)	PUNCT
ejpam-3860	243	11	(	(	PUNCT
ejpam-3860	243	12	2	2	NUM
ejpam-3860	243	13	,	,	PUNCT
ejpam-3860	243	14	11	11	NUM
ejpam-3860	243	15	)	)	PUNCT
ejpam-3860	243	16	(	(	PUNCT
ejpam-3860	243	17	2	2	NUM
ejpam-3860	243	18	,	,	PUNCT
ejpam-3860	243	19	1n	1n	NUM
ejpam-3860	243	20	−	−	PROPN
ejpam-3860	243	21	1	1	NUM
ejpam-3860	243	22	)	)	PUNCT
ejpam-3860	243	23	(	(	PUNCT
ejpam-3860	243	24	2	2	NUM
ejpam-3860	243	25	,	,	PUNCT
ejpam-3860	243	26	1n	1n	NUM
ejpam-3860	243	27	)	)	PUNCT
ejpam-3860	243	28	(	(	PUNCT
ejpam-3860	243	29	2	2	NUM
ejpam-3860	243	30	,	,	PUNCT
ejpam-3860	243	31	23	23	NUM
ejpam-3860	243	32	)	)	PUNCT
ejpam-3860	243	33	(	(	PUNCT
ejpam-3860	243	34	2	2	NUM
ejpam-3860	243	35	,	,	PUNCT
ejpam-3860	243	36	22	22	NUM
ejpam-3860	243	37	)	)	PUNCT
ejpam-3860	243	38	(	(	PUNCT
ejpam-3860	243	39	2	2	NUM
ejpam-3860	243	40	,	,	PUNCT
ejpam-3860	243	41	21	21	NUM
ejpam-3860	243	42	)	)	PUNCT
ejpam-3860	243	43	(	(	PUNCT
ejpam-3860	243	44	2	2	NUM
ejpam-3860	243	45	,	,	PUNCT
ejpam-3860	243	46	2n	2n	NUM
ejpam-3860	243	47	−	−	ADP
ejpam-3860	243	48	1	1	NUM
ejpam-3860	243	49	)	)	PUNCT
ejpam-3860	243	50	(	(	PUNCT
ejpam-3860	243	51	2	2	NUM
ejpam-3860	243	52	,	,	PUNCT
ejpam-3860	243	53	2n	2n	NUM
ejpam-3860	243	54	)	)	PUNCT
ejpam-3860	243	55	(	(	PUNCT
ejpam-3860	243	56	2,m3	2,m3	NUM
ejpam-3860	243	57	)	)	PUNCT
ejpam-3860	243	58	(	(	PUNCT
ejpam-3860	243	59	2,m2	2,m2	NUM
ejpam-3860	243	60	)	)	PUNCT
ejpam-3860	243	61	(	(	PUNCT
ejpam-3860	243	62	2,m1	2,m1	NUM
ejpam-3860	243	63	)	)	PUNCT
ejpam-3860	243	64	(	(	PUNCT
ejpam-3860	243	65	2,mn	2,mn	NUM
ejpam-3860	243	66	−	−	NOUN
ejpam-3860	243	67	1	1	NUM
ejpam-3860	243	68	)	)	PUNCT
ejpam-3860	243	69	(	(	PUNCT
ejpam-3860	243	70	2,mn	2,mn	NUM
ejpam-3860	243	71	)	)	PUNCT
ejpam-3860	243	72	·	·	PUNCT
ejpam-3860	243	73	·	·	PUNCT
ejpam-3860	243	74	·	·	PUNCT
ejpam-3860	243	75	(	(	PUNCT
ejpam-3860	243	76	2	2	NUM
ejpam-3860	243	77	,	,	PUNCT
ejpam-3860	243	78	0	0	NUM
ejpam-3860	243	79	)	)	PUNCT
ejpam-3860	243	80	(	(	PUNCT
ejpam-3860	243	81	k	k	NOUN
ejpam-3860	243	82	,	,	PUNCT
ejpam-3860	243	83	13	13	NUM
ejpam-3860	243	84	)	)	PUNCT
ejpam-3860	243	85	(	(	PUNCT
ejpam-3860	243	86	k	k	NOUN
ejpam-3860	243	87	,	,	PUNCT
ejpam-3860	243	88	12	12	NUM
ejpam-3860	243	89	)	)	PUNCT
ejpam-3860	243	90	(	(	PUNCT
ejpam-3860	243	91	k	k	NOUN
ejpam-3860	243	92	,	,	PUNCT
ejpam-3860	243	93	11	11	NUM
ejpam-3860	243	94	)	)	PUNCT
ejpam-3860	243	95	(	(	PUNCT
ejpam-3860	243	96	k	k	X
ejpam-3860	243	97	,	,	PUNCT
ejpam-3860	243	98	1n	1n	NUM
ejpam-3860	243	99	−	−	NOUN
ejpam-3860	243	100	1	1	NUM
ejpam-3860	243	101	)	)	PUNCT
ejpam-3860	243	102	(	(	PUNCT
ejpam-3860	243	103	k	k	X
ejpam-3860	243	104	,	,	PUNCT
ejpam-3860	243	105	1n	1n	NUM
ejpam-3860	243	106	)	)	PUNCT
ejpam-3860	243	107	(	(	PUNCT
ejpam-3860	243	108	k	k	NOUN
ejpam-3860	243	109	,	,	PUNCT
ejpam-3860	243	110	23	23	NUM
ejpam-3860	243	111	)	)	PUNCT
ejpam-3860	243	112	(	(	PUNCT
ejpam-3860	243	113	k	k	X
ejpam-3860	243	114	,	,	PUNCT
ejpam-3860	243	115	22	22	NUM
ejpam-3860	243	116	)	)	PUNCT
ejpam-3860	243	117	(	(	PUNCT
ejpam-3860	243	118	k	k	X
ejpam-3860	243	119	,	,	PUNCT
ejpam-3860	243	120	21	21	NUM
ejpam-3860	243	121	)	)	PUNCT
ejpam-3860	243	122	(	(	PUNCT
ejpam-3860	243	123	k	k	X
ejpam-3860	243	124	,	,	PUNCT
ejpam-3860	243	125	2n	2n	NUM
ejpam-3860	243	126	−	−	ADP
ejpam-3860	243	127	1	1	NUM
ejpam-3860	243	128	)	)	PUNCT
ejpam-3860	243	129	(	(	PUNCT
ejpam-3860	243	130	k	k	X
ejpam-3860	243	131	,	,	PUNCT
ejpam-3860	243	132	2n	2n	NUM
ejpam-3860	243	133	)	)	PUNCT
ejpam-3860	243	134	(	(	PUNCT
ejpam-3860	243	135	k	k	X
ejpam-3860	243	136	,	,	PUNCT
ejpam-3860	243	137	m3	m3	PROPN
ejpam-3860	243	138	)	)	PUNCT
ejpam-3860	243	139	(	(	PUNCT
ejpam-3860	243	140	k	k	X
ejpam-3860	243	141	,	,	PUNCT
ejpam-3860	243	142	m2	m2	PROPN
ejpam-3860	243	143	)	)	PUNCT
ejpam-3860	243	144	(	(	PUNCT
ejpam-3860	243	145	k	k	X
ejpam-3860	243	146	,	,	PUNCT
ejpam-3860	243	147	m1	m1	PROPN
ejpam-3860	243	148	)	)	PUNCT
ejpam-3860	243	149	(	(	PUNCT
ejpam-3860	243	150	k	k	X
ejpam-3860	243	151	,	,	PUNCT
ejpam-3860	243	152	mn	mn	PROPN
ejpam-3860	243	153	−	−	PROPN
ejpam-3860	243	154	1	1	NUM
ejpam-3860	243	155	)	)	PUNCT
ejpam-3860	243	156	(	(	PUNCT
ejpam-3860	243	157	k	k	X
ejpam-3860	243	158	,	,	PUNCT
ejpam-3860	243	159	mn	mn	PROPN
ejpam-3860	243	160	)	)	PUNCT
ejpam-3860	243	161	(	(	PUNCT
ejpam-3860	243	162	k	k	NOUN
ejpam-3860	243	163	,	,	PUNCT
ejpam-3860	243	164	0	0	NUM
ejpam-3860	243	165	)	)	PUNCT
ejpam-3860	243	166	·	·	PUNCT
ejpam-3860	243	167	·	·	PUNCT
ejpam-3860	243	168	·	·	PUNCT
ejpam-3860	243	169	now	now	ADV
ejpam-3860	243	170	,	,	PUNCT
ejpam-3860	243	171	we	we	PRON
ejpam-3860	243	172	will	will	AUX
ejpam-3860	243	173	show	show	VERB
ejpam-3860	243	174	that	that	SCONJ
ejpam-3860	243	175	⋃	⋃	ADP
ejpam-3860	243	176	v∈s	v∈s	ADJ
ejpam-3860	243	177	〈	〈	PROPN
ejpam-3860	243	178	n	n	PRON
ejpam-3860	243	179	[	[	X
ejpam-3860	243	180	v	v	NOUN
ejpam-3860	243	181	]	]	X
ejpam-3860	243	182	〉	〉	NOUN
ejpam-3860	243	183	=	=	SYM
ejpam-3860	243	184	pk	pk	PROPN
ejpam-3860	243	185	�	�	PROPN
ejpam-3860	243	186	bm	bm	PROPN
ejpam-3860	243	187	,	,	PUNCT
ejpam-3860	243	188	n.	n.	PROPN
ejpam-3860	243	189	assume	assume	VERB
ejpam-3860	243	190	to	to	ADP
ejpam-3860	243	191	the	the	DET
ejpam-3860	243	192	contrary	contrary	NOUN
ejpam-3860	243	193	that	that	SCONJ
ejpam-3860	243	194	⋃	⋃	PUNCT
ejpam-3860	243	195	v∈s	v∈s	ADJ
ejpam-3860	243	196	〈	〈	PROPN
ejpam-3860	243	197	n	n	PRON
ejpam-3860	243	198	[	[	X
ejpam-3860	243	199	v	v	NOUN
ejpam-3860	243	200	]	]	X
ejpam-3860	243	201	〉	〉	PROPN
ejpam-3860	243	202	6=	6=	SYM
ejpam-3860	243	203	pk	pk	PROPN
ejpam-3860	243	204	�	�	PROPN
ejpam-3860	243	205	bm	bm	PROPN
ejpam-3860	243	206	,	,	PUNCT
ejpam-3860	243	207	n.	n.	PROPN
ejpam-3860	243	208	then	then	ADV
ejpam-3860	243	209	there	there	PRON
ejpam-3860	243	210	exists	exist	VERB
ejpam-3860	243	211	xy	xy	PROPN
ejpam-3860	243	212	∈	∈	PROPN
ejpam-3860	243	213	e(pk	e(pk	PROPN
ejpam-3860	243	214	�	�	PROPN
ejpam-3860	243	215	bm	bm	PROPN
ejpam-3860	243	216	,	,	PUNCT
ejpam-3860	243	217	n	n	CCONJ
ejpam-3860	243	218	)	)	PUNCT
ejpam-3860	243	219	such	such	ADJ
ejpam-3860	243	220	that	that	PRON
ejpam-3860	243	221	xy	xy	PROPN
ejpam-3860	243	222	/∈	/∈	PUNCT
ejpam-3860	244	1	e	e	X
ejpam-3860	244	2	(	(	PUNCT
ejpam-3860	244	3	⋃	⋃	ADP
ejpam-3860	244	4	v∈s	v∈s	ADJ
ejpam-3860	244	5	〈	〈	PROPN
ejpam-3860	244	6	n	n	PRON
ejpam-3860	244	7	[	[	X
ejpam-3860	244	8	v	v	NOUN
ejpam-3860	244	9	]	]	X
ejpam-3860	244	10	〉	〉	NUM
ejpam-3860	244	11	)	)	PUNCT
ejpam-3860	244	12	.	.	PUNCT
ejpam-3860	245	1	case	case	NOUN
ejpam-3860	246	1	i	i	PRON
ejpam-3860	246	2	:	:	PUNCT
ejpam-3860	246	3	x	x	SYM
ejpam-3860	246	4	=	=	SYM
ejpam-3860	246	5	(	(	PUNCT
ejpam-3860	246	6	e1	e1	PROPN
ejpam-3860	246	7	,	,	PUNCT
ejpam-3860	246	8	i1j1	i1j1	NOUN
ejpam-3860	246	9	)	)	PUNCT
ejpam-3860	246	10	,	,	PUNCT
ejpam-3860	246	11	y	y	PROPN
ejpam-3860	246	12	=	=	PRON
ejpam-3860	246	13	(	(	PUNCT
ejpam-3860	246	14	e2	e2	PROPN
ejpam-3860	246	15	,	,	PUNCT
ejpam-3860	246	16	i2j2	i2j2	PROPN
ejpam-3860	246	17	)	)	PUNCT
ejpam-3860	246	18	i.	i.	NOUN
ejpam-3860	246	19	consider	consider	VERB
ejpam-3860	246	20	e1	e1	PROPN
ejpam-3860	246	21	=	=	SYM
ejpam-3860	246	22	e2	e2	PROPN
ejpam-3860	246	23	,	,	PUNCT
ejpam-3860	246	24	i1	i1	PROPN
ejpam-3860	246	25	=	=	PROPN
ejpam-3860	246	26	i2	i2	PROPN
ejpam-3860	246	27	and	and	CCONJ
ejpam-3860	246	28	either	either	CCONJ
ejpam-3860	246	29	j1	j1	PROPN
ejpam-3860	246	30	=	=	SYM
ejpam-3860	246	31	n	n	PROPN
ejpam-3860	246	32	or	or	CCONJ
ejpam-3860	246	33	j2	j2	PROPN
ejpam-3860	246	34	=	=	PROPN
ejpam-3860	246	35	n.	n.	PROPN
ejpam-3860	246	36	when	when	SCONJ
ejpam-3860	246	37	e1	e1	PROPN
ejpam-3860	246	38	=	=	SYM
ejpam-3860	246	39	e2	e2	PROPN
ejpam-3860	246	40	is	be	AUX
ejpam-3860	246	41	even	even	ADV
ejpam-3860	246	42	,	,	PUNCT
ejpam-3860	246	43	(	(	PUNCT
ejpam-3860	246	44	e	e	NOUN
ejpam-3860	246	45	,	,	PUNCT
ejpam-3860	246	46	in	in	ADP
ejpam-3860	246	47	)	)	PUNCT
ejpam-3860	246	48	∈	∈	PROPN
ejpam-3860	246	49	bq	bq	NOUN
ejpam-3860	247	1	⊆	⊆	NUM
ejpam-3860	247	2	s	s	NOUN
ejpam-3860	247	3	while	while	SCONJ
ejpam-3860	247	4	when	when	SCONJ
ejpam-3860	247	5	e1	e1	PROPN
ejpam-3860	247	6	=	=	PROPN
ejpam-3860	247	7	e2	e2	PROPN
ejpam-3860	247	8	is	be	AUX
ejpam-3860	247	9	odd	odd	ADJ
ejpam-3860	247	10	,	,	PUNCT
ejpam-3860	247	11	(	(	PUNCT
ejpam-3860	247	12	e	e	NOUN
ejpam-3860	247	13	,	,	PUNCT
ejpam-3860	247	14	ij	ij	NOUN
ejpam-3860	247	15	)	)	PUNCT
ejpam-3860	247	16	∈	∈	PROPN
ejpam-3860	247	17	ap	ap	PROPN
ejpam-3860	248	1	⊆	⊆	NUM
ejpam-3860	248	2	s.	s.	PROPN
ejpam-3860	248	3	this	this	PRON
ejpam-3860	248	4	implies	imply	VERB
ejpam-3860	248	5	either	either	CCONJ
ejpam-3860	248	6	(	(	PUNCT
ejpam-3860	248	7	e1	e1	NOUN
ejpam-3860	248	8	,	,	PUNCT
ejpam-3860	248	9	i1j1	i1j1	NOUN
ejpam-3860	248	10	)	)	PUNCT
ejpam-3860	248	11	∈	∈	PROPN
ejpam-3860	248	12	s	s	PART
ejpam-3860	248	13	or	or	CCONJ
ejpam-3860	248	14	(	(	PUNCT
ejpam-3860	248	15	e2	e2	PROPN
ejpam-3860	248	16	,	,	PUNCT
ejpam-3860	248	17	i2j2	i2j2	PROPN
ejpam-3860	248	18	)	)	PUNCT
ejpam-3860	248	19	∈	∈	PROPN
ejpam-3860	248	20	s	s	PART
ejpam-3860	248	21	and	and	CCONJ
ejpam-3860	248	22	follows	follow	VERB
ejpam-3860	248	23	that	that	PRON
ejpam-3860	248	24	(	(	PUNCT
ejpam-3860	248	25	e1	e1	PROPN
ejpam-3860	248	26	,	,	PUNCT
ejpam-3860	248	27	i1j1)(e2	i1j1)(e2	PROPN
ejpam-3860	248	28	,	,	PUNCT
ejpam-3860	248	29	i2j2	i2j2	PROPN
ejpam-3860	248	30	)	)	PUNCT
ejpam-3860	248	31	∈	∈	PROPN
ejpam-3860	248	32	e	e	X
ejpam-3860	248	33	(	(	PUNCT
ejpam-3860	248	34	⋃	⋃	ADP
ejpam-3860	248	35	v∈s	v∈s	ADJ
ejpam-3860	248	36	〈	〈	PROPN
ejpam-3860	248	37	n	n	PRON
ejpam-3860	248	38	[	[	X
ejpam-3860	248	39	v	v	NOUN
ejpam-3860	248	40	]	]	X
ejpam-3860	248	41	〉	〉	NOUN
ejpam-3860	248	42	)	)	PUNCT
ejpam-3860	248	43	which	which	PRON
ejpam-3860	248	44	is	be	AUX
ejpam-3860	248	45	a	a	DET
ejpam-3860	248	46	contradiction	contradiction	NOUN
ejpam-3860	248	47	.	.	PUNCT
ejpam-3860	249	1	ii	ii	X
ejpam-3860	249	2	.	.	PUNCT
ejpam-3860	249	3	consider	consider	VERB
ejpam-3860	249	4	e1	e1	PROPN
ejpam-3860	249	5	=	=	SYM
ejpam-3860	249	6	e2	e2	PROPN
ejpam-3860	249	7	+	+	CCONJ
ejpam-3860	249	8	1	1	NUM
ejpam-3860	249	9	,	,	PUNCT
ejpam-3860	249	10	i1	i1	PROPN
ejpam-3860	249	11	=	=	PROPN
ejpam-3860	249	12	i2	i2	PROPN
ejpam-3860	249	13	and	and	CCONJ
ejpam-3860	249	14	j1	j1	PROPN
ejpam-3860	249	15	=	=	SYM
ejpam-3860	249	16	j2	j2	PROPN
ejpam-3860	249	17	.	.	PUNCT
ejpam-3860	250	1	then	then	ADV
ejpam-3860	250	2	either	either	CCONJ
ejpam-3860	250	3	e1	e1	NOUN
ejpam-3860	250	4	is	be	AUX
ejpam-3860	250	5	odd	odd	ADJ
ejpam-3860	250	6	and	and	CCONJ
ejpam-3860	250	7	e2	e2	PROPN
ejpam-3860	250	8	is	be	AUX
ejpam-3860	250	9	even	even	ADV
ejpam-3860	250	10	or	or	CCONJ
ejpam-3860	250	11	e1	e1	NOUN
ejpam-3860	250	12	is	be	AUX
ejpam-3860	250	13	even	even	ADV
ejpam-3860	250	14	and	and	CCONJ
ejpam-3860	250	15	e2	e2	PROPN
ejpam-3860	250	16	is	be	AUX
ejpam-3860	250	17	odd	odd	ADJ
ejpam-3860	250	18	.	.	PUNCT
ejpam-3860	251	1	but	but	CCONJ
ejpam-3860	251	2	in	in	ADP
ejpam-3860	251	3	either	either	DET
ejpam-3860	251	4	cases	case	NOUN
ejpam-3860	251	5	,	,	PUNCT
ejpam-3860	251	6	(	(	PUNCT
ejpam-3860	251	7	e	e	NOUN
ejpam-3860	251	8	,	,	PUNCT
ejpam-3860	251	9	ij	ij	NOUN
ejpam-3860	251	10	)	)	PUNCT
ejpam-3860	251	11	∈	∈	PROPN
ejpam-3860	251	12	s	s	VERB
ejpam-3860	251	13	when	when	SCONJ
ejpam-3860	251	14	e	e	NOUN
ejpam-3860	251	15	is	be	AUX
ejpam-3860	251	16	odd	odd	ADJ
ejpam-3860	251	17	and	and	CCONJ
ejpam-3860	251	18	consequently	consequently	ADV
ejpam-3860	251	19	,	,	PUNCT
ejpam-3860	251	20	(	(	PUNCT
ejpam-3860	251	21	e1	e1	PROPN
ejpam-3860	251	22	,	,	PUNCT
ejpam-3860	251	23	i1j1)(e2	i1j1)(e2	PROPN
ejpam-3860	251	24	,	,	PUNCT
ejpam-3860	251	25	i2j2	i2j2	PROPN
ejpam-3860	251	26	)	)	PUNCT
ejpam-3860	251	27	∈	∈	PROPN
ejpam-3860	251	28	(	(	PUNCT
ejpam-3860	251	29	⋃	⋃	NOUN
ejpam-3860	251	30	v∈s	v∈s	ADJ
ejpam-3860	251	31	〈	〈	PROPN
ejpam-3860	251	32	n	n	PRON
ejpam-3860	251	33	[	[	X
ejpam-3860	251	34	v	v	NOUN
ejpam-3860	251	35	]	]	X
ejpam-3860	251	36	〉	〉	NUM
ejpam-3860	251	37	)	)	PUNCT
ejpam-3860	251	38	.	.	PUNCT
ejpam-3860	252	1	this	this	PRON
ejpam-3860	252	2	is	be	AUX
ejpam-3860	252	3	a	a	DET
ejpam-3860	252	4	contradiction	contradiction	NOUN
ejpam-3860	252	5	.	.	PUNCT
ejpam-3860	253	1	case	case	NOUN
ejpam-3860	253	2	ii	ii	NOUN
ejpam-3860	253	3	:	:	PUNCT
ejpam-3860	253	4	x	x	SYM
ejpam-3860	253	5	=	=	SYM
ejpam-3860	253	6	(	(	PUNCT
ejpam-3860	253	7	e1	e1	PROPN
ejpam-3860	253	8	,	,	PUNCT
ejpam-3860	253	9	i1	i1	PROPN
ejpam-3860	253	10	)	)	PUNCT
ejpam-3860	253	11	,	,	PUNCT
ejpam-3860	253	12	y	y	PROPN
ejpam-3860	253	13	=	=	PRON
ejpam-3860	253	14	(	(	PUNCT
ejpam-3860	253	15	e2	e2	PROPN
ejpam-3860	253	16	,	,	PUNCT
ejpam-3860	253	17	0	0	NUM
ejpam-3860	253	18	)	)	PUNCT
ejpam-3860	253	19	n.	n.	NOUN
ejpam-3860	253	20	abdulcarim	abdulcarim	PROPN
ejpam-3860	253	21	,	,	PUNCT
ejpam-3860	253	22	s.	s.	PROPN
ejpam-3860	253	23	dagondon	dagondon	PROPN
ejpam-3860	253	24	,	,	PUNCT
ejpam-3860	253	25	e.	e.	PROPN
ejpam-3860	253	26	chacon	chacon	PROPN
ejpam-3860	253	27	/	/	SYM
ejpam-3860	253	28	eur	eur	PROPN
ejpam-3860	253	29	.	.	PUNCT
ejpam-3860	254	1	j.	j.	PROPN
ejpam-3860	254	2	pure	pure	PROPN
ejpam-3860	254	3	appl	appl	PROPN
ejpam-3860	254	4	.	.	PROPN
ejpam-3860	254	5	math	math	PROPN
ejpam-3860	254	6	,	,	PUNCT
ejpam-3860	254	7	14	14	NUM
ejpam-3860	254	8	(	(	PUNCT
ejpam-3860	254	9	1	1	NUM
ejpam-3860	254	10	)	)	PUNCT
ejpam-3860	254	11	(	(	PUNCT
ejpam-3860	254	12	2021	2021	NUM
ejpam-3860	254	13	)	)	PUNCT
ejpam-3860	254	14	,	,	PUNCT
ejpam-3860	254	15	173	173	NUM
ejpam-3860	254	16	-	-	SYM
ejpam-3860	254	17	191	191	NUM
ejpam-3860	254	18	184	184	NUM
ejpam-3860	254	19	since	since	SCONJ
ejpam-3860	254	20	(	(	PUNCT
ejpam-3860	254	21	e1	e1	NOUN
ejpam-3860	254	22	,	,	PUNCT
ejpam-3860	254	23	i1)(e2	i1)(e2	NOUN
ejpam-3860	254	24	,	,	PUNCT
ejpam-3860	254	25	0	0	NUM
ejpam-3860	254	26	)	)	PUNCT
ejpam-3860	254	27	∈	∈	PROPN
ejpam-3860	254	28	e	e	X
ejpam-3860	254	29	(	(	PUNCT
ejpam-3860	254	30	pk	pk	PROPN
ejpam-3860	254	31	�	�	PROPN
ejpam-3860	254	32	bm	bm	PROPN
ejpam-3860	254	33	,	,	PUNCT
ejpam-3860	254	34	n	n	CCONJ
ejpam-3860	254	35	)	)	PUNCT
ejpam-3860	254	36	,	,	PUNCT
ejpam-3860	254	37	e1	e1	NOUN
ejpam-3860	254	38	=	=	PROPN
ejpam-3860	254	39	e2	e2	PROPN
ejpam-3860	254	40	.	.	PUNCT
ejpam-3860	255	1	then	then	ADV
ejpam-3860	255	2	e2	e2	PROPN
ejpam-3860	255	3	must	must	AUX
ejpam-3860	255	4	be	be	AUX
ejpam-3860	255	5	odd	odd	ADJ
ejpam-3860	255	6	.	.	PUNCT
ejpam-3860	256	1	but	but	CCONJ
ejpam-3860	256	2	(	(	PUNCT
ejpam-3860	256	3	e1	e1	PROPN
ejpam-3860	256	4	,	,	PUNCT
ejpam-3860	256	5	i1	i1	PROPN
ejpam-3860	256	6	)	)	PUNCT
ejpam-3860	256	7	∈	∈	PROPN
ejpam-3860	256	8	s	s	VERB
ejpam-3860	256	9	when	when	SCONJ
ejpam-3860	256	10	e1	e1	NOUN
ejpam-3860	256	11	is	be	AUX
ejpam-3860	256	12	odd	odd	ADJ
ejpam-3860	256	13	and	and	CCONJ
ejpam-3860	256	14	so	so	ADV
ejpam-3860	256	15	,	,	PUNCT
ejpam-3860	256	16	(	(	PUNCT
ejpam-3860	256	17	e1	e1	NOUN
ejpam-3860	256	18	,	,	PUNCT
ejpam-3860	256	19	i1)(e2	i1)(e2	NOUN
ejpam-3860	256	20	,	,	PUNCT
ejpam-3860	256	21	0	0	NUM
ejpam-3860	256	22	)	)	PUNCT
ejpam-3860	256	23	∈	∈	PROPN
ejpam-3860	256	24	e	e	X
ejpam-3860	256	25	(	(	PUNCT
ejpam-3860	256	26	⋃	⋃	ADP
ejpam-3860	256	27	v∈s	v∈s	ADJ
ejpam-3860	256	28	〈	〈	PROPN
ejpam-3860	256	29	n	n	PRON
ejpam-3860	256	30	[	[	X
ejpam-3860	256	31	v	v	NOUN
ejpam-3860	256	32	]	]	X
ejpam-3860	256	33	〉	〉	NOUN
ejpam-3860	256	34	)	)	PUNCT
ejpam-3860	256	35	which	which	PRON
ejpam-3860	256	36	is	be	AUX
ejpam-3860	256	37	a	a	DET
ejpam-3860	256	38	contradiction	contradiction	NOUN
ejpam-3860	256	39	.	.	PUNCT
ejpam-3860	257	1	case	case	NOUN
ejpam-3860	257	2	iii	iii	X
ejpam-3860	257	3	:	:	PUNCT
ejpam-3860	257	4	x	x	SYM
ejpam-3860	257	5	=	=	SYM
ejpam-3860	257	6	(	(	PUNCT
ejpam-3860	257	7	e1	e1	PROPN
ejpam-3860	257	8	,	,	PUNCT
ejpam-3860	257	9	0	0	NUM
ejpam-3860	257	10	)	)	PUNCT
ejpam-3860	257	11	,	,	PUNCT
ejpam-3860	257	12	y	y	PROPN
ejpam-3860	257	13	=	=	PRON
ejpam-3860	257	14	(	(	PUNCT
ejpam-3860	257	15	e2	e2	PROPN
ejpam-3860	257	16	,	,	PUNCT
ejpam-3860	257	17	0	0	NUM
ejpam-3860	257	18	)	)	PUNCT
ejpam-3860	257	19	clearly	clearly	ADV
ejpam-3860	257	20	,	,	PUNCT
ejpam-3860	257	21	when	when	SCONJ
ejpam-3860	257	22	e1	e1	PROPN
ejpam-3860	257	23	is	be	AUX
ejpam-3860	257	24	odd	odd	ADJ
ejpam-3860	257	25	,	,	PUNCT
ejpam-3860	257	26	e2	e2	PROPN
ejpam-3860	257	27	is	be	AUX
ejpam-3860	257	28	even	even	ADV
ejpam-3860	257	29	and	and	CCONJ
ejpam-3860	257	30	vice	vice	ADV
ejpam-3860	257	31	versa	versa	ADV
ejpam-3860	257	32	.	.	PUNCT
ejpam-3860	258	1	but	but	CCONJ
ejpam-3860	258	2	(	(	PUNCT
ejpam-3860	258	3	e	e	NOUN
ejpam-3860	258	4	,	,	PUNCT
ejpam-3860	258	5	0	0	NUM
ejpam-3860	258	6	)	)	PUNCT
ejpam-3860	258	7	∈	∈	PROPN
ejpam-3860	258	8	s	s	VERB
ejpam-3860	258	9	when	when	SCONJ
ejpam-3860	258	10	e	e	NOUN
ejpam-3860	258	11	is	be	AUX
ejpam-3860	258	12	even	even	ADV
ejpam-3860	258	13	.	.	PUNCT
ejpam-3860	259	1	this	this	PRON
ejpam-3860	259	2	implies	imply	VERB
ejpam-3860	259	3	either	either	CCONJ
ejpam-3860	259	4	(	(	PUNCT
ejpam-3860	259	5	e1	e1	NOUN
ejpam-3860	259	6	,	,	PUNCT
ejpam-3860	259	7	0	0	NUM
ejpam-3860	259	8	)	)	PUNCT
ejpam-3860	259	9	∈	∈	PROPN
ejpam-3860	259	10	s	s	PART
ejpam-3860	259	11	or	or	CCONJ
ejpam-3860	259	12	(	(	PUNCT
ejpam-3860	259	13	e2	e2	PROPN
ejpam-3860	259	14	,	,	PUNCT
ejpam-3860	259	15	0	0	NUM
ejpam-3860	259	16	)	)	PUNCT
ejpam-3860	259	17	∈	∈	PROPN
ejpam-3860	259	18	s.	s.	PROPN
ejpam-3860	260	1	so	so	ADV
ejpam-3860	260	2	,	,	PUNCT
ejpam-3860	260	3	(	(	PUNCT
ejpam-3860	260	4	e1	e1	NOUN
ejpam-3860	260	5	,	,	PUNCT
ejpam-3860	260	6	0)(e2	0)(e2	NOUN
ejpam-3860	260	7	,	,	PUNCT
ejpam-3860	260	8	0	0	NUM
ejpam-3860	260	9	)	)	PUNCT
ejpam-3860	260	10	∈	∈	PROPN
ejpam-3860	260	11	e	e	X
ejpam-3860	260	12	(	(	PUNCT
ejpam-3860	260	13	⋃	⋃	ADP
ejpam-3860	260	14	v∈s	v∈s	ADJ
ejpam-3860	260	15	〈	〈	PROPN
ejpam-3860	260	16	n	n	PRON
ejpam-3860	260	17	[	[	X
ejpam-3860	260	18	v	v	NOUN
ejpam-3860	260	19	]	]	X
ejpam-3860	260	20	〉	〉	NOUN
ejpam-3860	260	21	)	)	PUNCT
ejpam-3860	260	22	which	which	PRON
ejpam-3860	260	23	is	be	AUX
ejpam-3860	260	24	a	a	DET
ejpam-3860	260	25	contradiction	contradiction	NOUN
ejpam-3860	260	26	.	.	PUNCT
ejpam-3860	261	1	in	in	ADP
ejpam-3860	261	2	either	either	PRON
ejpam-3860	261	3	of	of	ADP
ejpam-3860	261	4	the	the	DET
ejpam-3860	261	5	above	above	ADJ
ejpam-3860	261	6	cases	case	NOUN
ejpam-3860	261	7	,	,	PUNCT
ejpam-3860	261	8	we	we	PRON
ejpam-3860	261	9	arrived	arrive	VERB
ejpam-3860	261	10	at	at	ADP
ejpam-3860	261	11	a	a	DET
ejpam-3860	261	12	contradiction	contradiction	NOUN
ejpam-3860	261	13	.	.	PUNCT
ejpam-3860	262	1	thus	thus	ADV
ejpam-3860	262	2	,	,	PUNCT
ejpam-3860	262	3	xy	xy	PROPN
ejpam-3860	262	4	∈	∈	PROPN
ejpam-3860	262	5	e	e	X
ejpam-3860	262	6	(	(	PUNCT
ejpam-3860	262	7	⋃	⋃	ADP
ejpam-3860	262	8	v∈s	v∈s	ADJ
ejpam-3860	262	9	〈	〈	PROPN
ejpam-3860	262	10	n	n	PRON
ejpam-3860	262	11	[	[	X
ejpam-3860	262	12	v	v	NOUN
ejpam-3860	262	13	]	]	X
ejpam-3860	262	14	〉	〉	NUM
ejpam-3860	262	15	)	)	PUNCT
ejpam-3860	262	16	.	.	PUNCT
ejpam-3860	263	1	consequently	consequently	ADV
ejpam-3860	263	2	,	,	PUNCT
ejpam-3860	263	3	⋃	⋃	PUNCT
ejpam-3860	263	4	v∈s	v∈s	ADJ
ejpam-3860	263	5	〈	〈	PROPN
ejpam-3860	263	6	n	n	PRON
ejpam-3860	263	7	[	[	X
ejpam-3860	263	8	v	v	NOUN
ejpam-3860	263	9	]	]	X
ejpam-3860	263	10	〉	〉	NOUN
ejpam-3860	263	11	=	=	SYM
ejpam-3860	263	12	pk	pk	PROPN
ejpam-3860	263	13	�	�	PROPN
ejpam-3860	263	14	bm	bm	PROPN
ejpam-3860	263	15	,	,	PUNCT
ejpam-3860	263	16	n.	n.	NOUN
ejpam-3860	263	17	following	follow	VERB
ejpam-3860	263	18	same	same	ADJ
ejpam-3860	263	19	argument	argument	NOUN
ejpam-3860	263	20	in	in	ADP
ejpam-3860	263	21	s	s	PROPN
ejpam-3860	263	22	,	,	PUNCT
ejpam-3860	263	23	we	we	PRON
ejpam-3860	263	24	can	can	AUX
ejpam-3860	263	25	easily	easily	ADV
ejpam-3860	263	26	show	show	VERB
ejpam-3860	263	27	that	that	SCONJ
ejpam-3860	263	28	t	t	PROPN
ejpam-3860	263	29	is	be	AUX
ejpam-3860	263	30	also	also	ADV
ejpam-3860	263	31	an	an	DET
ejpam-3860	263	32	independent	independent	ADJ
ejpam-3860	263	33	neighborhood	neighborhood	NOUN
ejpam-3860	263	34	set	set	VERB
ejpam-3860	263	35	in	in	ADP
ejpam-3860	263	36	pk	pk	PROPN
ejpam-3860	263	37	�	�	PROPN
ejpam-3860	263	38	bm	bm	PROPN
ejpam-3860	263	39	,	,	PUNCT
ejpam-3860	263	40	n.	n.	PROPN
ejpam-3860	263	41	now	now	ADV
ejpam-3860	263	42	,	,	PUNCT
ejpam-3860	263	43	observe	observe	VERB
ejpam-3860	263	44	that	that	SCONJ
ejpam-3860	263	45	|ap|	|ap|	PRON
ejpam-3860	263	46	=	=	PRON
ejpam-3860	263	47	{	{	PUNCT
ejpam-3860	263	48	(	(	PUNCT
ejpam-3860	263	49	e	e	NOUN
ejpam-3860	263	50	,	,	PUNCT
ejpam-3860	263	51	ij	ij	NOUN
ejpam-3860	263	52	)	)	PUNCT
ejpam-3860	263	53	:	:	PUNCT
ejpam-3860	264	1	e	e	NOUN
ejpam-3860	264	2	is	be	AUX
ejpam-3860	264	3	odd	odd	ADJ
ejpam-3860	264	4	,	,	PUNCT
ejpam-3860	264	5	i	i	PRON
ejpam-3860	264	6	=	=	NOUN
ejpam-3860	264	7	1	1	NUM
ejpam-3860	264	8	,	,	PUNCT
ejpam-3860	264	9	·	·	PUNCT
ejpam-3860	264	10	·	·	PUNCT
ejpam-3860	264	11	·	·	PUNCT
ejpam-3860	264	12	,	,	PUNCT
ejpam-3860	264	13	m	m	PROPN
ejpam-3860	264	14	,	,	PUNCT
ejpam-3860	264	15	j	j	PROPN
ejpam-3860	264	16	=	=	SYM
ejpam-3860	264	17	1	1	NUM
ejpam-3860	264	18	,	,	PUNCT
ejpam-3860	264	19	·	·	PUNCT
ejpam-3860	264	20	·	·	PUNCT
ejpam-3860	264	21	·	·	PUNCT
ejpam-3860	264	22	,	,	PUNCT
ejpam-3860	264	23	n−	n−	NOUN
ejpam-3860	264	24	1	1	NUM
ejpam-3860	264	25	}	}	PUNCT
ejpam-3860	264	26	=	=	PUNCT
ejpam-3860	264	27	⌈	⌈	NOUN
ejpam-3860	264	28	k	k	X
ejpam-3860	264	29	2	2	NUM
ejpam-3860	264	30	⌉	⌉	X
ejpam-3860	264	31	m(n−	m(n−	NOUN
ejpam-3860	264	32	1	1	NUM
ejpam-3860	264	33	)	)	PUNCT
ejpam-3860	264	34	,	,	PUNCT
ejpam-3860	264	35	|aq|	|aq|	NOUN
ejpam-3860	264	36	=	=	SYM
ejpam-3860	264	37	{	{	PUNCT
ejpam-3860	264	38	(	(	PUNCT
ejpam-3860	264	39	e	e	NOUN
ejpam-3860	264	40	,	,	PUNCT
ejpam-3860	264	41	ij	ij	NOUN
ejpam-3860	264	42	)	)	PUNCT
ejpam-3860	264	43	:	:	PUNCT
ejpam-3860	264	44	e	e	X
ejpam-3860	264	45	is	be	AUX
ejpam-3860	264	46	even	even	ADV
ejpam-3860	264	47	,	,	PUNCT
ejpam-3860	264	48	i	i	PRON
ejpam-3860	264	49	=	=	NOUN
ejpam-3860	264	50	1	1	NUM
ejpam-3860	264	51	,	,	PUNCT
ejpam-3860	264	52	·	·	PUNCT
ejpam-3860	264	53	·	·	PUNCT
ejpam-3860	264	54	·	·	PUNCT
ejpam-3860	264	55	,	,	PUNCT
ejpam-3860	264	56	m	m	PROPN
ejpam-3860	264	57	,	,	PUNCT
ejpam-3860	264	58	j	j	PROPN
ejpam-3860	264	59	=	=	SYM
ejpam-3860	264	60	1	1	NUM
ejpam-3860	264	61	,	,	PUNCT
ejpam-3860	264	62	·	·	PUNCT
ejpam-3860	264	63	·	·	PUNCT
ejpam-3860	264	64	·	·	PUNCT
ejpam-3860	264	65	,	,	PUNCT
ejpam-3860	264	66	n−	n−	NOUN
ejpam-3860	264	67	1	1	NUM
ejpam-3860	264	68	}	}	PUNCT
ejpam-3860	264	69	=	=	PUNCT
ejpam-3860	265	1	⌊	⌊	VERB
ejpam-3860	265	2	k	k	X
ejpam-3860	265	3	2	2	NUM
ejpam-3860	265	4	⌋	⌋	NOUN
ejpam-3860	265	5	m(n−	m(n−	NOUN
ejpam-3860	265	6	1	1	NUM
ejpam-3860	265	7	)	)	PUNCT
ejpam-3860	265	8	,	,	PUNCT
ejpam-3860	265	9	|bp|	|bp|	PROPN
ejpam-3860	265	10	=	=	PRON
ejpam-3860	265	11	{	{	PUNCT
ejpam-3860	265	12	(	(	PUNCT
ejpam-3860	265	13	e	e	NOUN
ejpam-3860	265	14	,	,	PUNCT
ejpam-3860	265	15	0	0	NUM
ejpam-3860	265	16	)	)	PUNCT
ejpam-3860	265	17	:	:	PUNCT
ejpam-3860	266	1	e	e	NOUN
ejpam-3860	266	2	is	be	AUX
ejpam-3860	266	3	odd	odd	ADJ
ejpam-3860	266	4	}	}	PUNCT
ejpam-3860	266	5	∪	∪	X
ejpam-3860	266	6	{	{	PUNCT
ejpam-3860	266	7	(	(	PUNCT
ejpam-3860	266	8	e	e	NOUN
ejpam-3860	266	9	,	,	PUNCT
ejpam-3860	266	10	in	in	ADP
ejpam-3860	266	11	)	)	PUNCT
ejpam-3860	266	12	:	:	PUNCT
ejpam-3860	267	1	e	e	NOUN
ejpam-3860	267	2	is	be	AUX
ejpam-3860	267	3	odd	odd	ADJ
ejpam-3860	267	4	,	,	PUNCT
ejpam-3860	267	5	i	i	PRON
ejpam-3860	267	6	=	=	NOUN
ejpam-3860	267	7	1	1	NUM
ejpam-3860	267	8	,	,	PUNCT
ejpam-3860	267	9	·	·	PUNCT
ejpam-3860	267	10	·	·	PUNCT
ejpam-3860	267	11	·	·	PUNCT
ejpam-3860	267	12	,	,	PUNCT
ejpam-3860	267	13	m	m	NOUN
ejpam-3860	267	14	}	}	PUNCT
ejpam-3860	267	15	=	=	SYM
ejpam-3860	267	16	⌈	⌈	SYM
ejpam-3860	267	17	k	k	X
ejpam-3860	267	18	2	2	NUM
ejpam-3860	267	19	⌉	⌉	NOUN
ejpam-3860	267	20	+	+	CCONJ
ejpam-3860	267	21	⌈	⌈	SYM
ejpam-3860	267	22	k	k	X
ejpam-3860	267	23	2	2	NUM
ejpam-3860	267	24	⌉	⌉	X
ejpam-3860	267	25	m	m	NOUN
ejpam-3860	267	26	=	=	PUNCT
ejpam-3860	267	27	⌈	⌈	SYM
ejpam-3860	267	28	k	k	X
ejpam-3860	267	29	2	2	NUM
ejpam-3860	267	30	⌉	⌉	X
ejpam-3860	267	31	(	(	PUNCT
ejpam-3860	267	32	m+	m+	NOUN
ejpam-3860	267	33	1	1	NUM
ejpam-3860	267	34	)	)	PUNCT
ejpam-3860	267	35	and	and	CCONJ
ejpam-3860	267	36	|bq|	|bq|	PROPN
ejpam-3860	267	37	=	=	SYM
ejpam-3860	267	38	{	{	PUNCT
ejpam-3860	267	39	(	(	PUNCT
ejpam-3860	267	40	e	e	NOUN
ejpam-3860	267	41	,	,	PUNCT
ejpam-3860	267	42	0	0	NUM
ejpam-3860	267	43	)	)	PUNCT
ejpam-3860	267	44	:	:	PUNCT
ejpam-3860	268	1	e	e	X
ejpam-3860	268	2	is	be	AUX
ejpam-3860	268	3	even	even	ADV
ejpam-3860	268	4	}	}	PUNCT
ejpam-3860	268	5	∪	∪	X
ejpam-3860	268	6	{	{	PUNCT
ejpam-3860	268	7	(	(	PUNCT
ejpam-3860	268	8	e	e	NOUN
ejpam-3860	268	9	,	,	PUNCT
ejpam-3860	268	10	in	in	ADP
ejpam-3860	268	11	)	)	PUNCT
ejpam-3860	268	12	:	:	PUNCT
ejpam-3860	268	13	e	e	X
ejpam-3860	268	14	is	be	AUX
ejpam-3860	268	15	even	even	ADV
ejpam-3860	268	16	,	,	PUNCT
ejpam-3860	268	17	i	i	PRON
ejpam-3860	268	18	=	=	NOUN
ejpam-3860	268	19	1	1	NUM
ejpam-3860	268	20	,	,	PUNCT
ejpam-3860	268	21	·	·	PUNCT
ejpam-3860	268	22	·	·	PUNCT
ejpam-3860	268	23	·	·	PUNCT
ejpam-3860	268	24	,	,	PUNCT
ejpam-3860	268	25	m	m	VERB
ejpam-3860	268	26	}	}	PUNCT
ejpam-3860	268	27	=	=	PUNCT
ejpam-3860	268	28	⌊	⌊	VERB
ejpam-3860	268	29	k	k	X
ejpam-3860	268	30	2	2	NUM
ejpam-3860	268	31	⌋	⌋	NOUN
ejpam-3860	268	32	+	+	CCONJ
ejpam-3860	268	33	⌊	⌊	X
ejpam-3860	268	34	k	k	PROPN
ejpam-3860	268	35	2	2	NUM
ejpam-3860	268	36	⌋	⌋	NOUN
ejpam-3860	268	37	m	m	NOUN
ejpam-3860	268	38	=	=	PUNCT
ejpam-3860	269	1	⌊	⌊	VERB
ejpam-3860	269	2	k	k	X
ejpam-3860	269	3	2	2	NUM
ejpam-3860	269	4	⌋	⌋	NOUN
ejpam-3860	269	5	(	(	PUNCT
ejpam-3860	269	6	m+	m+	NOUN
ejpam-3860	269	7	1	1	NUM
ejpam-3860	269	8	)	)	PUNCT
ejpam-3860	269	9	.	.	PUNCT
ejpam-3860	270	1	thus	thus	ADV
ejpam-3860	270	2	,	,	PUNCT
ejpam-3860	270	3	|s|	|s|	PROPN
ejpam-3860	270	4	=	=	SYM
ejpam-3860	270	5	|ap|+	|ap|+	PROPN
ejpam-3860	270	6	|bq|	|bq|	PROPN
ejpam-3860	270	7	=	=	PUNCT
ejpam-3860	271	1	⌈	⌈	PROPN
ejpam-3860	271	2	k	k	PROPN
ejpam-3860	271	3	2	2	NUM
ejpam-3860	271	4	⌉	⌉	X
ejpam-3860	271	5	m(n−	m(n−	NOUN
ejpam-3860	271	6	1	1	NUM
ejpam-3860	271	7	)	)	PUNCT
ejpam-3860	271	8	+	+	CCONJ
ejpam-3860	271	9	⌊	⌊	VERB
ejpam-3860	271	10	k	k	ADJ
ejpam-3860	271	11	2	2	NUM
ejpam-3860	271	12	⌋	⌋	NOUN
ejpam-3860	271	13	(	(	PUNCT
ejpam-3860	271	14	m+	m+	NOUN
ejpam-3860	271	15	1	1	NUM
ejpam-3860	271	16	)	)	PUNCT
ejpam-3860	271	17	n.	n.	NOUN
ejpam-3860	271	18	abdulcarim	abdulcarim	PROPN
ejpam-3860	271	19	,	,	PUNCT
ejpam-3860	271	20	s.	s.	PROPN
ejpam-3860	271	21	dagondon	dagondon	PROPN
ejpam-3860	271	22	,	,	PUNCT
ejpam-3860	271	23	e.	e.	PROPN
ejpam-3860	271	24	chacon	chacon	PROPN
ejpam-3860	271	25	/	/	SYM
ejpam-3860	271	26	eur	eur	PROPN
ejpam-3860	271	27	.	.	PUNCT
ejpam-3860	272	1	j.	j.	PROPN
ejpam-3860	272	2	pure	pure	PROPN
ejpam-3860	272	3	appl	appl	PROPN
ejpam-3860	272	4	.	.	PROPN
ejpam-3860	272	5	math	math	PROPN
ejpam-3860	272	6	,	,	PUNCT
ejpam-3860	272	7	14	14	NUM
ejpam-3860	272	8	(	(	PUNCT
ejpam-3860	272	9	1	1	NUM
ejpam-3860	272	10	)	)	PUNCT
ejpam-3860	272	11	(	(	PUNCT
ejpam-3860	272	12	2021	2021	NUM
ejpam-3860	272	13	)	)	PUNCT
ejpam-3860	272	14	,	,	PUNCT
ejpam-3860	272	15	173	173	NUM
ejpam-3860	272	16	-	-	SYM
ejpam-3860	272	17	191	191	NUM
ejpam-3860	272	18	185	185	NUM
ejpam-3860	272	19	and	and	CCONJ
ejpam-3860	272	20	|t	|t	VERB
ejpam-3860	272	21	|	|	ADV
ejpam-3860	272	22	=	=	PUNCT
ejpam-3860	272	23	|aq|+	|aq|+	NOUN
ejpam-3860	272	24	|bp|	|bp|	NOUN
ejpam-3860	272	25	=	=	PUNCT
ejpam-3860	273	1	⌊	⌊	AUX
ejpam-3860	273	2	k	k	NOUN
ejpam-3860	273	3	2	2	X
ejpam-3860	273	4	⌊	⌊	AUX
ejpam-3860	273	5	m(n−	m(n−	NOUN
ejpam-3860	273	6	1	1	NUM
ejpam-3860	273	7	)	)	PUNCT
ejpam-3860	274	1	+	+	CCONJ
ejpam-3860	274	2	⌈	⌈	SYM
ejpam-3860	274	3	k	k	PROPN
ejpam-3860	274	4	2	2	NUM
ejpam-3860	274	5	⌉	⌉	X
ejpam-3860	274	6	(	(	PUNCT
ejpam-3860	274	7	m+	m+	NOUN
ejpam-3860	274	8	1	1	NUM
ejpam-3860	274	9	)	)	PUNCT
ejpam-3860	274	10	.	.	PUNCT
ejpam-3860	275	1	therefore	therefore	ADV
ejpam-3860	275	2	,	,	PUNCT
ejpam-3860	275	3	ni(pm	ni(pm	PROPN
ejpam-3860	275	4	�	�	PROPN
ejpam-3860	275	5	bm	bm	PROPN
ejpam-3860	275	6	,	,	PUNCT
ejpam-3860	275	7	n	n	CCONJ
ejpam-3860	275	8	,	,	PUNCT
ejpam-3860	275	9	x	x	NOUN
ejpam-3860	275	10	)	)	PUNCT
ejpam-3860	275	11	=	=	SYM
ejpam-3860	275	12	xb	xb	PROPN
ejpam-3860	276	1	k	k	PROPN
ejpam-3860	276	2	2cm(n−1)+d	2cm(n−1)+d	NUM
ejpam-3860	276	3	k2e(m+1	k2e(m+1	PROPN
ejpam-3860	276	4	)	)	PUNCT
ejpam-3860	277	1	+	+	CCONJ
ejpam-3860	277	2	xd	xd	INTJ
ejpam-3860	277	3	k	k	PROPN
ejpam-3860	277	4	2em(n−1)+b	2em(n−1)+b	NUM
ejpam-3860	277	5	k2c(m+1	k2c(m+1	NOUN
ejpam-3860	277	6	)	)	PUNCT
ejpam-3860	277	7	.	.	PUNCT
ejpam-3860	278	1	theorem	theorem	NOUN
ejpam-3860	278	2	4	4	NUM
ejpam-3860	278	3	.	.	X
ejpam-3860	279	1	for	for	ADP
ejpam-3860	279	2	any	any	DET
ejpam-3860	279	3	path	path	NOUN
ejpam-3860	279	4	pk	pk	NOUN
ejpam-3860	279	5	and	and	CCONJ
ejpam-3860	279	6	firecracker	firecracker	NOUN
ejpam-3860	279	7	graph	graph	NOUN
ejpam-3860	279	8	fm	fm	PROPN
ejpam-3860	279	9	,	,	PUNCT
ejpam-3860	279	10	n	n	CCONJ
ejpam-3860	279	11	,	,	PUNCT
ejpam-3860	279	12	ni(pk	ni(pk	PROPN
ejpam-3860	279	13	�	�	PROPN
ejpam-3860	279	14	fm	fm	PROPN
ejpam-3860	279	15	,	,	PUNCT
ejpam-3860	279	16	n	n	CCONJ
ejpam-3860	279	17	,	,	PUNCT
ejpam-3860	279	18	x	x	NOUN
ejpam-3860	279	19	)	)	PUNCT
ejpam-3860	279	20	=	=	PUNCT
ejpam-3860	280	1	xd	xd	NUM
ejpam-3860	280	2	k	k	PROPN
ejpam-3860	280	3	2e(dm2	2e(dm2	PROPN
ejpam-3860	280	4	e(n−1)+bm2	e(n−1)+bm2	NOUN
ejpam-3860	280	5	c)+b	c)+b	PROPN
ejpam-3860	280	6	k2c(dm2	k2c(dm2	PROPN
ejpam-3860	280	7	e+bm2	e+bm2	ADJ
ejpam-3860	280	8	c(n−1	c(n−1	PROPN
ejpam-3860	280	9	)	)	PUNCT
ejpam-3860	280	10	)	)	PUNCT
ejpam-3860	281	1	+	+	CCONJ
ejpam-3860	281	2	xb	xb	PROPN
ejpam-3860	281	3	k	k	PROPN
ejpam-3860	281	4	2c(dm2	2c(dm2	PROPN
ejpam-3860	281	5	e(n−1)+bm2	e(n−1)+bm2	NOUN
ejpam-3860	281	6	c)+d	c)+d	NOUN
ejpam-3860	281	7	k2e(dm2	k2e(dm2	PROPN
ejpam-3860	281	8	e+bm2	e+bm2	ADJ
ejpam-3860	281	9	c(n−1	c(n−1	PROPN
ejpam-3860	281	10	)	)	PUNCT
ejpam-3860	281	11	)	)	PUNCT
ejpam-3860	281	12	for	for	ADP
ejpam-3860	281	13	any	any	DET
ejpam-3860	281	14	k	k	PROPN
ejpam-3860	281	15	,	,	PUNCT
ejpam-3860	281	16	m	m	PROPN
ejpam-3860	281	17	,	,	PUNCT
ejpam-3860	281	18	n	n	PROPN
ejpam-3860	281	19	∈	∈	PROPN
ejpam-3860	281	20	zn	zn	X
ejpam-3860	281	21	.	.	PUNCT
ejpam-3860	282	1	proof	proof	NOUN
ejpam-3860	282	2	:	:	PUNCT
ejpam-3860	282	3	label	label	VERB
ejpam-3860	282	4	the	the	DET
ejpam-3860	282	5	vertices	vertex	NOUN
ejpam-3860	282	6	of	of	ADP
ejpam-3860	282	7	fm	fm	PROPN
ejpam-3860	282	8	,	,	PUNCT
ejpam-3860	282	9	n	n	X
ejpam-3860	282	10	by	by	ADP
ejpam-3860	282	11	ij	ij	NOUN
ejpam-3860	282	12	,	,	PUNCT
ejpam-3860	282	13	i	i	PRON
ejpam-3860	282	14	=	=	NOUN
ejpam-3860	282	15	1	1	NUM
ejpam-3860	282	16	,	,	PUNCT
ejpam-3860	282	17	·	·	PUNCT
ejpam-3860	282	18	·	·	PUNCT
ejpam-3860	282	19	·	·	PUNCT
ejpam-3860	282	20	,	,	PUNCT
ejpam-3860	282	21	m	m	PROPN
ejpam-3860	282	22	,	,	PUNCT
ejpam-3860	282	23	j	j	PROPN
ejpam-3860	283	1	=	=	SYM
ejpam-3860	283	2	1	1	NUM
ejpam-3860	283	3	,	,	PUNCT
ejpam-3860	283	4	·	·	PUNCT
ejpam-3860	283	5	·	·	PUNCT
ejpam-3860	283	6	·	·	PUNCT
ejpam-3860	283	7	,	,	PUNCT
ejpam-3860	283	8	n	n	CCONJ
ejpam-3860	283	9	as	as	SCONJ
ejpam-3860	283	10	shown	show	VERB
ejpam-3860	283	11	in	in	ADP
ejpam-3860	283	12	the	the	DET
ejpam-3860	283	13	figure	figure	NOUN
ejpam-3860	283	14	below	below	ADV
ejpam-3860	283	15	:	:	PUNCT
ejpam-3860	283	16	1n	1n	NUM
ejpam-3860	283	17	13	13	NUM
ejpam-3860	283	18	12	12	NUM
ejpam-3860	283	19	11	11	NUM
ejpam-3860	283	20	1n−	1n−	NUM
ejpam-3860	283	21	1	1	NUM
ejpam-3860	283	22	2n	2n	NUM
ejpam-3860	283	23	23	23	NUM
ejpam-3860	283	24	22	22	NUM
ejpam-3860	283	25	21	21	NUM
ejpam-3860	283	26	2n−	2n−	PROPN
ejpam-3860	283	27	1	1	NUM
ejpam-3860	283	28	mn	mn	PROPN
ejpam-3860	283	29	m3	m3	PROPN
ejpam-3860	283	30	m2	m2	PROPN
ejpam-3860	283	31	m1	m1	PROPN
ejpam-3860	284	1	mn−	mn−	PROPN
ejpam-3860	284	2	1	1	NUM
ejpam-3860	284	3	then	then	ADV
ejpam-3860	284	4	v	v	NOUN
ejpam-3860	284	5	(	(	PUNCT
ejpam-3860	284	6	pk	pk	PROPN
ejpam-3860	284	7	�	�	PROPN
ejpam-3860	284	8	fm	fm	PROPN
ejpam-3860	284	9	,	,	PUNCT
ejpam-3860	284	10	n	n	CCONJ
ejpam-3860	284	11	)	)	PUNCT
ejpam-3860	284	12	=	=	PRON
ejpam-3860	284	13	{	{	PUNCT
ejpam-3860	284	14	(	(	PUNCT
ejpam-3860	284	15	e	e	NOUN
ejpam-3860	284	16	,	,	PUNCT
ejpam-3860	284	17	ij	ij	NOUN
ejpam-3860	284	18	)	)	PUNCT
ejpam-3860	284	19	:	:	PUNCT
ejpam-3860	285	1	e	e	X
ejpam-3860	285	2	=	=	SYM
ejpam-3860	285	3	1	1	NUM
ejpam-3860	285	4	,	,	PUNCT
ejpam-3860	285	5	·	·	PUNCT
ejpam-3860	285	6	·	·	PUNCT
ejpam-3860	285	7	·	·	PUNCT
ejpam-3860	285	8	,	,	PUNCT
ejpam-3860	285	9	k	k	X
ejpam-3860	285	10	,	,	PUNCT
ejpam-3860	285	11	i	i	NOUN
ejpam-3860	285	12	=	=	NOUN
ejpam-3860	285	13	1	1	NUM
ejpam-3860	285	14	,	,	PUNCT
ejpam-3860	285	15	·	·	PUNCT
ejpam-3860	285	16	·	·	PUNCT
ejpam-3860	285	17	·	·	PUNCT
ejpam-3860	285	18	,	,	PUNCT
ejpam-3860	285	19	m	m	PROPN
ejpam-3860	285	20	,	,	PUNCT
ejpam-3860	285	21	j	j	PROPN
ejpam-3860	285	22	=	=	SYM
ejpam-3860	285	23	1	1	NUM
ejpam-3860	285	24	,	,	PUNCT
ejpam-3860	285	25	·	·	PUNCT
ejpam-3860	285	26	·	·	PUNCT
ejpam-3860	285	27	·	·	PUNCT
ejpam-3860	285	28	,	,	PUNCT
ejpam-3860	285	29	n	n	CCONJ
ejpam-3860	285	30	}	}	PUNCT
ejpam-3860	285	31	and	and	CCONJ
ejpam-3860	285	32	e(pk	e(pk	NOUN
ejpam-3860	285	33	�	�	NOUN
ejpam-3860	285	34	fm	fm	PROPN
ejpam-3860	285	35	,	,	PUNCT
ejpam-3860	285	36	n	n	CCONJ
ejpam-3860	285	37	)	)	PUNCT
ejpam-3860	285	38	=	=	PRON
ejpam-3860	285	39	{	{	PUNCT
ejpam-3860	285	40	(	(	PUNCT
ejpam-3860	285	41	e1	e1	PROPN
ejpam-3860	285	42	,	,	PUNCT
ejpam-3860	285	43	i1j1)(e2	i1j1)(e2	PROPN
ejpam-3860	285	44	,	,	PUNCT
ejpam-3860	285	45	i2j2	i2j2	PROPN
ejpam-3860	285	46	)	)	PUNCT
ejpam-3860	285	47	:	:	PUNCT
ejpam-3860	285	48	e1	e1	PROPN
ejpam-3860	285	49	=	=	PROPN
ejpam-3860	285	50	e2	e2	PROPN
ejpam-3860	285	51	and	and	CCONJ
ejpam-3860	285	52	i1j1i2j2	i1j1i2j2	PROPN
ejpam-3860	285	53	∈	∈	PROPN
ejpam-3860	285	54	e(fm	e(fm	PROPN
ejpam-3860	285	55	,	,	PUNCT
ejpam-3860	285	56	n	n	CCONJ
ejpam-3860	285	57	)	)	PUNCT
ejpam-3860	285	58	or	or	CCONJ
ejpam-3860	285	59	e1e2	e1e2	NOUN
ejpam-3860	285	60	∈	∈	NOUN
ejpam-3860	285	61	e(pk	e(pk	NOUN
ejpam-3860	285	62	)	)	PUNCT
ejpam-3860	285	63	and	and	CCONJ
ejpam-3860	285	64	i1	i1	PROPN
ejpam-3860	285	65	=	=	PROPN
ejpam-3860	285	66	i2	i2	PROPN
ejpam-3860	285	67	,	,	PUNCT
ejpam-3860	285	68	j1	j1	PROPN
ejpam-3860	285	69	=	=	SYM
ejpam-3860	285	70	j2	j2	PROPN
ejpam-3860	285	71	}	}	PUNCT
ejpam-3860	285	72	as	as	SCONJ
ejpam-3860	285	73	shown	show	VERB
ejpam-3860	285	74	in	in	ADP
ejpam-3860	285	75	the	the	DET
ejpam-3860	285	76	figure	figure	NOUN
ejpam-3860	285	77	below	below	ADV
ejpam-3860	285	78	:	:	PUNCT
ejpam-3860	285	79	observe	observe	VERB
ejpam-3860	285	80	that	that	SCONJ
ejpam-3860	285	81	for	for	ADP
ejpam-3860	285	82	any	any	DET
ejpam-3860	285	83	(	(	PUNCT
ejpam-3860	285	84	e1	e1	PROPN
ejpam-3860	285	85	,	,	PUNCT
ejpam-3860	285	86	i1j1)(e2	i1j1)(e2	PROPN
ejpam-3860	285	87	,	,	PUNCT
ejpam-3860	285	88	i2j2	i2j2	PROPN
ejpam-3860	285	89	)	)	PUNCT
ejpam-3860	285	90	∈	∈	PROPN
ejpam-3860	285	91	e(pk	e(pk	PROPN
ejpam-3860	285	92	�	�	NOUN
ejpam-3860	285	93	fm	fm	PROPN
ejpam-3860	285	94	,	,	PUNCT
ejpam-3860	285	95	n	n	CCONJ
ejpam-3860	285	96	)	)	PUNCT
ejpam-3860	285	97	,	,	PUNCT
ejpam-3860	285	98	either	either	CCONJ
ejpam-3860	285	99	i.	i.	NOUN
ejpam-3860	285	100	)	)	PUNCT
ejpam-3860	285	101	e1	e1	PROPN
ejpam-3860	285	102	=	=	PROPN
ejpam-3860	285	103	e2	e2	PROPN
ejpam-3860	285	104	,	,	PUNCT
ejpam-3860	285	105	i1	i1	PROPN
ejpam-3860	285	106	=	=	PROPN
ejpam-3860	285	107	i2	i2	PROPN
ejpam-3860	285	108	,	,	PUNCT
ejpam-3860	285	109	j1	j1	PROPN
ejpam-3860	285	110	=	=	SYM
ejpam-3860	285	111	n	n	PROPN
ejpam-3860	285	112	or	or	CCONJ
ejpam-3860	285	113	j2	j2	PROPN
ejpam-3860	285	114	=	=	SYM
ejpam-3860	285	115	n	n	CCONJ
ejpam-3860	285	116	;	;	PUNCT
ejpam-3860	285	117	ii	ii	PROPN
ejpam-3860	285	118	.	.	PUNCT
ejpam-3860	285	119	)	)	PUNCT
ejpam-3860	285	120	e1	e1	PROPN
ejpam-3860	285	121	=	=	PROPN
ejpam-3860	285	122	e2	e2	PROPN
ejpam-3860	285	123	,	,	PUNCT
ejpam-3860	285	124	i1	i1	PROPN
ejpam-3860	285	125	=	=	PROPN
ejpam-3860	285	126	i2	i2	PROPN
ejpam-3860	285	127	+	+	CCONJ
ejpam-3860	285	128	1	1	NUM
ejpam-3860	285	129	,	,	PUNCT
ejpam-3860	285	130	j1	j1	NOUN
ejpam-3860	285	131	=	=	SYM
ejpam-3860	285	132	1	1	NUM
ejpam-3860	285	133	=	=	SYM
ejpam-3860	285	134	j2	j2	PROPN
ejpam-3860	285	135	;	;	PUNCT
ejpam-3860	285	136	or	or	CCONJ
ejpam-3860	285	137	iii	iii	NOUN
ejpam-3860	285	138	.	.	PUNCT
ejpam-3860	285	139	)	)	PUNCT
ejpam-3860	285	140	e1	e1	PROPN
ejpam-3860	285	141	=	=	PROPN
ejpam-3860	285	142	e2	e2	PROPN
ejpam-3860	285	143	+	+	CCONJ
ejpam-3860	285	144	1	1	NUM
ejpam-3860	285	145	,	,	PUNCT
ejpam-3860	285	146	i1	i1	PROPN
ejpam-3860	285	147	=	=	PROPN
ejpam-3860	285	148	i2	i2	PROPN
ejpam-3860	285	149	,	,	PUNCT
ejpam-3860	285	150	j1	j1	PROPN
ejpam-3860	285	151	=	=	SYM
ejpam-3860	285	152	j2	j2	PROPN
ejpam-3860	285	153	.	.	PUNCT
ejpam-3860	285	154	n.	n.	PROPN
ejpam-3860	285	155	abdulcarim	abdulcarim	PROPN
ejpam-3860	285	156	,	,	PUNCT
ejpam-3860	285	157	s.	s.	PROPN
ejpam-3860	285	158	dagondon	dagondon	PROPN
ejpam-3860	285	159	,	,	PUNCT
ejpam-3860	285	160	e.	e.	PROPN
ejpam-3860	285	161	chacon	chacon	PROPN
ejpam-3860	285	162	/	/	SYM
ejpam-3860	285	163	eur	eur	PROPN
ejpam-3860	285	164	.	.	PUNCT
ejpam-3860	286	1	j.	j.	PROPN
ejpam-3860	286	2	pure	pure	PROPN
ejpam-3860	286	3	appl	appl	PROPN
ejpam-3860	286	4	.	.	PROPN
ejpam-3860	286	5	math	math	PROPN
ejpam-3860	286	6	,	,	PUNCT
ejpam-3860	286	7	14	14	NUM
ejpam-3860	286	8	(	(	PUNCT
ejpam-3860	286	9	1	1	NUM
ejpam-3860	286	10	)	)	PUNCT
ejpam-3860	286	11	(	(	PUNCT
ejpam-3860	286	12	2021	2021	NUM
ejpam-3860	286	13	)	)	PUNCT
ejpam-3860	286	14	,	,	PUNCT
ejpam-3860	286	15	173	173	NUM
ejpam-3860	286	16	-	-	SYM
ejpam-3860	286	17	191	191	NUM
ejpam-3860	286	18	186	186	NUM
ejpam-3860	286	19	(	(	PUNCT
ejpam-3860	286	20	1	1	NUM
ejpam-3860	286	21	,	,	PUNCT
ejpam-3860	286	22	13	13	NUM
ejpam-3860	286	23	)	)	PUNCT
ejpam-3860	286	24	(	(	PUNCT
ejpam-3860	286	25	1	1	NUM
ejpam-3860	286	26	,	,	PUNCT
ejpam-3860	286	27	12	12	NUM
ejpam-3860	286	28	)	)	PUNCT
ejpam-3860	286	29	(	(	PUNCT
ejpam-3860	286	30	1	1	NUM
ejpam-3860	286	31	,	,	PUNCT
ejpam-3860	286	32	11	11	NUM
ejpam-3860	286	33	)	)	PUNCT
ejpam-3860	286	34	(	(	PUNCT
ejpam-3860	286	35	1	1	NUM
ejpam-3860	286	36	,	,	PUNCT
ejpam-3860	286	37	1n	1n	NUM
ejpam-3860	286	38	−	−	PROPN
ejpam-3860	286	39	1	1	NUM
ejpam-3860	286	40	)	)	PUNCT
ejpam-3860	286	41	(	(	PUNCT
ejpam-3860	286	42	1	1	NUM
ejpam-3860	286	43	,	,	PUNCT
ejpam-3860	286	44	1n	1n	NUM
ejpam-3860	286	45	)	)	PUNCT
ejpam-3860	286	46	(	(	PUNCT
ejpam-3860	286	47	1	1	NUM
ejpam-3860	286	48	,	,	PUNCT
ejpam-3860	286	49	23	23	NUM
ejpam-3860	286	50	)	)	PUNCT
ejpam-3860	286	51	(	(	PUNCT
ejpam-3860	286	52	1	1	NUM
ejpam-3860	286	53	,	,	PUNCT
ejpam-3860	286	54	22	22	NUM
ejpam-3860	286	55	)	)	PUNCT
ejpam-3860	286	56	(	(	PUNCT
ejpam-3860	286	57	1	1	NUM
ejpam-3860	286	58	,	,	PUNCT
ejpam-3860	286	59	21	21	NUM
ejpam-3860	286	60	)	)	PUNCT
ejpam-3860	286	61	(	(	PUNCT
ejpam-3860	286	62	1	1	NUM
ejpam-3860	286	63	,	,	PUNCT
ejpam-3860	286	64	2n	2n	NUM
ejpam-3860	286	65	−	−	ADP
ejpam-3860	286	66	1	1	NUM
ejpam-3860	286	67	)	)	PUNCT
ejpam-3860	286	68	(	(	PUNCT
ejpam-3860	286	69	1	1	NUM
ejpam-3860	286	70	,	,	PUNCT
ejpam-3860	286	71	2n	2n	NUM
ejpam-3860	286	72	)	)	PUNCT
ejpam-3860	286	73	(	(	PUNCT
ejpam-3860	286	74	1,m3	1,m3	NUM
ejpam-3860	286	75	)	)	PUNCT
ejpam-3860	286	76	(	(	PUNCT
ejpam-3860	286	77	1,m2	1,m2	NUM
ejpam-3860	286	78	)	)	PUNCT
ejpam-3860	286	79	(	(	PUNCT
ejpam-3860	286	80	1,m1	1,m1	NUM
ejpam-3860	286	81	)	)	PUNCT
ejpam-3860	286	82	(	(	PUNCT
ejpam-3860	286	83	1,mn	1,mn	NUM
ejpam-3860	286	84	−	−	NOUN
ejpam-3860	286	85	1	1	NUM
ejpam-3860	286	86	)	)	PUNCT
ejpam-3860	286	87	(	(	PUNCT
ejpam-3860	286	88	1,mn	1,mn	NUM
ejpam-3860	286	89	)	)	PUNCT
ejpam-3860	286	90	·	·	PUNCT
ejpam-3860	286	91	·	·	PUNCT
ejpam-3860	286	92	·	·	PUNCT
ejpam-3860	287	1	(	(	PUNCT
ejpam-3860	287	2	2	2	NUM
ejpam-3860	287	3	,	,	PUNCT
ejpam-3860	287	4	13	13	NUM
ejpam-3860	287	5	)	)	PUNCT
ejpam-3860	287	6	(	(	PUNCT
ejpam-3860	287	7	2	2	NUM
ejpam-3860	287	8	,	,	PUNCT
ejpam-3860	287	9	12	12	NUM
ejpam-3860	287	10	)	)	PUNCT
ejpam-3860	287	11	(	(	PUNCT
ejpam-3860	287	12	2	2	NUM
ejpam-3860	287	13	,	,	PUNCT
ejpam-3860	287	14	11	11	NUM
ejpam-3860	287	15	)	)	PUNCT
ejpam-3860	287	16	(	(	PUNCT
ejpam-3860	287	17	2	2	NUM
ejpam-3860	287	18	,	,	PUNCT
ejpam-3860	287	19	1n	1n	NUM
ejpam-3860	287	20	−	−	PROPN
ejpam-3860	287	21	1	1	NUM
ejpam-3860	287	22	)	)	PUNCT
ejpam-3860	287	23	(	(	PUNCT
ejpam-3860	287	24	2	2	NUM
ejpam-3860	287	25	,	,	PUNCT
ejpam-3860	287	26	1n	1n	NUM
ejpam-3860	287	27	)	)	PUNCT
ejpam-3860	287	28	(	(	PUNCT
ejpam-3860	287	29	2	2	NUM
ejpam-3860	287	30	,	,	PUNCT
ejpam-3860	287	31	23	23	NUM
ejpam-3860	287	32	)	)	PUNCT
ejpam-3860	287	33	(	(	PUNCT
ejpam-3860	287	34	2	2	NUM
ejpam-3860	287	35	,	,	PUNCT
ejpam-3860	287	36	22	22	NUM
ejpam-3860	287	37	)	)	PUNCT
ejpam-3860	287	38	(	(	PUNCT
ejpam-3860	287	39	2	2	NUM
ejpam-3860	287	40	,	,	PUNCT
ejpam-3860	287	41	21	21	NUM
ejpam-3860	287	42	)	)	PUNCT
ejpam-3860	287	43	(	(	PUNCT
ejpam-3860	287	44	2	2	NUM
ejpam-3860	287	45	,	,	PUNCT
ejpam-3860	287	46	2n	2n	NUM
ejpam-3860	287	47	−	−	ADP
ejpam-3860	287	48	1	1	NUM
ejpam-3860	287	49	)	)	PUNCT
ejpam-3860	287	50	(	(	PUNCT
ejpam-3860	287	51	2	2	NUM
ejpam-3860	287	52	,	,	PUNCT
ejpam-3860	287	53	2n	2n	NUM
ejpam-3860	287	54	)	)	PUNCT
ejpam-3860	287	55	(	(	PUNCT
ejpam-3860	287	56	2,m3	2,m3	NUM
ejpam-3860	287	57	)	)	PUNCT
ejpam-3860	287	58	(	(	PUNCT
ejpam-3860	287	59	2,m2	2,m2	NUM
ejpam-3860	287	60	)	)	PUNCT
ejpam-3860	287	61	(	(	PUNCT
ejpam-3860	287	62	2,m1	2,m1	NUM
ejpam-3860	287	63	)	)	PUNCT
ejpam-3860	287	64	(	(	PUNCT
ejpam-3860	287	65	2,mn	2,mn	NUM
ejpam-3860	287	66	−	−	NOUN
ejpam-3860	287	67	1	1	NUM
ejpam-3860	287	68	)	)	PUNCT
ejpam-3860	287	69	(	(	PUNCT
ejpam-3860	287	70	2,mn	2,mn	NUM
ejpam-3860	287	71	)	)	PUNCT
ejpam-3860	287	72	·	·	PUNCT
ejpam-3860	287	73	·	·	PUNCT
ejpam-3860	287	74	·	·	PUNCT
ejpam-3860	287	75	(	(	PUNCT
ejpam-3860	287	76	k	k	X
ejpam-3860	287	77	,	,	PUNCT
ejpam-3860	287	78	13	13	NUM
ejpam-3860	287	79	)	)	PUNCT
ejpam-3860	287	80	(	(	PUNCT
ejpam-3860	287	81	k	k	NOUN
ejpam-3860	287	82	,	,	PUNCT
ejpam-3860	287	83	12	12	NUM
ejpam-3860	287	84	)	)	PUNCT
ejpam-3860	287	85	(	(	PUNCT
ejpam-3860	287	86	k	k	NOUN
ejpam-3860	287	87	,	,	PUNCT
ejpam-3860	287	88	11	11	NUM
ejpam-3860	287	89	)	)	PUNCT
ejpam-3860	287	90	(	(	PUNCT
ejpam-3860	287	91	k	k	X
ejpam-3860	287	92	,	,	PUNCT
ejpam-3860	287	93	1n	1n	NUM
ejpam-3860	287	94	−	−	NOUN
ejpam-3860	287	95	1	1	NUM
ejpam-3860	287	96	)	)	PUNCT
ejpam-3860	287	97	(	(	PUNCT
ejpam-3860	287	98	k	k	X
ejpam-3860	287	99	,	,	PUNCT
ejpam-3860	287	100	1n	1n	NUM
ejpam-3860	287	101	)	)	PUNCT
ejpam-3860	287	102	(	(	PUNCT
ejpam-3860	287	103	k	k	NOUN
ejpam-3860	287	104	,	,	PUNCT
ejpam-3860	287	105	23	23	NUM
ejpam-3860	287	106	)	)	PUNCT
ejpam-3860	287	107	(	(	PUNCT
ejpam-3860	287	108	k	k	X
ejpam-3860	287	109	,	,	PUNCT
ejpam-3860	287	110	22	22	NUM
ejpam-3860	287	111	)	)	PUNCT
ejpam-3860	287	112	(	(	PUNCT
ejpam-3860	287	113	k	k	X
ejpam-3860	287	114	,	,	PUNCT
ejpam-3860	287	115	21	21	NUM
ejpam-3860	287	116	)	)	PUNCT
ejpam-3860	287	117	(	(	PUNCT
ejpam-3860	287	118	k	k	X
ejpam-3860	287	119	,	,	PUNCT
ejpam-3860	287	120	2n	2n	NUM
ejpam-3860	287	121	−	−	ADP
ejpam-3860	287	122	1	1	NUM
ejpam-3860	287	123	)	)	PUNCT
ejpam-3860	287	124	(	(	PUNCT
ejpam-3860	287	125	k	k	X
ejpam-3860	287	126	,	,	PUNCT
ejpam-3860	287	127	2n	2n	NUM
ejpam-3860	287	128	)	)	PUNCT
ejpam-3860	287	129	(	(	PUNCT
ejpam-3860	287	130	k	k	X
ejpam-3860	287	131	,	,	PUNCT
ejpam-3860	287	132	m3	m3	PROPN
ejpam-3860	287	133	)	)	PUNCT
ejpam-3860	287	134	(	(	PUNCT
ejpam-3860	287	135	k	k	X
ejpam-3860	287	136	,	,	PUNCT
ejpam-3860	287	137	m2	m2	PROPN
ejpam-3860	287	138	)	)	PUNCT
ejpam-3860	287	139	(	(	PUNCT
ejpam-3860	287	140	k	k	X
ejpam-3860	287	141	,	,	PUNCT
ejpam-3860	287	142	m1	m1	PROPN
ejpam-3860	287	143	)	)	PUNCT
ejpam-3860	287	144	(	(	PUNCT
ejpam-3860	287	145	k	k	X
ejpam-3860	287	146	,	,	PUNCT
ejpam-3860	287	147	mn	mn	PROPN
ejpam-3860	287	148	−	−	PROPN
ejpam-3860	287	149	1	1	NUM
ejpam-3860	287	150	)	)	PUNCT
ejpam-3860	287	151	(	(	PUNCT
ejpam-3860	287	152	k	k	X
ejpam-3860	287	153	,	,	PUNCT
ejpam-3860	287	154	mn	mn	PROPN
ejpam-3860	287	155	)	)	PUNCT
ejpam-3860	287	156	·	·	PUNCT
ejpam-3860	287	157	·	·	PUNCT
ejpam-3860	287	158	·	·	PUNCT
ejpam-3860	287	159	consider	consider	VERB
ejpam-3860	287	160	the	the	DET
ejpam-3860	287	161	following	follow	VERB
ejpam-3860	287	162	sets	set	NOUN
ejpam-3860	287	163	:	:	PUNCT
ejpam-3860	287	164	ap	ap	PROPN
ejpam-3860	288	1	=	=	PUNCT
ejpam-3860	289	1	{	{	PUNCT
ejpam-3860	290	1	(	(	PUNCT
ejpam-3860	290	2	p	p	NOUN
ejpam-3860	290	3	,	,	PUNCT
ejpam-3860	290	4	ij	ij	NOUN
ejpam-3860	290	5	)	)	PUNCT
ejpam-3860	290	6	:	:	PUNCT
ejpam-3860	291	1	p	p	PRON
ejpam-3860	291	2	is	be	AUX
ejpam-3860	291	3	odd	odd	ADJ
ejpam-3860	291	4	,	,	PUNCT
ejpam-3860	291	5	i	i	PRON
ejpam-3860	291	6	is	be	AUX
ejpam-3860	291	7	odd	odd	ADJ
ejpam-3860	291	8	,	,	PUNCT
ejpam-3860	291	9	j	j	PROPN
ejpam-3860	291	10	=	=	SYM
ejpam-3860	291	11	1	1	NUM
ejpam-3860	291	12	,	,	PUNCT
ejpam-3860	291	13	·	·	PUNCT
ejpam-3860	291	14	·	·	PUNCT
ejpam-3860	291	15	·	·	PUNCT
ejpam-3860	291	16	,	,	PUNCT
ejpam-3860	291	17	n−	n−	NOUN
ejpam-3860	291	18	1	1	NUM
ejpam-3860	291	19	}	}	PUNCT
ejpam-3860	291	20	,	,	PUNCT
ejpam-3860	291	21	bp	bp	PROPN
ejpam-3860	291	22	=	=	PRON
ejpam-3860	291	23	{	{	PUNCT
ejpam-3860	291	24	(	(	PUNCT
ejpam-3860	291	25	p	p	X
ejpam-3860	291	26	,	,	PUNCT
ejpam-3860	291	27	in	in	ADP
ejpam-3860	291	28	)	)	PUNCT
ejpam-3860	291	29	:	:	PUNCT
ejpam-3860	292	1	p	p	PRON
ejpam-3860	292	2	is	be	AUX
ejpam-3860	292	3	odd	odd	ADJ
ejpam-3860	292	4	,	,	PUNCT
ejpam-3860	292	5	i	i	PRON
ejpam-3860	292	6	is	be	AUX
ejpam-3860	292	7	odd	odd	ADJ
ejpam-3860	292	8	}	}	PUNCT
ejpam-3860	292	9	aq	aq	X
ejpam-3860	292	10	=	=	PUNCT
ejpam-3860	292	11	{	{	PUNCT
ejpam-3860	292	12	(	(	PUNCT
ejpam-3860	292	13	q	q	ADJ
ejpam-3860	292	14	,	,	PUNCT
ejpam-3860	292	15	ij	ij	NOUN
ejpam-3860	292	16	)	)	PUNCT
ejpam-3860	292	17	:	:	PUNCT
ejpam-3860	292	18	q	q	X
ejpam-3860	292	19	is	be	AUX
ejpam-3860	292	20	even	even	ADV
ejpam-3860	292	21	,	,	PUNCT
ejpam-3860	292	22	i	i	PRON
ejpam-3860	292	23	is	be	AUX
ejpam-3860	292	24	odd	odd	ADJ
ejpam-3860	292	25	,	,	PUNCT
ejpam-3860	292	26	j	j	PROPN
ejpam-3860	292	27	=	=	SYM
ejpam-3860	292	28	1	1	NUM
ejpam-3860	292	29	,	,	PUNCT
ejpam-3860	292	30	·	·	PUNCT
ejpam-3860	292	31	·	·	PUNCT
ejpam-3860	292	32	·	·	PUNCT
ejpam-3860	292	33	,	,	PUNCT
ejpam-3860	292	34	n−	n−	NOUN
ejpam-3860	292	35	1	1	NUM
ejpam-3860	292	36	}	}	PUNCT
ejpam-3860	292	37	,	,	PUNCT
ejpam-3860	292	38	bq	bq	INTJ
ejpam-3860	292	39	=	=	SYM
ejpam-3860	292	40	{	{	PUNCT
ejpam-3860	292	41	(	(	PUNCT
ejpam-3860	292	42	q	q	INTJ
ejpam-3860	292	43	,	,	PUNCT
ejpam-3860	292	44	in	in	ADP
ejpam-3860	292	45	)	)	PUNCT
ejpam-3860	292	46	:	:	PUNCT
ejpam-3860	292	47	q	q	X
ejpam-3860	292	48	is	be	AUX
ejpam-3860	292	49	even	even	ADV
ejpam-3860	292	50	,	,	PUNCT
ejpam-3860	292	51	i	i	PRON
ejpam-3860	292	52	is	be	AUX
ejpam-3860	292	53	odd	odd	ADJ
ejpam-3860	292	54	}	}	PUNCT
ejpam-3860	292	55	cp	cp	NOUN
ejpam-3860	292	56	=	=	SYM
ejpam-3860	292	57	{	{	PUNCT
ejpam-3860	292	58	(	(	PUNCT
ejpam-3860	292	59	p	p	NOUN
ejpam-3860	292	60	,	,	PUNCT
ejpam-3860	292	61	ij	ij	NOUN
ejpam-3860	292	62	)	)	PUNCT
ejpam-3860	292	63	:	:	PUNCT
ejpam-3860	293	1	p	p	PRON
ejpam-3860	293	2	is	be	AUX
ejpam-3860	293	3	odd	odd	ADJ
ejpam-3860	293	4	,	,	PUNCT
ejpam-3860	293	5	i	i	PRON
ejpam-3860	293	6	is	be	AUX
ejpam-3860	293	7	even	even	ADV
ejpam-3860	293	8	,	,	PUNCT
ejpam-3860	293	9	j	j	PROPN
ejpam-3860	293	10	=	=	SYM
ejpam-3860	293	11	1	1	NUM
ejpam-3860	293	12	,	,	PUNCT
ejpam-3860	293	13	·	·	PUNCT
ejpam-3860	293	14	·	·	PUNCT
ejpam-3860	293	15	·	·	PUNCT
ejpam-3860	293	16	,	,	PUNCT
ejpam-3860	293	17	n−	n−	NOUN
ejpam-3860	293	18	1	1	NUM
ejpam-3860	293	19	}	}	PUNCT
ejpam-3860	293	20	,	,	PUNCT
ejpam-3860	293	21	dp	dp	NOUN
ejpam-3860	293	22	=	=	SYM
ejpam-3860	293	23	{	{	PUNCT
ejpam-3860	293	24	(	(	PUNCT
ejpam-3860	293	25	p	p	X
ejpam-3860	293	26	,	,	PUNCT
ejpam-3860	293	27	in	in	ADP
ejpam-3860	293	28	)	)	PUNCT
ejpam-3860	293	29	:	:	PUNCT
ejpam-3860	294	1	p	p	PRON
ejpam-3860	294	2	is	be	AUX
ejpam-3860	294	3	odd	odd	ADJ
ejpam-3860	294	4	,	,	PUNCT
ejpam-3860	294	5	i	i	PRON
ejpam-3860	294	6	is	be	AUX
ejpam-3860	294	7	even	even	ADV
ejpam-3860	294	8	}	}	PUNCT
ejpam-3860	294	9	cq	cq	NOUN
ejpam-3860	295	1	=	=	PUNCT
ejpam-3860	295	2	{	{	PUNCT
ejpam-3860	295	3	(	(	PUNCT
ejpam-3860	295	4	q	q	ADJ
ejpam-3860	295	5	,	,	PUNCT
ejpam-3860	295	6	ij	ij	NOUN
ejpam-3860	295	7	)	)	PUNCT
ejpam-3860	295	8	:	:	PUNCT
ejpam-3860	295	9	q	q	X
ejpam-3860	295	10	is	be	AUX
ejpam-3860	295	11	even	even	ADV
ejpam-3860	295	12	,	,	PUNCT
ejpam-3860	295	13	i	i	PRON
ejpam-3860	295	14	is	be	AUX
ejpam-3860	295	15	even	even	ADV
ejpam-3860	295	16	,	,	PUNCT
ejpam-3860	295	17	j	j	PROPN
ejpam-3860	295	18	=	=	SYM
ejpam-3860	295	19	1	1	NUM
ejpam-3860	295	20	,	,	PUNCT
ejpam-3860	295	21	·	·	PUNCT
ejpam-3860	295	22	·	·	PUNCT
ejpam-3860	295	23	·	·	PUNCT
ejpam-3860	295	24	,	,	PUNCT
ejpam-3860	295	25	n−	n−	NOUN
ejpam-3860	295	26	1	1	NUM
ejpam-3860	295	27	}	}	PUNCT
ejpam-3860	295	28	,	,	PUNCT
ejpam-3860	295	29	dq	dq	PROPN
ejpam-3860	295	30	=	=	SYM
ejpam-3860	295	31	{	{	PUNCT
ejpam-3860	295	32	(	(	PUNCT
ejpam-3860	295	33	q	q	INTJ
ejpam-3860	295	34	,	,	PUNCT
ejpam-3860	295	35	in	in	ADP
ejpam-3860	295	36	)	)	PUNCT
ejpam-3860	295	37	:	:	PUNCT
ejpam-3860	295	38	q	q	X
ejpam-3860	295	39	is	be	AUX
ejpam-3860	295	40	even	even	ADV
ejpam-3860	295	41	,	,	PUNCT
ejpam-3860	295	42	i	i	PRON
ejpam-3860	295	43	is	be	AUX
ejpam-3860	295	44	even	even	ADV
ejpam-3860	295	45	}	}	PUNCT
ejpam-3860	295	46	let	let	VERB
ejpam-3860	295	47	s	s	PRON
ejpam-3860	295	48	=	=	X
ejpam-3860	295	49	ap	ap	PROPN
ejpam-3860	295	50	∪dp	∪dp	PROPN
ejpam-3860	295	51	∪	∪	PROPN
ejpam-3860	295	52	bq	bq	PROPN
ejpam-3860	295	53	∪	∪	PROPN
ejpam-3860	295	54	cq	cq	PROPN
ejpam-3860	295	55	and	and	CCONJ
ejpam-3860	295	56	t	t	PROPN
ejpam-3860	295	57	=	=	SYM
ejpam-3860	295	58	aq	aq	PROPN
ejpam-3860	295	59	∪dq	∪dq	PROPN
ejpam-3860	295	60	∪	∪	ADP
ejpam-3860	295	61	bp	bp	PROPN
ejpam-3860	295	62	∪	∪	X
ejpam-3860	295	63	cp	cp	PROPN
ejpam-3860	295	64	.	.	PUNCT
ejpam-3860	296	1	we	we	PRON
ejpam-3860	296	2	claim	claim	VERB
ejpam-3860	296	3	that	that	SCONJ
ejpam-3860	296	4	s	s	VERB
ejpam-3860	296	5	and	and	CCONJ
ejpam-3860	296	6	t	t	PROPN
ejpam-3860	296	7	are	be	AUX
ejpam-3860	296	8	the	the	DET
ejpam-3860	296	9	independent	independent	ADJ
ejpam-3860	296	10	neighborhood	neighborhood	NOUN
ejpam-3860	296	11	sets	set	NOUN
ejpam-3860	296	12	of	of	ADP
ejpam-3860	296	13	pk	pk	NOUN
ejpam-3860	296	14	�	�	PROPN
ejpam-3860	296	15	fm	fm	PROPN
ejpam-3860	296	16	,	,	PUNCT
ejpam-3860	296	17	n.	n.	PROPN
ejpam-3860	296	18	first	first	ADV
ejpam-3860	296	19	,	,	PUNCT
ejpam-3860	296	20	we	we	PRON
ejpam-3860	296	21	show	show	VERB
ejpam-3860	296	22	that	that	SCONJ
ejpam-3860	296	23	no	no	DET
ejpam-3860	296	24	two	two	NUM
ejpam-3860	296	25	vertices	vertex	NOUN
ejpam-3860	296	26	in	in	ADP
ejpam-3860	296	27	s	s	NOUN
ejpam-3860	296	28	are	be	AUX
ejpam-3860	296	29	adjacent	adjacent	ADJ
ejpam-3860	296	30	.	.	PUNCT
ejpam-3860	297	1	since	since	SCONJ
ejpam-3860	297	2	each	each	DET
ejpam-3860	297	3	ap	ap	PROPN
ejpam-3860	297	4	and	and	CCONJ
ejpam-3860	297	5	cq	cq	INTJ
ejpam-3860	297	6	consist	consist	NOUN
ejpam-3860	297	7	of	of	ADP
ejpam-3860	297	8	the	the	DET
ejpam-3860	297	9	pendant	pendant	ADJ
ejpam-3860	297	10	vertices	vertex	NOUN
ejpam-3860	297	11	in	in	ADP
ejpam-3860	297	12	each	each	DET
ejpam-3860	297	13	star	star	NOUN
ejpam-3860	297	14	,	,	PUNCT
ejpam-3860	297	15	ap	ap	PROPN
ejpam-3860	297	16	and	and	CCONJ
ejpam-3860	297	17	cq	cq	PROPN
ejpam-3860	297	18	are	be	AUX
ejpam-3860	297	19	independent	independent	ADJ
ejpam-3860	297	20	sets	set	NOUN
ejpam-3860	297	21	.	.	PUNCT
ejpam-3860	298	1	also	also	ADV
ejpam-3860	298	2	,	,	PUNCT
ejpam-3860	298	3	since	since	SCONJ
ejpam-3860	298	4	each	each	DET
ejpam-3860	298	5	bq	bq	NOUN
ejpam-3860	298	6	and	and	CCONJ
ejpam-3860	298	7	dp	dp	NOUN
ejpam-3860	298	8	consist	consist	NOUN
ejpam-3860	298	9	of	of	ADP
ejpam-3860	298	10	apex	apex	NOUN
ejpam-3860	298	11	vertices	vertex	NOUN
ejpam-3860	298	12	in	in	ADP
ejpam-3860	298	13	each	each	DET
ejpam-3860	298	14	star	star	NOUN
ejpam-3860	298	15	,	,	PUNCT
ejpam-3860	298	16	bq	bq	INTJ
ejpam-3860	298	17	and	and	CCONJ
ejpam-3860	298	18	dp	dp	NOUN
ejpam-3860	298	19	are	be	AUX
ejpam-3860	298	20	independent	independent	ADJ
ejpam-3860	298	21	sets	set	NOUN
ejpam-3860	298	22	.	.	PUNCT
ejpam-3860	299	1	we	we	PRON
ejpam-3860	299	2	note	note	VERB
ejpam-3860	299	3	that	that	SCONJ
ejpam-3860	299	4	elements	element	NOUN
ejpam-3860	299	5	of	of	ADP
ejpam-3860	299	6	ap	ap	PROPN
ejpam-3860	299	7	and	and	CCONJ
ejpam-3860	299	8	dp	dp	NOUN
ejpam-3860	299	9	are	be	AUX
ejpam-3860	299	10	not	not	PART
ejpam-3860	299	11	adjacent	adjacent	ADJ
ejpam-3860	299	12	since	since	SCONJ
ejpam-3860	299	13	i	i	PRON
ejpam-3860	299	14	is	be	AUX
ejpam-3860	299	15	odd	odd	ADJ
ejpam-3860	299	16	in	in	ADP
ejpam-3860	299	17	ap	ap	PROPN
ejpam-3860	300	1	and	and	CCONJ
ejpam-3860	300	2	i	i	PRON
ejpam-3860	300	3	is	be	AUX
ejpam-3860	300	4	even	even	ADV
ejpam-3860	300	5	in	in	ADP
ejpam-3860	300	6	dp	dp	PROPN
ejpam-3860	300	7	.	.	PUNCT
ejpam-3860	301	1	similarly	similarly	ADV
ejpam-3860	301	2	,	,	PUNCT
ejpam-3860	301	3	elements	element	NOUN
ejpam-3860	301	4	of	of	ADP
ejpam-3860	301	5	bq	bq	NOUN
ejpam-3860	301	6	and	and	CCONJ
ejpam-3860	301	7	cq	cq	PROPN
ejpam-3860	301	8	are	be	AUX
ejpam-3860	301	9	non	non	ADJ
ejpam-3860	301	10	-	-	ADJ
ejpam-3860	301	11	adjacent	adjacent	ADJ
ejpam-3860	301	12	.	.	PUNCT
ejpam-3860	302	1	hence	hence	ADV
ejpam-3860	302	2	,	,	PUNCT
ejpam-3860	302	3	the	the	DET
ejpam-3860	302	4	set	set	NOUN
ejpam-3860	302	5	ap	ap	PROPN
ejpam-3860	302	6	∪dp	∪dp	PROPN
ejpam-3860	302	7	∪bq	∪bq	PROPN
ejpam-3860	302	8	∪	∪	X
ejpam-3860	302	9	cq	cq	NOUN
ejpam-3860	302	10	have	have	VERB
ejpam-3860	302	11	non	non	ADJ
ejpam-3860	302	12	-	-	ADJ
ejpam-3860	302	13	adjacent	adjacent	ADJ
ejpam-3860	302	14	vertices	vertex	NOUN
ejpam-3860	302	15	.	.	PUNCT
ejpam-3860	303	1	next	next	ADV
ejpam-3860	303	2	,	,	PUNCT
ejpam-3860	303	3	we	we	PRON
ejpam-3860	303	4	show	show	VERB
ejpam-3860	303	5	that	that	SCONJ
ejpam-3860	303	6	⋃	⋃	ADP
ejpam-3860	303	7	v∈s	v∈s	ADJ
ejpam-3860	303	8	〈	〈	PROPN
ejpam-3860	303	9	n	n	PRON
ejpam-3860	303	10	[	[	X
ejpam-3860	303	11	v	v	NOUN
ejpam-3860	303	12	]	]	X
ejpam-3860	303	13	〉	〉	NOUN
ejpam-3860	303	14	=	=	SYM
ejpam-3860	303	15	pk	pk	PROPN
ejpam-3860	303	16	�	�	PROPN
ejpam-3860	303	17	fm	fm	PROPN
ejpam-3860	303	18	,	,	PUNCT
ejpam-3860	303	19	n.	n.	PROPN
ejpam-3860	303	20	assume	assume	VERB
ejpam-3860	303	21	to	to	ADP
ejpam-3860	303	22	the	the	DET
ejpam-3860	303	23	contrary	contrary	NOUN
ejpam-3860	303	24	that	that	SCONJ
ejpam-3860	303	25	⋃	⋃	PUNCT
ejpam-3860	303	26	v∈s	v∈s	ADJ
ejpam-3860	303	27	〈	〈	PROPN
ejpam-3860	303	28	n	n	PRON
ejpam-3860	303	29	[	[	X
ejpam-3860	303	30	v	v	NOUN
ejpam-3860	303	31	]	]	X
ejpam-3860	303	32	〉	〉	PROPN
ejpam-3860	303	33	6=	6=	SYM
ejpam-3860	303	34	pk	pk	PROPN
ejpam-3860	303	35	�	�	PROPN
ejpam-3860	303	36	fm	fm	PROPN
ejpam-3860	303	37	,	,	PUNCT
ejpam-3860	303	38	n.	n.	PROPN
ejpam-3860	303	39	then	then	ADV
ejpam-3860	303	40	there	there	PRON
ejpam-3860	303	41	exists	exist	VERB
ejpam-3860	303	42	(	(	PUNCT
ejpam-3860	303	43	e1	e1	PROPN
ejpam-3860	303	44	,	,	PUNCT
ejpam-3860	303	45	i1j1)(e2	i1j1)(e2	PROPN
ejpam-3860	303	46	,	,	PUNCT
ejpam-3860	303	47	i2j2	i2j2	PROPN
ejpam-3860	303	48	)	)	PUNCT
ejpam-3860	303	49	∈	∈	PROPN
ejpam-3860	303	50	e	e	X
ejpam-3860	303	51	(	(	PUNCT
ejpam-3860	303	52	pk	pk	PROPN
ejpam-3860	303	53	�	�	PROPN
ejpam-3860	303	54	fm	fm	PROPN
ejpam-3860	303	55	,	,	PUNCT
ejpam-3860	303	56	n	n	CCONJ
ejpam-3860	303	57	)	)	PUNCT
ejpam-3860	303	58	such	such	ADJ
ejpam-3860	303	59	that	that	SCONJ
ejpam-3860	303	60	(	(	PUNCT
ejpam-3860	303	61	e1	e1	PROPN
ejpam-3860	303	62	,	,	PUNCT
ejpam-3860	303	63	i1j1)(e2	i1j1)(e2	PROPN
ejpam-3860	303	64	,	,	PUNCT
ejpam-3860	303	65	i2j2	i2j2	PROPN
ejpam-3860	303	66	)	)	PUNCT
ejpam-3860	303	67	/∈	/∈	PUNCT
ejpam-3860	304	1	e	e	NOUN
ejpam-3860	304	2	(	(	PUNCT
ejpam-3860	304	3	⋃	⋃	ADP
ejpam-3860	304	4	v∈s	v∈s	ADJ
ejpam-3860	304	5	〈	〈	PROPN
ejpam-3860	304	6	n	n	PRON
ejpam-3860	304	7	[	[	X
ejpam-3860	304	8	v	v	NOUN
ejpam-3860	304	9	]	]	X
ejpam-3860	304	10	〉	〉	NUM
ejpam-3860	304	11	)	)	PUNCT
ejpam-3860	304	12	.	.	PUNCT
ejpam-3860	305	1	this	this	PRON
ejpam-3860	305	2	implies	imply	VERB
ejpam-3860	305	3	(	(	PUNCT
ejpam-3860	305	4	e1	e1	NOUN
ejpam-3860	305	5	,	,	PUNCT
ejpam-3860	305	6	i1j1	i1j1	NOUN
ejpam-3860	305	7	)	)	PUNCT
ejpam-3860	305	8	,	,	PUNCT
ejpam-3860	305	9	(	(	PUNCT
ejpam-3860	305	10	e2	e2	PROPN
ejpam-3860	305	11	,	,	PUNCT
ejpam-3860	305	12	i2j2	i2j2	PROPN
ejpam-3860	305	13	)	)	PUNCT
ejpam-3860	305	14	/∈	/∈	PUNCT
ejpam-3860	306	1	s.	s.	PROPN
ejpam-3860	306	2	case	case	NOUN
ejpam-3860	306	3	1	1	NUM
ejpam-3860	306	4	:	:	PUNCT
ejpam-3860	306	5	e1	e1	PROPN
ejpam-3860	306	6	=	=	PROPN
ejpam-3860	306	7	e2	e2	PROPN
ejpam-3860	306	8	,	,	PUNCT
ejpam-3860	306	9	i1	i1	PROPN
ejpam-3860	306	10	=	=	PROPN
ejpam-3860	306	11	i2	i2	PROPN
ejpam-3860	306	12	,	,	PUNCT
ejpam-3860	306	13	either	either	CCONJ
ejpam-3860	306	14	j1	j1	PROPN
ejpam-3860	306	15	=	=	SYM
ejpam-3860	306	16	n	n	PROPN
ejpam-3860	306	17	or	or	CCONJ
ejpam-3860	306	18	j2	j2	PROPN
ejpam-3860	306	19	=	=	PROPN
ejpam-3860	306	20	n.	n.	PROPN
ejpam-3860	306	21	wlog	wlog	PROPN
ejpam-3860	306	22	,	,	PUNCT
ejpam-3860	306	23	we	we	PRON
ejpam-3860	306	24	may	may	AUX
ejpam-3860	306	25	assume	assume	VERB
ejpam-3860	306	26	j1	j1	PROPN
ejpam-3860	306	27	=	=	SYM
ejpam-3860	306	28	n.	n.	PROPN
ejpam-3860	306	29	since	since	SCONJ
ejpam-3860	306	30	(	(	PUNCT
ejpam-3860	306	31	e1	e1	PROPN
ejpam-3860	306	32	,	,	PUNCT
ejpam-3860	306	33	i1j1	i1j1	NOUN
ejpam-3860	306	34	)	)	PUNCT
ejpam-3860	306	35	/∈	/∈	PUNCT
ejpam-3860	307	1	s	s	X
ejpam-3860	307	2	,	,	PUNCT
ejpam-3860	307	3	either	either	CCONJ
ejpam-3860	307	4	either	either	CCONJ
ejpam-3860	307	5	e1	e1	PROPN
ejpam-3860	307	6	and	and	CCONJ
ejpam-3860	307	7	i1	i1	PROPN
ejpam-3860	307	8	are	be	AUX
ejpam-3860	307	9	odd	odd	ADJ
ejpam-3860	307	10	or	or	CCONJ
ejpam-3860	307	11	e1	e1	PROPN
ejpam-3860	307	12	and	and	CCONJ
ejpam-3860	307	13	i1	i1	PROPN
ejpam-3860	307	14	are	be	AUX
ejpam-3860	307	15	even	even	ADV
ejpam-3860	307	16	.	.	PUNCT
ejpam-3860	308	1	consider	consider	VERB
ejpam-3860	308	2	e1	e1	PROPN
ejpam-3860	308	3	and	and	CCONJ
ejpam-3860	308	4	i1	i1	PROPN
ejpam-3860	308	5	are	be	AUX
ejpam-3860	308	6	odd	odd	ADJ
ejpam-3860	308	7	.	.	PUNCT
ejpam-3860	309	1	since	since	SCONJ
ejpam-3860	309	2	e1	e1	PROPN
ejpam-3860	309	3	=	=	SYM
ejpam-3860	309	4	e2	e2	PROPN
ejpam-3860	309	5	and	and	CCONJ
ejpam-3860	309	6	i1	i1	PROPN
ejpam-3860	309	7	=	=	PROPN
ejpam-3860	309	8	i2	i2	PROPN
ejpam-3860	309	9	,	,	PUNCT
ejpam-3860	309	10	e2	e2	PROPN
ejpam-3860	309	11	n.	n.	PROPN
ejpam-3860	309	12	abdulcarim	abdulcarim	PROPN
ejpam-3860	309	13	,	,	PUNCT
ejpam-3860	309	14	s.	s.	PROPN
ejpam-3860	309	15	dagondon	dagondon	PROPN
ejpam-3860	309	16	,	,	PUNCT
ejpam-3860	309	17	e.	e.	PROPN
ejpam-3860	309	18	chacon	chacon	PROPN
ejpam-3860	309	19	/	/	SYM
ejpam-3860	309	20	eur	eur	PROPN
ejpam-3860	309	21	.	.	PUNCT
ejpam-3860	310	1	j.	j.	PROPN
ejpam-3860	310	2	pure	pure	PROPN
ejpam-3860	310	3	appl	appl	PROPN
ejpam-3860	310	4	.	.	PROPN
ejpam-3860	310	5	math	math	PROPN
ejpam-3860	310	6	,	,	PUNCT
ejpam-3860	310	7	14	14	NUM
ejpam-3860	310	8	(	(	PUNCT
ejpam-3860	310	9	1	1	NUM
ejpam-3860	310	10	)	)	PUNCT
ejpam-3860	310	11	(	(	PUNCT
ejpam-3860	310	12	2021	2021	NUM
ejpam-3860	310	13	)	)	PUNCT
ejpam-3860	310	14	,	,	PUNCT
ejpam-3860	310	15	173	173	NUM
ejpam-3860	310	16	-	-	SYM
ejpam-3860	310	17	191	191	NUM
ejpam-3860	310	18	187	187	NUM
ejpam-3860	310	19	and	and	CCONJ
ejpam-3860	310	20	i2	i2	PROPN
ejpam-3860	310	21	are	be	AUX
ejpam-3860	310	22	odd	odd	ADJ
ejpam-3860	310	23	.	.	PUNCT
ejpam-3860	311	1	but	but	CCONJ
ejpam-3860	311	2	(	(	PUNCT
ejpam-3860	311	3	e2	e2	PROPN
ejpam-3860	311	4	,	,	PUNCT
ejpam-3860	311	5	i2j2	i2j2	PROPN
ejpam-3860	311	6	)	)	PUNCT
ejpam-3860	311	7	∈	∈	PROPN
ejpam-3860	311	8	ap	ap	PROPN
ejpam-3860	312	1	⊆	⊆	NUM
ejpam-3860	312	2	s.	s.	PROPN
ejpam-3860	312	3	this	this	PRON
ejpam-3860	312	4	is	be	AUX
ejpam-3860	312	5	a	a	DET
ejpam-3860	312	6	contradiction	contradiction	NOUN
ejpam-3860	312	7	.	.	PUNCT
ejpam-3860	313	1	similarly	similarly	ADV
ejpam-3860	313	2	,	,	PUNCT
ejpam-3860	313	3	if	if	SCONJ
ejpam-3860	313	4	we	we	PRON
ejpam-3860	313	5	consider	consider	VERB
ejpam-3860	313	6	e1	e1	NOUN
ejpam-3860	313	7	and	and	CCONJ
ejpam-3860	313	8	i1	i1	PROPN
ejpam-3860	313	9	to	to	PART
ejpam-3860	313	10	be	be	AUX
ejpam-3860	313	11	even	even	ADV
ejpam-3860	313	12	,	,	PUNCT
ejpam-3860	313	13	then	then	ADV
ejpam-3860	313	14	(	(	PUNCT
ejpam-3860	313	15	e2	e2	PROPN
ejpam-3860	313	16	,	,	PUNCT
ejpam-3860	313	17	i2j2	i2j2	PROPN
ejpam-3860	313	18	)	)	PUNCT
ejpam-3860	313	19	∈	∈	PROPN
ejpam-3860	314	1	cq	cq	ADP
ejpam-3860	314	2	⊆	⊆	NUM
ejpam-3860	314	3	s	s	NOUN
ejpam-3860	314	4	case	case	NOUN
ejpam-3860	314	5	2	2	NUM
ejpam-3860	314	6	:	:	PUNCT
ejpam-3860	314	7	e1	e1	PROPN
ejpam-3860	314	8	=	=	PROPN
ejpam-3860	314	9	e2	e2	PROPN
ejpam-3860	314	10	,	,	PUNCT
ejpam-3860	314	11	i1	i1	PROPN
ejpam-3860	314	12	=	=	PROPN
ejpam-3860	314	13	i2	i2	PROPN
ejpam-3860	314	14	+	+	CCONJ
ejpam-3860	314	15	1	1	NUM
ejpam-3860	314	16	and	and	CCONJ
ejpam-3860	314	17	j1	j1	PROPN
ejpam-3860	314	18	=	=	SYM
ejpam-3860	314	19	1	1	NUM
ejpam-3860	314	20	=	=	SYM
ejpam-3860	314	21	j2	j2	PROPN
ejpam-3860	314	22	.	.	PUNCT
ejpam-3860	315	1	since	since	SCONJ
ejpam-3860	315	2	(	(	PUNCT
ejpam-3860	315	3	e1	e1	PROPN
ejpam-3860	315	4	,	,	PUNCT
ejpam-3860	315	5	i1j1	i1j1	NOUN
ejpam-3860	315	6	)	)	PUNCT
ejpam-3860	315	7	/∈	/∈	PUNCT
ejpam-3860	315	8	s	s	X
ejpam-3860	315	9	,	,	PUNCT
ejpam-3860	315	10	either	either	CCONJ
ejpam-3860	315	11	e1	e1	NOUN
ejpam-3860	315	12	is	be	AUX
ejpam-3860	315	13	odd	odd	ADJ
ejpam-3860	315	14	and	and	CCONJ
ejpam-3860	315	15	i1	i1	PROPN
ejpam-3860	315	16	is	be	AUX
ejpam-3860	315	17	even	even	ADV
ejpam-3860	315	18	or	or	CCONJ
ejpam-3860	315	19	e1	e1	NOUN
ejpam-3860	315	20	is	be	AUX
ejpam-3860	315	21	even	even	ADV
ejpam-3860	315	22	and	and	CCONJ
ejpam-3860	315	23	i1	i1	PROPN
ejpam-3860	315	24	is	be	AUX
ejpam-3860	315	25	odd	odd	ADJ
ejpam-3860	315	26	.	.	PUNCT
ejpam-3860	316	1	when	when	SCONJ
ejpam-3860	316	2	e1	e1	NOUN
ejpam-3860	316	3	is	be	AUX
ejpam-3860	316	4	odd	odd	ADJ
ejpam-3860	316	5	and	and	CCONJ
ejpam-3860	316	6	i1	i1	PROPN
ejpam-3860	316	7	is	be	AUX
ejpam-3860	316	8	even	even	ADV
ejpam-3860	316	9	,	,	PUNCT
ejpam-3860	316	10	e2	e2	PROPN
ejpam-3860	316	11	and	and	CCONJ
ejpam-3860	316	12	i2	i2	PROPN
ejpam-3860	316	13	are	be	AUX
ejpam-3860	316	14	odd	odd	ADJ
ejpam-3860	316	15	.	.	PUNCT
ejpam-3860	317	1	but	but	CCONJ
ejpam-3860	317	2	(	(	PUNCT
ejpam-3860	317	3	e2	e2	PROPN
ejpam-3860	317	4	,	,	PUNCT
ejpam-3860	317	5	i2j2	i2j2	PROPN
ejpam-3860	317	6	)	)	PUNCT
ejpam-3860	317	7	∈	∈	PROPN
ejpam-3860	317	8	ap	ap	PROPN
ejpam-3860	318	1	⊆	⊆	NUM
ejpam-3860	318	2	s.	s.	PROPN
ejpam-3860	318	3	this	this	PRON
ejpam-3860	318	4	is	be	AUX
ejpam-3860	318	5	a	a	DET
ejpam-3860	318	6	contradiction	contradiction	NOUN
ejpam-3860	318	7	.	.	PUNCT
ejpam-3860	319	1	similarly	similarly	ADV
ejpam-3860	319	2	,	,	PUNCT
ejpam-3860	319	3	a	a	DET
ejpam-3860	319	4	contradiction	contradiction	NOUN
ejpam-3860	319	5	will	will	AUX
ejpam-3860	319	6	arrive	arrive	VERB
ejpam-3860	319	7	when	when	SCONJ
ejpam-3860	319	8	e1	e1	NOUN
ejpam-3860	319	9	is	be	AUX
ejpam-3860	319	10	even	even	ADV
ejpam-3860	319	11	and	and	CCONJ
ejpam-3860	319	12	i1	i1	PROPN
ejpam-3860	319	13	is	be	AUX
ejpam-3860	319	14	odd	odd	ADJ
ejpam-3860	319	15	.	.	PUNCT
ejpam-3860	320	1	case	case	NOUN
ejpam-3860	320	2	3	3	NUM
ejpam-3860	320	3	:	:	PUNCT
ejpam-3860	320	4	e1	e1	PROPN
ejpam-3860	320	5	=	=	PROPN
ejpam-3860	320	6	e2	e2	PROPN
ejpam-3860	320	7	+	+	CCONJ
ejpam-3860	320	8	1	1	NUM
ejpam-3860	320	9	,	,	PUNCT
ejpam-3860	320	10	i1	i1	PROPN
ejpam-3860	320	11	=	=	PROPN
ejpam-3860	320	12	i2	i2	PROPN
ejpam-3860	320	13	and	and	CCONJ
ejpam-3860	320	14	j1	j1	PROPN
ejpam-3860	320	15	=	=	SYM
ejpam-3860	320	16	j2	j2	PROPN
ejpam-3860	320	17	.	.	PUNCT
ejpam-3860	321	1	since	since	SCONJ
ejpam-3860	321	2	(	(	PUNCT
ejpam-3860	321	3	e1	e1	PROPN
ejpam-3860	321	4	,	,	PUNCT
ejpam-3860	321	5	i1j1	i1j1	NOUN
ejpam-3860	321	6	)	)	PUNCT
ejpam-3860	321	7	/∈	/∈	PUNCT
ejpam-3860	322	1	s	s	X
ejpam-3860	322	2	,	,	PUNCT
ejpam-3860	322	3	we	we	PRON
ejpam-3860	322	4	consider	consider	VERB
ejpam-3860	322	5	the	the	DET
ejpam-3860	322	6	following	follow	VERB
ejpam-3860	322	7	cases	case	NOUN
ejpam-3860	322	8	:	:	PUNCT
ejpam-3860	322	9	for	for	ADP
ejpam-3860	322	10	j	j	PROPN
ejpam-3860	322	11	=	=	SYM
ejpam-3860	322	12	1	1	NUM
ejpam-3860	322	13	,	,	PUNCT
ejpam-3860	322	14	·	·	PUNCT
ejpam-3860	322	15	·	·	PUNCT
ejpam-3860	322	16	·	·	PUNCT
ejpam-3860	322	17	,	,	PUNCT
ejpam-3860	322	18	n	n	CCONJ
ejpam-3860	322	19	−	−	PROPN
ejpam-3860	322	20	1	1	NUM
ejpam-3860	322	21	,	,	PUNCT
ejpam-3860	322	22	if	if	SCONJ
ejpam-3860	322	23	e1	e1	NOUN
ejpam-3860	322	24	is	be	AUX
ejpam-3860	322	25	even	even	ADV
ejpam-3860	322	26	,	,	PUNCT
ejpam-3860	322	27	i1	i1	PROPN
ejpam-3860	322	28	is	be	AUX
ejpam-3860	322	29	odd	odd	ADJ
ejpam-3860	322	30	,	,	PUNCT
ejpam-3860	322	31	then	then	ADV
ejpam-3860	322	32	it	it	PRON
ejpam-3860	322	33	follows	follow	VERB
ejpam-3860	322	34	that	that	SCONJ
ejpam-3860	322	35	e2	e2	PROPN
ejpam-3860	322	36	and	and	CCONJ
ejpam-3860	322	37	i2	i2	PROPN
ejpam-3860	322	38	are	be	AUX
ejpam-3860	322	39	odd	odd	ADJ
ejpam-3860	322	40	.	.	PUNCT
ejpam-3860	323	1	but	but	CCONJ
ejpam-3860	323	2	(	(	PUNCT
ejpam-3860	323	3	e2	e2	PROPN
ejpam-3860	323	4	,	,	PUNCT
ejpam-3860	323	5	i2j2	i2j2	PROPN
ejpam-3860	323	6	)	)	PUNCT
ejpam-3860	323	7	∈	∈	PROPN
ejpam-3860	323	8	s.	s.	PROPN
ejpam-3860	324	1	this	this	PRON
ejpam-3860	324	2	is	be	AUX
ejpam-3860	324	3	a	a	DET
ejpam-3860	324	4	contradiction	contradiction	NOUN
ejpam-3860	324	5	.	.	PUNCT
ejpam-3860	325	1	similarly	similarly	ADV
ejpam-3860	325	2	,	,	PUNCT
ejpam-3860	325	3	when	when	SCONJ
ejpam-3860	325	4	e1	e1	PROPN
ejpam-3860	325	5	is	be	AUX
ejpam-3860	325	6	odd	odd	ADJ
ejpam-3860	325	7	and	and	CCONJ
ejpam-3860	325	8	i1	i1	PROPN
ejpam-3860	325	9	is	be	AUX
ejpam-3860	325	10	even	even	ADV
ejpam-3860	325	11	,	,	PUNCT
ejpam-3860	325	12	then	then	ADV
ejpam-3860	325	13	e2	e2	PROPN
ejpam-3860	325	14	and	and	CCONJ
ejpam-3860	325	15	i2	i2	PROPN
ejpam-3860	325	16	are	be	AUX
ejpam-3860	325	17	even	even	ADV
ejpam-3860	325	18	for	for	ADP
ejpam-3860	325	19	which	which	PRON
ejpam-3860	325	20	(	(	PUNCT
ejpam-3860	325	21	e2i2j2	e2i2j2	NOUN
ejpam-3860	325	22	)	)	PUNCT
ejpam-3860	325	23	∈	∈	PROPN
ejpam-3860	325	24	s	s	PROPN
ejpam-3860	325	25	,	,	PUNCT
ejpam-3860	325	26	a	a	DET
ejpam-3860	325	27	contradiction	contradiction	NOUN
ejpam-3860	325	28	.	.	PUNCT
ejpam-3860	326	1	for	for	ADP
ejpam-3860	326	2	j	j	PROPN
ejpam-3860	326	3	=	=	SYM
ejpam-3860	326	4	n	n	CCONJ
ejpam-3860	326	5	,	,	PUNCT
ejpam-3860	326	6	if	if	SCONJ
ejpam-3860	326	7	e1	e1	PROPN
ejpam-3860	326	8	and	and	CCONJ
ejpam-3860	326	9	i1	i1	PROPN
ejpam-3860	326	10	are	be	AUX
ejpam-3860	326	11	even	even	ADV
ejpam-3860	326	12	,	,	PUNCT
ejpam-3860	326	13	then	then	ADV
ejpam-3860	326	14	e2	e2	PROPN
ejpam-3860	326	15	is	be	AUX
ejpam-3860	326	16	odd	odd	ADJ
ejpam-3860	326	17	and	and	CCONJ
ejpam-3860	326	18	i1	i1	PROPN
ejpam-3860	326	19	is	be	AUX
ejpam-3860	326	20	even	even	ADV
ejpam-3860	326	21	.	.	PUNCT
ejpam-3860	327	1	so	so	ADV
ejpam-3860	327	2	,	,	PUNCT
ejpam-3860	327	3	(	(	PUNCT
ejpam-3860	327	4	e2	e2	PROPN
ejpam-3860	327	5	,	,	PUNCT
ejpam-3860	327	6	i2j2	i2j2	PROPN
ejpam-3860	327	7	)	)	PUNCT
ejpam-3860	327	8	∈	∈	PROPN
ejpam-3860	327	9	s	s	PROPN
ejpam-3860	327	10	,	,	PUNCT
ejpam-3860	327	11	a	a	DET
ejpam-3860	327	12	contradiction	contradiction	NOUN
ejpam-3860	327	13	.	.	PUNCT
ejpam-3860	328	1	also	also	ADV
ejpam-3860	328	2	,	,	PUNCT
ejpam-3860	328	3	for	for	ADP
ejpam-3860	328	4	if	if	SCONJ
ejpam-3860	328	5	e1	e1	PROPN
ejpam-3860	328	6	and	and	CCONJ
ejpam-3860	328	7	i1	i1	PROPN
ejpam-3860	328	8	are	be	AUX
ejpam-3860	328	9	odd	odd	ADJ
ejpam-3860	328	10	,	,	PUNCT
ejpam-3860	328	11	e2	e2	PROPN
ejpam-3860	328	12	is	be	AUX
ejpam-3860	328	13	even	even	ADV
ejpam-3860	328	14	and	and	CCONJ
ejpam-3860	328	15	i2	i2	PROPN
ejpam-3860	328	16	is	be	AUX
ejpam-3860	328	17	odd	odd	ADJ
ejpam-3860	328	18	and	and	CCONJ
ejpam-3860	328	19	that	that	SCONJ
ejpam-3860	328	20	(	(	PUNCT
ejpam-3860	328	21	e2	e2	PROPN
ejpam-3860	328	22	,	,	PUNCT
ejpam-3860	328	23	i2j2	i2j2	PROPN
ejpam-3860	328	24	)	)	PUNCT
ejpam-3860	328	25	∈	∈	PROPN
ejpam-3860	328	26	s	s	PART
ejpam-3860	328	27	which	which	PRON
ejpam-3860	328	28	is	be	AUX
ejpam-3860	328	29	a	a	DET
ejpam-3860	328	30	contradiction	contradiction	NOUN
ejpam-3860	328	31	.	.	PUNCT
ejpam-3860	329	1	thus	thus	ADV
ejpam-3860	329	2	,	,	PUNCT
ejpam-3860	329	3	in	in	ADP
ejpam-3860	329	4	either	either	PRON
ejpam-3860	329	5	of	of	ADP
ejpam-3860	329	6	the	the	DET
ejpam-3860	329	7	above	above	ADJ
ejpam-3860	329	8	cases	case	NOUN
ejpam-3860	329	9	,	,	PUNCT
ejpam-3860	329	10	we	we	PRON
ejpam-3860	329	11	arrived	arrive	VERB
ejpam-3860	329	12	a	a	DET
ejpam-3860	329	13	contradiction	contradiction	NOUN
ejpam-3860	329	14	.	.	PUNCT
ejpam-3860	330	1	hence	hence	ADV
ejpam-3860	330	2	,	,	PUNCT
ejpam-3860	330	3	(	(	PUNCT
ejpam-3860	330	4	e1	e1	PROPN
ejpam-3860	330	5	,	,	PUNCT
ejpam-3860	330	6	i1j1)(e2	i1j1)(e2	PROPN
ejpam-3860	330	7	,	,	PUNCT
ejpam-3860	330	8	i2j2	i2j2	PROPN
ejpam-3860	330	9	)	)	PUNCT
ejpam-3860	330	10	∈	∈	PROPN
ejpam-3860	330	11	e	e	X
ejpam-3860	330	12	(	(	PUNCT
ejpam-3860	330	13	⋃	⋃	ADP
ejpam-3860	330	14	v∈s	v∈s	ADJ
ejpam-3860	330	15	〈	〈	PROPN
ejpam-3860	330	16	n	n	PRON
ejpam-3860	330	17	[	[	X
ejpam-3860	330	18	v	v	NOUN
ejpam-3860	330	19	]	]	X
ejpam-3860	330	20	〉	〉	NUM
ejpam-3860	330	21	)	)	PUNCT
ejpam-3860	330	22	.	.	PUNCT
ejpam-3860	331	1	consequently	consequently	ADV
ejpam-3860	331	2	,	,	PUNCT
ejpam-3860	331	3	⋃	⋃	PUNCT
ejpam-3860	331	4	v∈s	v∈s	ADJ
ejpam-3860	331	5	〈	〈	PROPN
ejpam-3860	331	6	n	n	PRON
ejpam-3860	331	7	[	[	X
ejpam-3860	331	8	v	v	NOUN
ejpam-3860	331	9	]	]	X
ejpam-3860	331	10	〉	〉	NOUN
ejpam-3860	331	11	=	=	SYM
ejpam-3860	331	12	pk	pk	PROPN
ejpam-3860	331	13	�	�	PROPN
ejpam-3860	331	14	fm	fm	PROPN
ejpam-3860	331	15	,	,	PUNCT
ejpam-3860	331	16	n.	n.	PROPN
ejpam-3860	331	17	following	follow	VERB
ejpam-3860	331	18	the	the	DET
ejpam-3860	331	19	same	same	ADJ
ejpam-3860	331	20	argument	argument	NOUN
ejpam-3860	331	21	in	in	ADP
ejpam-3860	331	22	s	s	PROPN
ejpam-3860	331	23	,	,	PUNCT
ejpam-3860	331	24	we	we	PRON
ejpam-3860	331	25	can	can	AUX
ejpam-3860	331	26	verify	verify	VERB
ejpam-3860	331	27	that	that	SCONJ
ejpam-3860	331	28	t	t	PROPN
ejpam-3860	331	29	is	be	AUX
ejpam-3860	331	30	also	also	ADV
ejpam-3860	331	31	an	an	DET
ejpam-3860	331	32	independent	independent	ADJ
ejpam-3860	331	33	neighborhood	neighborhood	NOUN
ejpam-3860	331	34	set	set	NOUN
ejpam-3860	331	35	of	of	ADP
ejpam-3860	331	36	pk	pk	PROPN
ejpam-3860	331	37	�	�	PROPN
ejpam-3860	331	38	fm	fm	PROPN
ejpam-3860	331	39	,	,	PUNCT
ejpam-3860	331	40	n.	n.	PROPN
ejpam-3860	331	41	finally	finally	ADV
ejpam-3860	331	42	,	,	PUNCT
ejpam-3860	331	43	|s|	|s|	PROPN
ejpam-3860	331	44	=	=	SYM
ejpam-3860	331	45	|ap|+	|ap|+	PROPN
ejpam-3860	331	46	|dp|+	|dp|+	PROPN
ejpam-3860	331	47	|bq|+	|bq|+	PROPN
ejpam-3860	331	48	|cq|	|cq|	NOUN
ejpam-3860	331	49	=	=	PUNCT
ejpam-3860	331	50	⌈	⌈	SYM
ejpam-3860	331	51	k	k	ADJ
ejpam-3860	331	52	2	2	NUM
ejpam-3860	331	53	⌉⌈m	⌉⌈m	NOUN
ejpam-3860	331	54	2	2	NUM
ejpam-3860	331	55	⌉	⌉	X
ejpam-3860	331	56	(	(	PUNCT
ejpam-3860	331	57	n−	n−	NOUN
ejpam-3860	331	58	1	1	NUM
ejpam-3860	331	59	)	)	PUNCT
ejpam-3860	331	60	+	+	CCONJ
ejpam-3860	331	61	⌈	⌈	SYM
ejpam-3860	331	62	k	k	PROPN
ejpam-3860	331	63	2	2	NUM
ejpam-3860	331	64	⌉	⌉	X
ejpam-3860	331	65	⌊m	⌊m	ADP
ejpam-3860	331	66	2	2	NUM
ejpam-3860	331	67	⌋	⌋	NOUN
ejpam-3860	331	68	+	+	CCONJ
ejpam-3860	331	69	⌊	⌊	AUX
ejpam-3860	331	70	k	k	ADJ
ejpam-3860	331	71	2	2	NUM
ejpam-3860	331	72	⌋⌈m	⌋⌈m	VERB
ejpam-3860	331	73	2	2	NUM
ejpam-3860	331	74	⌉	⌉	NOUN
ejpam-3860	331	75	+	+	CCONJ
ejpam-3860	331	76	⌊	⌊	VERB
ejpam-3860	331	77	k	k	NOUN
ejpam-3860	331	78	2	2	NUM
ejpam-3860	331	79	⌋⌊m	⌋⌊m	SYM
ejpam-3860	331	80	2	2	NUM
ejpam-3860	331	81	⌋	⌋	NOUN
ejpam-3860	331	82	(	(	PUNCT
ejpam-3860	331	83	n−	n−	NOUN
ejpam-3860	331	84	1	1	NUM
ejpam-3860	331	85	)	)	PUNCT
ejpam-3860	331	86	=	=	PUNCT
ejpam-3860	331	87	⌈	⌈	NOUN
ejpam-3860	331	88	k	k	ADJ
ejpam-3860	331	89	2	2	NUM
ejpam-3860	331	90	⌉(⌈m	⌉(⌈m	NOUN
ejpam-3860	331	91	2	2	NUM
ejpam-3860	331	92	⌉	⌉	NOUN
ejpam-3860	331	93	(	(	PUNCT
ejpam-3860	331	94	n−	n−	NOUN
ejpam-3860	331	95	1	1	NUM
ejpam-3860	331	96	)	)	PUNCT
ejpam-3860	331	97	+	+	CCONJ
ejpam-3860	331	98	⌊m	⌊m	ADP
ejpam-3860	331	99	2	2	NUM
ejpam-3860	331	100	⌋	⌋	NOUN
ejpam-3860	331	101	)	)	PUNCT
ejpam-3860	332	1	+	+	CCONJ
ejpam-3860	332	2	⌊	⌊	X
ejpam-3860	332	3	k	k	ADJ
ejpam-3860	332	4	2	2	NUM
ejpam-3860	332	5	⌋(⌈m	⌋(⌈m	NUM
ejpam-3860	332	6	2	2	NUM
ejpam-3860	332	7	⌉	⌉	PRON
ejpam-3860	332	8	+	+	ADJ
ejpam-3860	332	9	⌊m	⌊m	X
ejpam-3860	332	10	2	2	NUM
ejpam-3860	332	11	⌋	⌋	NOUN
ejpam-3860	332	12	(	(	PUNCT
ejpam-3860	332	13	n−	n−	NOUN
ejpam-3860	332	14	1	1	NUM
ejpam-3860	332	15	)	)	PUNCT
ejpam-3860	332	16	)	)	PUNCT
ejpam-3860	332	17	and	and	CCONJ
ejpam-3860	332	18	|t	|t	VERB
ejpam-3860	333	1	|	|	ADV
ejpam-3860	333	2	=	=	NOUN
ejpam-3860	333	3	|aq|+	|aq|+	NOUN
ejpam-3860	333	4	|dq|+	|dq|+	NOUN
ejpam-3860	333	5	|bp|+	|bp|+	NOUN
ejpam-3860	333	6	|cp|	|cp|	PROPN
ejpam-3860	333	7	=	=	SYM
ejpam-3860	333	8	⌊	⌊	VERB
ejpam-3860	333	9	k	k	NOUN
ejpam-3860	333	10	2	2	NUM
ejpam-3860	333	11	⌋⌈m	⌋⌈m	VERB
ejpam-3860	333	12	2	2	NUM
ejpam-3860	333	13	⌉	⌉	NOUN
ejpam-3860	333	14	(	(	PUNCT
ejpam-3860	333	15	n−	n−	NOUN
ejpam-3860	333	16	1	1	NUM
ejpam-3860	333	17	)	)	PUNCT
ejpam-3860	334	1	+	+	CCONJ
ejpam-3860	334	2	⌊	⌊	X
ejpam-3860	334	3	k	k	NOUN
ejpam-3860	334	4	2	2	NUM
ejpam-3860	334	5	⌋⌊m	⌋⌊m	SYM
ejpam-3860	334	6	2	2	NUM
ejpam-3860	334	7	⌋	⌋	NOUN
ejpam-3860	334	8	+	+	CCONJ
ejpam-3860	334	9	⌈	⌈	SYM
ejpam-3860	334	10	k	k	ADJ
ejpam-3860	334	11	2	2	NUM
ejpam-3860	334	12	⌉⌈m	⌉⌈m	NOUN
ejpam-3860	334	13	2	2	NUM
ejpam-3860	334	14	⌉	⌉	NOUN
ejpam-3860	334	15	+	+	CCONJ
ejpam-3860	334	16	⌈	⌈	SYM
ejpam-3860	334	17	k	k	ADJ
ejpam-3860	334	18	2	2	NUM
ejpam-3860	334	19	⌉⌊m	⌉⌊m	NOUN
ejpam-3860	334	20	2	2	NUM
ejpam-3860	334	21	⌋	⌋	NOUN
ejpam-3860	334	22	(	(	PUNCT
ejpam-3860	334	23	n−	n−	NOUN
ejpam-3860	334	24	1	1	NUM
ejpam-3860	334	25	)	)	PUNCT
ejpam-3860	334	26	=	=	PUNCT
ejpam-3860	335	1	⌊	⌊	VERB
ejpam-3860	335	2	k	k	NUM
ejpam-3860	335	3	2	2	NUM
ejpam-3860	335	4	⌋(⌈m	⌋(⌈m	NUM
ejpam-3860	335	5	2	2	NUM
ejpam-3860	335	6	⌉	⌉	NOUN
ejpam-3860	335	7	(	(	PUNCT
ejpam-3860	335	8	n−	n−	NOUN
ejpam-3860	335	9	1	1	NUM
ejpam-3860	335	10	)	)	PUNCT
ejpam-3860	335	11	+	+	CCONJ
ejpam-3860	335	12	⌊m	⌊m	ADP
ejpam-3860	335	13	2	2	NUM
ejpam-3860	335	14	⌋	⌋	NOUN
ejpam-3860	335	15	)	)	PUNCT
ejpam-3860	336	1	+	+	CCONJ
ejpam-3860	336	2	⌈	⌈	SYM
ejpam-3860	336	3	k	k	ADJ
ejpam-3860	336	4	2	2	NUM
ejpam-3860	336	5	⌉(⌈m	⌉(⌈m	NOUN
ejpam-3860	336	6	2	2	NUM
ejpam-3860	336	7	⌉	⌉	NOUN
ejpam-3860	336	8	+	+	ADJ
ejpam-3860	336	9	⌊m	⌊m	X
ejpam-3860	336	10	2	2	NUM
ejpam-3860	336	11	⌋	⌋	NOUN
ejpam-3860	336	12	(	(	PUNCT
ejpam-3860	336	13	n−	n−	NOUN
ejpam-3860	336	14	1	1	NUM
ejpam-3860	336	15	)	)	PUNCT
ejpam-3860	336	16	)	)	PUNCT
ejpam-3860	336	17	.	.	PUNCT
ejpam-3860	337	1	therefore	therefore	ADV
ejpam-3860	337	2	,	,	PUNCT
ejpam-3860	337	3	ni(pk	ni(pk	PROPN
ejpam-3860	337	4	�	�	PROPN
ejpam-3860	337	5	fm	fm	PROPN
ejpam-3860	337	6	,	,	PUNCT
ejpam-3860	337	7	n	n	CCONJ
ejpam-3860	337	8	,	,	PUNCT
ejpam-3860	337	9	x	x	NOUN
ejpam-3860	337	10	)	)	PUNCT
ejpam-3860	337	11	=	=	PUNCT
ejpam-3860	338	1	xd	xd	NUM
ejpam-3860	338	2	k	k	PROPN
ejpam-3860	338	3	2e(dm2	2e(dm2	PROPN
ejpam-3860	338	4	e(n−1)+bm2	e(n−1)+bm2	NOUN
ejpam-3860	338	5	c)+b	c)+b	PROPN
ejpam-3860	338	6	k2c(dm2	k2c(dm2	PROPN
ejpam-3860	338	7	e+bm2	e+bm2	ADJ
ejpam-3860	338	8	c(n−1	c(n−1	PROPN
ejpam-3860	338	9	)	)	PUNCT
ejpam-3860	338	10	)	)	PUNCT
ejpam-3860	339	1	+	+	CCONJ
ejpam-3860	339	2	xb	xb	PROPN
ejpam-3860	339	3	k	k	PROPN
ejpam-3860	339	4	2c(dm2	2c(dm2	PROPN
ejpam-3860	339	5	e(n−1)+bm2	e(n−1)+bm2	NOUN
ejpam-3860	339	6	c)+d	c)+d	NOUN
ejpam-3860	339	7	k2e(dm2	k2e(dm2	PROPN
ejpam-3860	339	8	e+bm2	e+bm2	ADJ
ejpam-3860	339	9	c(n−1	c(n−1	PROPN
ejpam-3860	339	10	)	)	PUNCT
ejpam-3860	339	11	)	)	PUNCT
ejpam-3860	339	12	.	.	PUNCT
ejpam-3860	340	1	theorem	theorem	NOUN
ejpam-3860	340	2	5	5	NUM
ejpam-3860	340	3	.	.	X
ejpam-3860	341	1	for	for	ADP
ejpam-3860	341	2	any	any	DET
ejpam-3860	341	3	path	path	NOUN
ejpam-3860	341	4	pk	pk	NOUN
ejpam-3860	341	5	and	and	CCONJ
ejpam-3860	341	6	centipede	centipede	NOUN
ejpam-3860	341	7	graph	graph	NOUN
ejpam-3860	341	8	cenn	cenn	NOUN
ejpam-3860	341	9	,	,	PUNCT
ejpam-3860	341	10	ni(pk	ni(pk	PROPN
ejpam-3860	341	11	�	�	NOUN
ejpam-3860	341	12	cenn	cenn	NOUN
ejpam-3860	341	13	,	,	PUNCT
ejpam-3860	341	14	x	x	NOUN
ejpam-3860	341	15	)	)	PUNCT
ejpam-3860	342	1	=	=	SYM
ejpam-3860	342	2	2xnk	2xnk	NUM
ejpam-3860	342	3	for	for	ADP
ejpam-3860	342	4	any	any	DET
ejpam-3860	342	5	k	k	NOUN
ejpam-3860	342	6	,	,	PUNCT
ejpam-3860	342	7	n	n	PROPN
ejpam-3860	342	8	∈	∈	PROPN
ejpam-3860	342	9	z+	z+	PUNCT
ejpam-3860	342	10	.	.	PUNCT
ejpam-3860	343	1	n.	n.	PROPN
ejpam-3860	343	2	abdulcarim	abdulcarim	PROPN
ejpam-3860	343	3	,	,	PUNCT
ejpam-3860	343	4	s.	s.	PROPN
ejpam-3860	343	5	dagondon	dagondon	PROPN
ejpam-3860	343	6	,	,	PUNCT
ejpam-3860	343	7	e.	e.	PROPN
ejpam-3860	343	8	chacon	chacon	PROPN
ejpam-3860	343	9	/	/	SYM
ejpam-3860	343	10	eur	eur	PROPN
ejpam-3860	343	11	.	.	PUNCT
ejpam-3860	344	1	j.	j.	PROPN
ejpam-3860	344	2	pure	pure	PROPN
ejpam-3860	344	3	appl	appl	PROPN
ejpam-3860	344	4	.	.	PROPN
ejpam-3860	344	5	math	math	PROPN
ejpam-3860	344	6	,	,	PUNCT
ejpam-3860	344	7	14	14	NUM
ejpam-3860	344	8	(	(	PUNCT
ejpam-3860	344	9	1	1	NUM
ejpam-3860	344	10	)	)	PUNCT
ejpam-3860	344	11	(	(	PUNCT
ejpam-3860	344	12	2021	2021	NUM
ejpam-3860	344	13	)	)	PUNCT
ejpam-3860	344	14	,	,	PUNCT
ejpam-3860	344	15	173	173	NUM
ejpam-3860	344	16	-	-	SYM
ejpam-3860	344	17	191	191	NUM
ejpam-3860	344	18	188	188	NUM
ejpam-3860	344	19	1a	1a	NOUN
ejpam-3860	344	20	1b	1b	NUM
ejpam-3860	344	21	2a	2a	NUM
ejpam-3860	344	22	2b	2b	NUM
ejpam-3860	344	23	3a	3a	NUM
ejpam-3860	344	24	3b	3b	NUM
ejpam-3860	344	25	na	na	NOUN
ejpam-3860	344	26	nb	nb	NOUN
ejpam-3860	344	27	proof	proof	NOUN
ejpam-3860	344	28	:	:	PUNCT
ejpam-3860	344	29	label	label	VERB
ejpam-3860	344	30	the	the	DET
ejpam-3860	344	31	vertices	vertex	NOUN
ejpam-3860	344	32	of	of	ADP
ejpam-3860	344	33	cenn	cenn	NOUN
ejpam-3860	344	34	by	by	ADP
ejpam-3860	344	35	ja	ja	PROPN
ejpam-3860	344	36	,	,	PUNCT
ejpam-3860	344	37	jb	jb	PROPN
ejpam-3860	344	38	:	:	PUNCT
ejpam-3860	344	39	j	j	PROPN
ejpam-3860	344	40	=	=	SYM
ejpam-3860	344	41	1	1	NUM
ejpam-3860	344	42	,	,	PUNCT
ejpam-3860	344	43	·	·	PUNCT
ejpam-3860	344	44	·	·	PUNCT
ejpam-3860	344	45	·	·	PUNCT
ejpam-3860	344	46	,	,	PUNCT
ejpam-3860	344	47	n	n	PROPN
ejpam-3860	344	48	and	and	CCONJ
ejpam-3860	344	49	define	define	VERB
ejpam-3860	344	50	its	its	PRON
ejpam-3860	344	51	edges	edge	NOUN
ejpam-3860	344	52	by	by	ADP
ejpam-3860	344	53	e(cenn	e(cenn	PROPN
ejpam-3860	344	54	)	)	PUNCT
ejpam-3860	344	55	=	=	PRON
ejpam-3860	345	1	{	{	PUNCT
ejpam-3860	345	2	jajb	jajb	NOUN
ejpam-3860	345	3	:	:	PUNCT
ejpam-3860	345	4	j	j	PROPN
ejpam-3860	345	5	=	=	SYM
ejpam-3860	345	6	1	1	NUM
ejpam-3860	345	7	,	,	PUNCT
ejpam-3860	345	8	·	·	PUNCT
ejpam-3860	345	9	·	·	PUNCT
ejpam-3860	345	10	·	·	PUNCT
ejpam-3860	345	11	,	,	PUNCT
ejpam-3860	345	12	n	n	CCONJ
ejpam-3860	345	13	}	}	PUNCT
ejpam-3860	345	14	∪	∪	X
ejpam-3860	345	15	{	{	PUNCT
ejpam-3860	345	16	jb(j	jb(j	X
ejpam-3860	345	17	+	+	X
ejpam-3860	345	18	1)b	1)b	NUM
ejpam-3860	345	19	:	:	PUNCT
ejpam-3860	345	20	j	j	X
ejpam-3860	345	21	=	=	SYM
ejpam-3860	345	22	1	1	NUM
ejpam-3860	345	23	·	·	PUNCT
ejpam-3860	345	24	·	·	PUNCT
ejpam-3860	345	25	·	·	PUNCT
ejpam-3860	345	26	,	,	PUNCT
ejpam-3860	345	27	n	n	CCONJ
ejpam-3860	345	28	−	−	PROPN
ejpam-3860	345	29	1	1	NUM
ejpam-3860	345	30	}	}	PUNCT
ejpam-3860	345	31	as	as	SCONJ
ejpam-3860	345	32	shown	show	VERB
ejpam-3860	345	33	in	in	ADP
ejpam-3860	345	34	the	the	DET
ejpam-3860	345	35	figure	figure	NOUN
ejpam-3860	345	36	below	below	ADV
ejpam-3860	345	37	:	:	PUNCT
ejpam-3860	345	38	then	then	ADV
ejpam-3860	345	39	v	v	X
ejpam-3860	345	40	(	(	PUNCT
ejpam-3860	345	41	pk	pk	NOUN
ejpam-3860	345	42	�	�	NOUN
ejpam-3860	345	43	cenn	cenn	NOUN
ejpam-3860	345	44	)	)	PUNCT
ejpam-3860	345	45	=	=	PRON
ejpam-3860	345	46	{	{	PUNCT
ejpam-3860	345	47	(	(	PUNCT
ejpam-3860	345	48	i	i	PROPN
ejpam-3860	345	49	,	,	PUNCT
ejpam-3860	345	50	ja	ja	PROPN
ejpam-3860	345	51	)	)	PUNCT
ejpam-3860	345	52	,	,	PUNCT
ejpam-3860	345	53	(	(	PUNCT
ejpam-3860	345	54	i	i	PRON
ejpam-3860	345	55	,	,	PUNCT
ejpam-3860	345	56	jb	jb	PROPN
ejpam-3860	345	57	)	)	PUNCT
ejpam-3860	345	58	:	:	PUNCT
ejpam-3860	346	1	i	i	PRON
ejpam-3860	346	2	=	=	NOUN
ejpam-3860	346	3	1	1	NUM
ejpam-3860	346	4	,	,	PUNCT
ejpam-3860	346	5	·	·	PUNCT
ejpam-3860	346	6	·	·	PUNCT
ejpam-3860	346	7	·	·	PUNCT
ejpam-3860	346	8	,	,	PUNCT
ejpam-3860	346	9	k	k	X
ejpam-3860	346	10	,	,	PUNCT
ejpam-3860	346	11	j	j	PROPN
ejpam-3860	346	12	=	=	SYM
ejpam-3860	346	13	1	1	NUM
ejpam-3860	346	14	,	,	PUNCT
ejpam-3860	346	15	·	·	PUNCT
ejpam-3860	346	16	·	·	PUNCT
ejpam-3860	346	17	·	·	PUNCT
ejpam-3860	346	18	,	,	PUNCT
ejpam-3860	346	19	n	n	CCONJ
ejpam-3860	346	20	}	}	PUNCT
ejpam-3860	346	21	.	.	PUNCT
ejpam-3860	347	1	(	(	PUNCT
ejpam-3860	347	2	1	1	NUM
ejpam-3860	347	3	,	,	PUNCT
ejpam-3860	347	4	1a	1a	NUM
ejpam-3860	347	5	)	)	PUNCT
ejpam-3860	347	6	(	(	PUNCT
ejpam-3860	347	7	1	1	NUM
ejpam-3860	347	8	,	,	PUNCT
ejpam-3860	347	9	2a	2a	NUM
ejpam-3860	347	10	)	)	PUNCT
ejpam-3860	347	11	(	(	PUNCT
ejpam-3860	347	12	1	1	NUM
ejpam-3860	347	13	,	,	PUNCT
ejpam-3860	347	14	3a	3a	NUM
ejpam-3860	347	15	)	)	PUNCT
ejpam-3860	347	16	(	(	PUNCT
ejpam-3860	347	17	1	1	NUM
ejpam-3860	347	18	,	,	PUNCT
ejpam-3860	347	19	na	na	NOUN
ejpam-3860	347	20	)	)	PUNCT
ejpam-3860	347	21	(	(	PUNCT
ejpam-3860	347	22	1	1	NUM
ejpam-3860	347	23	,	,	PUNCT
ejpam-3860	347	24	1b	1b	NUM
ejpam-3860	347	25	)	)	PUNCT
ejpam-3860	347	26	(	(	PUNCT
ejpam-3860	347	27	1	1	NUM
ejpam-3860	347	28	,	,	PUNCT
ejpam-3860	347	29	2b	2b	NUM
ejpam-3860	347	30	)	)	PUNCT
ejpam-3860	347	31	(	(	PUNCT
ejpam-3860	347	32	1	1	NUM
ejpam-3860	347	33	,	,	PUNCT
ejpam-3860	347	34	3b	3b	NUM
ejpam-3860	347	35	)	)	PUNCT
ejpam-3860	347	36	(	(	PUNCT
ejpam-3860	347	37	1	1	NUM
ejpam-3860	347	38	,	,	PUNCT
ejpam-3860	347	39	nb	nb	PROPN
ejpam-3860	347	40	)	)	PUNCT
ejpam-3860	347	41	(	(	PUNCT
ejpam-3860	347	42	2	2	NUM
ejpam-3860	347	43	,	,	PUNCT
ejpam-3860	347	44	1a	1a	NUM
ejpam-3860	347	45	)	)	PUNCT
ejpam-3860	347	46	(	(	PUNCT
ejpam-3860	347	47	2	2	NUM
ejpam-3860	347	48	,	,	PUNCT
ejpam-3860	347	49	2a	2a	NUM
ejpam-3860	347	50	)	)	PUNCT
ejpam-3860	347	51	(	(	PUNCT
ejpam-3860	347	52	2	2	NUM
ejpam-3860	347	53	,	,	PUNCT
ejpam-3860	347	54	3a	3a	NUM
ejpam-3860	347	55	)	)	PUNCT
ejpam-3860	347	56	(	(	PUNCT
ejpam-3860	347	57	2	2	NUM
ejpam-3860	347	58	,	,	PUNCT
ejpam-3860	347	59	na	na	NOUN
ejpam-3860	347	60	)	)	PUNCT
ejpam-3860	347	61	(	(	PUNCT
ejpam-3860	347	62	2	2	NUM
ejpam-3860	347	63	,	,	PUNCT
ejpam-3860	347	64	1b	1b	NUM
ejpam-3860	347	65	)	)	PUNCT
ejpam-3860	347	66	(	(	PUNCT
ejpam-3860	347	67	2	2	NUM
ejpam-3860	347	68	,	,	PUNCT
ejpam-3860	347	69	2b	2b	NUM
ejpam-3860	347	70	)	)	PUNCT
ejpam-3860	347	71	(	(	PUNCT
ejpam-3860	347	72	2	2	NUM
ejpam-3860	347	73	,	,	PUNCT
ejpam-3860	347	74	3b	3b	NUM
ejpam-3860	347	75	)	)	PUNCT
ejpam-3860	347	76	(	(	PUNCT
ejpam-3860	347	77	2	2	NUM
ejpam-3860	347	78	,	,	PUNCT
ejpam-3860	347	79	nb	nb	PROPN
ejpam-3860	347	80	)	)	PUNCT
ejpam-3860	347	81	(	(	PUNCT
ejpam-3860	347	82	k	k	X
ejpam-3860	347	83	,	,	PUNCT
ejpam-3860	347	84	1a	1a	NUM
ejpam-3860	347	85	)	)	PUNCT
ejpam-3860	347	86	(	(	PUNCT
ejpam-3860	347	87	k	k	X
ejpam-3860	347	88	,	,	PUNCT
ejpam-3860	347	89	2a	2a	NUM
ejpam-3860	347	90	)	)	PUNCT
ejpam-3860	347	91	(	(	PUNCT
ejpam-3860	347	92	k	k	X
ejpam-3860	347	93	,	,	PUNCT
ejpam-3860	347	94	3a	3a	NUM
ejpam-3860	347	95	)	)	PUNCT
ejpam-3860	347	96	(	(	PUNCT
ejpam-3860	347	97	k	k	X
ejpam-3860	347	98	,	,	PUNCT
ejpam-3860	347	99	na	na	NOUN
ejpam-3860	347	100	)	)	PUNCT
ejpam-3860	347	101	(	(	PUNCT
ejpam-3860	347	102	k	k	NOUN
ejpam-3860	347	103	,	,	PUNCT
ejpam-3860	347	104	1b	1b	NUM
ejpam-3860	347	105	)	)	PUNCT
ejpam-3860	347	106	(	(	PUNCT
ejpam-3860	347	107	k	k	X
ejpam-3860	347	108	,	,	PUNCT
ejpam-3860	347	109	2b	2b	NUM
ejpam-3860	347	110	)	)	PUNCT
ejpam-3860	347	111	(	(	PUNCT
ejpam-3860	347	112	k	k	NOUN
ejpam-3860	347	113	,	,	PUNCT
ejpam-3860	347	114	3b	3b	NUM
ejpam-3860	347	115	)	)	PUNCT
ejpam-3860	347	116	(	(	PUNCT
ejpam-3860	347	117	k	k	X
ejpam-3860	347	118	,	,	PUNCT
ejpam-3860	347	119	nb	nb	PROPN
ejpam-3860	347	120	)	)	PUNCT
ejpam-3860	347	121	n.	n.	PROPN
ejpam-3860	347	122	abdulcarim	abdulcarim	PROPN
ejpam-3860	347	123	,	,	PUNCT
ejpam-3860	347	124	s.	s.	PROPN
ejpam-3860	347	125	dagondon	dagondon	PROPN
ejpam-3860	347	126	,	,	PUNCT
ejpam-3860	347	127	e.	e.	PROPN
ejpam-3860	347	128	chacon	chacon	PROPN
ejpam-3860	347	129	/	/	SYM
ejpam-3860	347	130	eur	eur	PROPN
ejpam-3860	347	131	.	.	PUNCT
ejpam-3860	348	1	j.	j.	PROPN
ejpam-3860	348	2	pure	pure	PROPN
ejpam-3860	348	3	appl	appl	PROPN
ejpam-3860	348	4	.	.	PROPN
ejpam-3860	348	5	math	math	PROPN
ejpam-3860	348	6	,	,	PUNCT
ejpam-3860	348	7	14	14	NUM
ejpam-3860	348	8	(	(	PUNCT
ejpam-3860	348	9	1	1	NUM
ejpam-3860	348	10	)	)	PUNCT
ejpam-3860	348	11	(	(	PUNCT
ejpam-3860	348	12	2021	2021	NUM
ejpam-3860	348	13	)	)	PUNCT
ejpam-3860	348	14	,	,	PUNCT
ejpam-3860	348	15	173	173	NUM
ejpam-3860	348	16	-	-	SYM
ejpam-3860	348	17	191	191	NUM
ejpam-3860	348	18	189	189	NUM
ejpam-3860	348	19	observe	observe	VERB
ejpam-3860	348	20	that	that	SCONJ
ejpam-3860	348	21	•	•	NOUN
ejpam-3860	348	22	(	(	PUNCT
ejpam-3860	348	23	i1	i1	PROPN
ejpam-3860	348	24	,	,	PUNCT
ejpam-3860	348	25	j1a)(i2	j1a)(i2	NOUN
ejpam-3860	348	26	,	,	PUNCT
ejpam-3860	348	27	j2b	j2b	PROPN
ejpam-3860	348	28	)	)	PUNCT
ejpam-3860	348	29	∈	∈	PROPN
ejpam-3860	348	30	e(pk	e(pk	NOUN
ejpam-3860	348	31	�	�	NOUN
ejpam-3860	348	32	cenn	cenn	NOUN
ejpam-3860	348	33	)	)	PUNCT
ejpam-3860	348	34	if	if	SCONJ
ejpam-3860	348	35	i1	i1	PROPN
ejpam-3860	348	36	=	=	PROPN
ejpam-3860	348	37	i2	i2	PROPN
ejpam-3860	348	38	and	and	CCONJ
ejpam-3860	348	39	j1	j1	PROPN
ejpam-3860	348	40	=	=	SYM
ejpam-3860	348	41	j2	j2	PROPN
ejpam-3860	348	42	,	,	PUNCT
ejpam-3860	348	43	•	•	PRON
ejpam-3860	348	44	(	(	PUNCT
ejpam-3860	348	45	i1	i1	PROPN
ejpam-3860	348	46	,	,	PUNCT
ejpam-3860	348	47	j1a)(i2	j1a)(i2	NOUN
ejpam-3860	348	48	,	,	PUNCT
ejpam-3860	348	49	j2a	j2a	NOUN
ejpam-3860	348	50	)	)	PUNCT
ejpam-3860	348	51	∈	∈	PROPN
ejpam-3860	348	52	e(pk	e(pk	NOUN
ejpam-3860	348	53	�	�	NOUN
ejpam-3860	348	54	cenn	cenn	NOUN
ejpam-3860	348	55	)	)	PUNCT
ejpam-3860	348	56	if	if	SCONJ
ejpam-3860	348	57	i1	i1	PROPN
ejpam-3860	348	58	=	=	PROPN
ejpam-3860	348	59	i2	i2	PROPN
ejpam-3860	348	60	+	+	CCONJ
ejpam-3860	348	61	1	1	NUM
ejpam-3860	348	62	and	and	CCONJ
ejpam-3860	348	63	j1	j1	PROPN
ejpam-3860	348	64	=	=	SYM
ejpam-3860	348	65	j2	j2	PROPN
ejpam-3860	348	66	and	and	CCONJ
ejpam-3860	348	67	•	•	NOUN
ejpam-3860	348	68	(	(	PUNCT
ejpam-3860	348	69	i1	i1	PROPN
ejpam-3860	348	70	,	,	PUNCT
ejpam-3860	348	71	j1b)(i2	j1b)(i2	NOUN
ejpam-3860	348	72	,	,	PUNCT
ejpam-3860	348	73	j2b	j2b	PROPN
ejpam-3860	348	74	)	)	PUNCT
ejpam-3860	348	75	∈	∈	PROPN
ejpam-3860	348	76	e(pk	e(pk	NOUN
ejpam-3860	348	77	�	�	NOUN
ejpam-3860	348	78	cenn	cenn	NOUN
ejpam-3860	348	79	)	)	PUNCT
ejpam-3860	348	80	if	if	SCONJ
ejpam-3860	348	81	either	either	PRON
ejpam-3860	348	82	i.	i.	PROPN
ejpam-3860	348	83	)	)	PUNCT
ejpam-3860	348	84	i1	i1	PROPN
ejpam-3860	348	85	=	=	PROPN
ejpam-3860	348	86	i2	i2	PROPN
ejpam-3860	348	87	,	,	PUNCT
ejpam-3860	348	88	j1	j1	PROPN
ejpam-3860	348	89	=	=	SYM
ejpam-3860	348	90	j2	j2	PROPN
ejpam-3860	348	91	+	+	CCONJ
ejpam-3860	348	92	1	1	NUM
ejpam-3860	348	93	or	or	CCONJ
ejpam-3860	348	94	ii	ii	NOUN
ejpam-3860	348	95	.	.	PUNCT
ejpam-3860	348	96	)	)	PUNCT
ejpam-3860	349	1	i1	i1	PROPN
ejpam-3860	349	2	=	=	PROPN
ejpam-3860	349	3	i2	i2	PROPN
ejpam-3860	349	4	+	+	CCONJ
ejpam-3860	349	5	1	1	NUM
ejpam-3860	349	6	,	,	PUNCT
ejpam-3860	349	7	j1	j1	PROPN
ejpam-3860	349	8	=	=	SYM
ejpam-3860	349	9	j2	j2	PROPN
ejpam-3860	349	10	.	.	PUNCT
ejpam-3860	349	11	consider	consider	VERB
ejpam-3860	349	12	the	the	DET
ejpam-3860	349	13	following	follow	VERB
ejpam-3860	349	14	sets	set	NOUN
ejpam-3860	349	15	:	:	PUNCT
ejpam-3860	349	16	ap	ap	PROPN
ejpam-3860	350	1	=	=	PUNCT
ejpam-3860	351	1	{	{	PUNCT
ejpam-3860	352	1	(	(	PUNCT
ejpam-3860	352	2	i	i	PROPN
ejpam-3860	352	3	,	,	PUNCT
ejpam-3860	352	4	ja	ja	PROPN
ejpam-3860	352	5	)	)	PUNCT
ejpam-3860	352	6	:	:	PUNCT
ejpam-3860	353	1	i	i	PRON
ejpam-3860	353	2	and	and	CCONJ
ejpam-3860	353	3	j	j	PROPN
ejpam-3860	353	4	are	be	AUX
ejpam-3860	353	5	odd	odd	ADJ
ejpam-3860	353	6	}	}	PUNCT
ejpam-3860	353	7	,	,	PUNCT
ejpam-3860	353	8	bp	bp	PROPN
ejpam-3860	353	9	=	=	PRON
ejpam-3860	353	10	{	{	PUNCT
ejpam-3860	353	11	(	(	PUNCT
ejpam-3860	353	12	i	i	PROPN
ejpam-3860	353	13	,	,	PUNCT
ejpam-3860	353	14	ja	ja	PROPN
ejpam-3860	353	15	)	)	PUNCT
ejpam-3860	353	16	:	:	PUNCT
ejpam-3860	354	1	i	i	PRON
ejpam-3860	354	2	is	be	AUX
ejpam-3860	354	3	odd	odd	ADJ
ejpam-3860	354	4	and	and	CCONJ
ejpam-3860	354	5	j	j	PROPN
ejpam-3860	354	6	is	be	AUX
ejpam-3860	354	7	even	even	ADV
ejpam-3860	354	8	}	}	PUNCT
ejpam-3860	354	9	aq	aq	X
ejpam-3860	354	10	=	=	SYM
ejpam-3860	354	11	{	{	PUNCT
ejpam-3860	354	12	(	(	PUNCT
ejpam-3860	354	13	i	i	PROPN
ejpam-3860	354	14	,	,	PUNCT
ejpam-3860	354	15	ja	ja	PROPN
ejpam-3860	354	16	)	)	PUNCT
ejpam-3860	354	17	:	:	PUNCT
ejpam-3860	355	1	i	i	PRON
ejpam-3860	355	2	is	be	AUX
ejpam-3860	355	3	even	even	ADV
ejpam-3860	355	4	and	and	CCONJ
ejpam-3860	355	5	j	j	PROPN
ejpam-3860	355	6	is	be	AUX
ejpam-3860	355	7	odd	odd	ADJ
ejpam-3860	355	8	}	}	PUNCT
ejpam-3860	355	9	,	,	PUNCT
ejpam-3860	355	10	bq	bq	INTJ
ejpam-3860	355	11	=	=	PRON
ejpam-3860	355	12	{	{	PUNCT
ejpam-3860	355	13	(	(	PUNCT
ejpam-3860	355	14	i	i	PROPN
ejpam-3860	355	15	,	,	PUNCT
ejpam-3860	355	16	ja	ja	PROPN
ejpam-3860	355	17	)	)	PUNCT
ejpam-3860	355	18	:	:	PUNCT
ejpam-3860	356	1	i	i	PRON
ejpam-3860	356	2	and	and	CCONJ
ejpam-3860	356	3	j	j	PROPN
ejpam-3860	356	4	are	be	AUX
ejpam-3860	356	5	even	even	ADV
ejpam-3860	356	6	}	}	PUNCT
ejpam-3860	356	7	cp	cp	NOUN
ejpam-3860	356	8	=	=	SYM
ejpam-3860	356	9	{	{	PUNCT
ejpam-3860	356	10	(	(	PUNCT
ejpam-3860	356	11	i	i	PROPN
ejpam-3860	356	12	,	,	PUNCT
ejpam-3860	356	13	jb	jb	PROPN
ejpam-3860	356	14	)	)	PUNCT
ejpam-3860	356	15	:	:	PUNCT
ejpam-3860	357	1	i	i	PRON
ejpam-3860	357	2	and	and	CCONJ
ejpam-3860	357	3	j	j	PROPN
ejpam-3860	357	4	are	be	AUX
ejpam-3860	357	5	odd	odd	ADJ
ejpam-3860	357	6	}	}	PUNCT
ejpam-3860	357	7	,	,	PUNCT
ejpam-3860	357	8	dp	dp	NOUN
ejpam-3860	357	9	=	=	SYM
ejpam-3860	357	10	{	{	PUNCT
ejpam-3860	357	11	(	(	PUNCT
ejpam-3860	357	12	i	i	PROPN
ejpam-3860	357	13	,	,	PUNCT
ejpam-3860	357	14	jb	jb	PROPN
ejpam-3860	357	15	)	)	PUNCT
ejpam-3860	357	16	:	:	PUNCT
ejpam-3860	358	1	i	i	PRON
ejpam-3860	358	2	is	be	AUX
ejpam-3860	358	3	odd	odd	ADJ
ejpam-3860	358	4	and	and	CCONJ
ejpam-3860	358	5	j	j	PROPN
ejpam-3860	358	6	is	be	AUX
ejpam-3860	358	7	even	even	ADV
ejpam-3860	358	8	}	}	PUNCT
ejpam-3860	358	9	cq	cq	NOUN
ejpam-3860	359	1	=	=	PUNCT
ejpam-3860	359	2	{	{	PUNCT
ejpam-3860	359	3	(	(	PUNCT
ejpam-3860	359	4	i	i	PROPN
ejpam-3860	359	5	,	,	PUNCT
ejpam-3860	359	6	jb	jb	PROPN
ejpam-3860	359	7	)	)	PUNCT
ejpam-3860	359	8	:	:	PUNCT
ejpam-3860	360	1	i	i	PRON
ejpam-3860	360	2	is	be	AUX
ejpam-3860	360	3	even	even	ADV
ejpam-3860	360	4	and	and	CCONJ
ejpam-3860	360	5	j	j	PROPN
ejpam-3860	360	6	is	be	AUX
ejpam-3860	360	7	odd	odd	ADJ
ejpam-3860	360	8	}	}	PUNCT
ejpam-3860	360	9	,	,	PUNCT
ejpam-3860	360	10	dq	dq	PROPN
ejpam-3860	360	11	=	=	SYM
ejpam-3860	360	12	{	{	PUNCT
ejpam-3860	360	13	(	(	PUNCT
ejpam-3860	360	14	i	i	PROPN
ejpam-3860	360	15	,	,	PUNCT
ejpam-3860	360	16	jb	jb	PROPN
ejpam-3860	360	17	)	)	PUNCT
ejpam-3860	360	18	:	:	PUNCT
ejpam-3860	361	1	i	i	PRON
ejpam-3860	361	2	and	and	CCONJ
ejpam-3860	361	3	j	j	PROPN
ejpam-3860	361	4	are	be	AUX
ejpam-3860	361	5	even	even	ADV
ejpam-3860	361	6	}	}	PUNCT
ejpam-3860	361	7	.	.	PUNCT
ejpam-3860	362	1	let	let	VERB
ejpam-3860	362	2	s	s	PRON
ejpam-3860	362	3	=	=	X
ejpam-3860	362	4	ap	ap	PROPN
ejpam-3860	362	5	∪dp	∪dp	PROPN
ejpam-3860	362	6	∪bq	∪bq	PROPN
ejpam-3860	362	7	∪	∪	X
ejpam-3860	362	8	cq	cq	PROPN
ejpam-3860	362	9	and	and	CCONJ
ejpam-3860	362	10	t	t	PROPN
ejpam-3860	362	11	=	=	SYM
ejpam-3860	362	12	aq	aq	PROPN
ejpam-3860	362	13	∪dq	∪dq	PROPN
ejpam-3860	362	14	∪bp	∪bp	PROPN
ejpam-3860	362	15	∪	∪	PROPN
ejpam-3860	362	16	cp	cp	PROPN
ejpam-3860	362	17	,	,	PUNCT
ejpam-3860	362	18	that	that	ADV
ejpam-3860	362	19	is	be	AUX
ejpam-3860	362	20	,	,	PUNCT
ejpam-3860	362	21	s	s	PART
ejpam-3860	362	22	=	=	PUNCT
ejpam-3860	362	23			X
ejpam-3860	362	24	(	(	PUNCT
ejpam-3860	362	25	i	i	NOUN
ejpam-3860	362	26	,	,	PUNCT
ejpam-3860	362	27	ja	ja	PROPN
ejpam-3860	362	28	)	)	PUNCT
ejpam-3860	362	29	:	:	PUNCT
ejpam-3860	363	1	i	i	PRON
ejpam-3860	363	2	and	and	CCONJ
ejpam-3860	363	3	j	j	PROPN
ejpam-3860	363	4	are	be	AUX
ejpam-3860	363	5	odd	odd	ADJ
ejpam-3860	363	6	(	(	PUNCT
ejpam-3860	363	7	i	i	PROPN
ejpam-3860	363	8	,	,	PUNCT
ejpam-3860	363	9	ja	ja	PROPN
ejpam-3860	363	10	)	)	PUNCT
ejpam-3860	363	11	:	:	PUNCT
ejpam-3860	364	1	i	i	PRON
ejpam-3860	364	2	and	and	CCONJ
ejpam-3860	364	3	j	j	PROPN
ejpam-3860	364	4	are	be	AUX
ejpam-3860	364	5	even	even	ADV
ejpam-3860	364	6	(	(	PUNCT
ejpam-3860	364	7	i	i	PROPN
ejpam-3860	364	8	,	,	PUNCT
ejpam-3860	364	9	jb	jb	PROPN
ejpam-3860	364	10	)	)	PUNCT
ejpam-3860	364	11	:	:	PUNCT
ejpam-3860	365	1	i	i	PRON
ejpam-3860	365	2	is	be	AUX
ejpam-3860	365	3	even	even	ADV
ejpam-3860	365	4	and	and	CCONJ
ejpam-3860	365	5	j	j	PROPN
ejpam-3860	365	6	is	be	AUX
ejpam-3860	365	7	odd	odd	ADJ
ejpam-3860	365	8	(	(	PUNCT
ejpam-3860	365	9	i	i	PROPN
ejpam-3860	365	10	,	,	PUNCT
ejpam-3860	365	11	jb	jb	PROPN
ejpam-3860	365	12	)	)	PUNCT
ejpam-3860	365	13	:	:	PUNCT
ejpam-3860	366	1	i	i	PRON
ejpam-3860	366	2	is	be	AUX
ejpam-3860	366	3	odd	odd	ADJ
ejpam-3860	366	4	and	and	CCONJ
ejpam-3860	366	5	j	j	PROPN
ejpam-3860	366	6	is	be	AUX
ejpam-3860	366	7	even	even	ADV
ejpam-3860	366	8	and	and	CCONJ
ejpam-3860	366	9	t	t	X
ejpam-3860	366	10	=	=	PUNCT
ejpam-3860	366	11			PROPN
ejpam-3860	366	12	(	(	PUNCT
ejpam-3860	366	13	i	i	NOUN
ejpam-3860	366	14	,	,	PUNCT
ejpam-3860	366	15	ja	ja	PROPN
ejpam-3860	366	16	)	)	PUNCT
ejpam-3860	366	17	:	:	PUNCT
ejpam-3860	367	1	i	i	PRON
ejpam-3860	367	2	is	be	AUX
ejpam-3860	367	3	even	even	ADV
ejpam-3860	367	4	and	and	CCONJ
ejpam-3860	367	5	j	j	PROPN
ejpam-3860	367	6	is	be	AUX
ejpam-3860	367	7	odd	odd	ADJ
ejpam-3860	367	8	(	(	PUNCT
ejpam-3860	367	9	i	i	PROPN
ejpam-3860	367	10	,	,	PUNCT
ejpam-3860	367	11	ja	ja	PROPN
ejpam-3860	367	12	)	)	PUNCT
ejpam-3860	367	13	:	:	PUNCT
ejpam-3860	368	1	i	i	PRON
ejpam-3860	368	2	is	be	AUX
ejpam-3860	368	3	odd	odd	ADJ
ejpam-3860	368	4	and	and	CCONJ
ejpam-3860	368	5	j	j	PROPN
ejpam-3860	368	6	is	be	AUX
ejpam-3860	368	7	even	even	ADV
ejpam-3860	368	8	(	(	PUNCT
ejpam-3860	368	9	i	i	PROPN
ejpam-3860	368	10	,	,	PUNCT
ejpam-3860	368	11	jb	jb	PROPN
ejpam-3860	368	12	)	)	PUNCT
ejpam-3860	368	13	:	:	PUNCT
ejpam-3860	369	1	i	i	PRON
ejpam-3860	369	2	and	and	CCONJ
ejpam-3860	369	3	j	j	PROPN
ejpam-3860	369	4	are	be	AUX
ejpam-3860	369	5	odd	odd	ADJ
ejpam-3860	369	6	(	(	PUNCT
ejpam-3860	369	7	i	i	PROPN
ejpam-3860	369	8	,	,	PUNCT
ejpam-3860	369	9	jb	jb	PROPN
ejpam-3860	369	10	)	)	PUNCT
ejpam-3860	369	11	:	:	PUNCT
ejpam-3860	370	1	i	i	PRON
ejpam-3860	370	2	and	and	CCONJ
ejpam-3860	370	3	j	j	PROPN
ejpam-3860	370	4	are	be	AUX
ejpam-3860	370	5	even	even	ADV
ejpam-3860	370	6	.	.	PUNCT
ejpam-3860	371	1	we	we	PRON
ejpam-3860	371	2	claim	claim	VERB
ejpam-3860	371	3	that	that	SCONJ
ejpam-3860	371	4	s	s	VERB
ejpam-3860	371	5	and	and	CCONJ
ejpam-3860	371	6	t	t	PROPN
ejpam-3860	371	7	are	be	AUX
ejpam-3860	371	8	the	the	DET
ejpam-3860	371	9	independent	independent	ADJ
ejpam-3860	371	10	neighborhood	neighborhood	NOUN
ejpam-3860	371	11	sets	set	NOUN
ejpam-3860	371	12	of	of	ADP
ejpam-3860	371	13	pk	pk	NOUN
ejpam-3860	371	14	�	�	NOUN
ejpam-3860	371	15	cenn	cenn	NOUN
ejpam-3860	371	16	.	.	PUNCT
ejpam-3860	372	1	first	first	ADV
ejpam-3860	372	2	,	,	PUNCT
ejpam-3860	372	3	we	we	PRON
ejpam-3860	372	4	show	show	VERB
ejpam-3860	372	5	that	that	SCONJ
ejpam-3860	372	6	no	no	DET
ejpam-3860	372	7	two	two	NUM
ejpam-3860	372	8	vertices	vertex	NOUN
ejpam-3860	372	9	in	in	ADP
ejpam-3860	372	10	s	s	NOUN
ejpam-3860	372	11	are	be	AUX
ejpam-3860	372	12	adjacent	adjacent	ADJ
ejpam-3860	372	13	.	.	PUNCT
ejpam-3860	373	1	observe	observe	VERB
ejpam-3860	373	2	that	that	SCONJ
ejpam-3860	373	3	for	for	ADP
ejpam-3860	373	4	any	any	DET
ejpam-3860	373	5	(	(	PUNCT
ejpam-3860	373	6	i1	i1	PROPN
ejpam-3860	373	7	,	,	PUNCT
ejpam-3860	373	8	j1a	j1a	PROPN
ejpam-3860	373	9	)	)	PUNCT
ejpam-3860	373	10	,	,	PUNCT
ejpam-3860	373	11	(	(	PUNCT
ejpam-3860	373	12	i2	i2	PROPN
ejpam-3860	373	13	,	,	PUNCT
ejpam-3860	373	14	j2a	j2a	PROPN
ejpam-3860	373	15	)	)	PUNCT
ejpam-3860	373	16	∈	∈	PROPN
ejpam-3860	373	17	s	s	PROPN
ejpam-3860	373	18	,	,	PUNCT
ejpam-3860	373	19	(	(	PUNCT
ejpam-3860	373	20	i1	i1	PROPN
ejpam-3860	373	21	,	,	PUNCT
ejpam-3860	373	22	j1a)(i2	j1a)(i2	NOUN
ejpam-3860	373	23	,	,	PUNCT
ejpam-3860	373	24	j2a	j2a	PROPN
ejpam-3860	373	25	)	)	PUNCT
ejpam-3860	373	26	/∈	/∈	PUNCT
ejpam-3860	374	1	e(pk	e(pk	NOUN
ejpam-3860	374	2	�	�	NOUN
ejpam-3860	374	3	cenn	cenn	NOUN
ejpam-3860	374	4	)	)	PUNCT
ejpam-3860	374	5	since	since	SCONJ
ejpam-3860	374	6	j1	j1	PROPN
ejpam-3860	374	7	6=	6=	NUM
ejpam-3860	374	8	j2	j2	PROPN
ejpam-3860	374	9	.	.	PUNCT
ejpam-3860	375	1	also	also	ADV
ejpam-3860	375	2	,	,	PUNCT
ejpam-3860	375	3	for	for	ADP
ejpam-3860	375	4	any	any	DET
ejpam-3860	375	5	(	(	PUNCT
ejpam-3860	375	6	i1	i1	PROPN
ejpam-3860	375	7	,	,	PUNCT
ejpam-3860	375	8	j1a	j1a	PROPN
ejpam-3860	375	9	)	)	PUNCT
ejpam-3860	375	10	,	,	PUNCT
ejpam-3860	375	11	(	(	PUNCT
ejpam-3860	375	12	i2	i2	PROPN
ejpam-3860	375	13	,	,	PUNCT
ejpam-3860	375	14	j2b	j2b	PROPN
ejpam-3860	375	15	)	)	PUNCT
ejpam-3860	375	16	∈	∈	PROPN
ejpam-3860	375	17	s	s	PROPN
ejpam-3860	375	18	,	,	PUNCT
ejpam-3860	375	19	(	(	PUNCT
ejpam-3860	375	20	i1	i1	PROPN
ejpam-3860	375	21	,	,	PUNCT
ejpam-3860	375	22	j1a)(i2	j1a)(i2	NOUN
ejpam-3860	375	23	,	,	PUNCT
ejpam-3860	375	24	j2b	j2b	PROPN
ejpam-3860	375	25	)	)	PUNCT
ejpam-3860	375	26	/∈	/∈	PUNCT
ejpam-3860	376	1	e(pk	e(pk	NOUN
ejpam-3860	376	2	�	�	NOUN
ejpam-3860	376	3	cenn	cenn	NOUN
ejpam-3860	376	4	)	)	PUNCT
ejpam-3860	376	5	since	since	SCONJ
ejpam-3860	376	6	when	when	SCONJ
ejpam-3860	376	7	i1	i1	PROPN
ejpam-3860	376	8	=	=	PROPN
ejpam-3860	376	9	i2	i2	PROPN
ejpam-3860	376	10	,	,	PUNCT
ejpam-3860	376	11	j1	j1	PROPN
ejpam-3860	376	12	6=	6=	NUM
ejpam-3860	376	13	j2	j2	PROPN
ejpam-3860	376	14	and	and	CCONJ
ejpam-3860	376	15	when	when	SCONJ
ejpam-3860	376	16	j1	j1	PROPN
ejpam-3860	376	17	=	=	SYM
ejpam-3860	376	18	j2	j2	PROPN
ejpam-3860	376	19	,	,	PUNCT
ejpam-3860	376	20	i1	i1	PROPN
ejpam-3860	376	21	6=	6=	PROPN
ejpam-3860	376	22	i2	i2	PROPN
ejpam-3860	376	23	.	.	PUNCT
ejpam-3860	377	1	furthermore	furthermore	ADV
ejpam-3860	377	2	,	,	PUNCT
ejpam-3860	377	3	any	any	DET
ejpam-3860	377	4	(	(	PUNCT
ejpam-3860	377	5	i1	i1	NOUN
ejpam-3860	377	6	,	,	PUNCT
ejpam-3860	377	7	j1b	j1b	PROPN
ejpam-3860	377	8	)	)	PUNCT
ejpam-3860	377	9	,	,	PUNCT
ejpam-3860	377	10	(	(	PUNCT
ejpam-3860	377	11	i2	i2	PROPN
ejpam-3860	377	12	,	,	PUNCT
ejpam-3860	377	13	j2b	j2b	PROPN
ejpam-3860	377	14	)	)	PUNCT
ejpam-3860	377	15	∈	∈	PROPN
ejpam-3860	377	16	s	s	PROPN
ejpam-3860	377	17	,	,	PUNCT
ejpam-3860	377	18	(	(	PUNCT
ejpam-3860	377	19	i1	i1	PROPN
ejpam-3860	377	20	,	,	PUNCT
ejpam-3860	377	21	j1b)(i2	j1b)(i2	NOUN
ejpam-3860	377	22	,	,	PUNCT
ejpam-3860	377	23	j2b	j2b	PROPN
ejpam-3860	377	24	)	)	PUNCT
ejpam-3860	377	25	/∈	/∈	PUNCT
ejpam-3860	378	1	e(pk	e(pk	NOUN
ejpam-3860	378	2	�	�	NOUN
ejpam-3860	378	3	cenn	cenn	NOUN
ejpam-3860	378	4	)	)	PUNCT
ejpam-3860	378	5	since	since	SCONJ
ejpam-3860	378	6	both	both	DET
ejpam-3860	378	7	i1	i1	PROPN
ejpam-3860	378	8	6=	6=	PROPN
ejpam-3860	378	9	i2	i2	PROPN
ejpam-3860	378	10	and	and	CCONJ
ejpam-3860	378	11	j1	j1	PROPN
ejpam-3860	378	12	6=	6=	PROPN
ejpam-3860	378	13	j2	j2	PROPN
ejpam-3860	378	14	.	.	PUNCT
ejpam-3860	379	1	hence	hence	ADV
ejpam-3860	379	2	,	,	PUNCT
ejpam-3860	379	3	no	no	DET
ejpam-3860	379	4	two	two	NUM
ejpam-3860	379	5	vertices	vertex	NOUN
ejpam-3860	379	6	in	in	ADP
ejpam-3860	379	7	s	s	NOUN
ejpam-3860	379	8	are	be	AUX
ejpam-3860	379	9	adjacent	adjacent	ADJ
ejpam-3860	379	10	.	.	PUNCT
ejpam-3860	380	1	next	next	ADV
ejpam-3860	380	2	,	,	PUNCT
ejpam-3860	380	3	we	we	PRON
ejpam-3860	380	4	will	will	AUX
ejpam-3860	380	5	show	show	VERB
ejpam-3860	380	6	that	that	SCONJ
ejpam-3860	380	7	⋃	⋃	ADP
ejpam-3860	380	8	v∈s	v∈s	ADJ
ejpam-3860	380	9	〈	〈	PROPN
ejpam-3860	380	10	n	n	PRON
ejpam-3860	380	11	[	[	X
ejpam-3860	380	12	v	v	NOUN
ejpam-3860	380	13	]	]	X
ejpam-3860	380	14	〉	〉	NOUN
ejpam-3860	380	15	=	=	SYM
ejpam-3860	380	16	pk�cenn.assume	pk�cenn.assume	PROPN
ejpam-3860	380	17	to	to	ADP
ejpam-3860	380	18	the	the	DET
ejpam-3860	380	19	contrary	contrary	NOUN
ejpam-3860	380	20	that	that	SCONJ
ejpam-3860	380	21	⋃	⋃	PUNCT
ejpam-3860	380	22	v∈s	v∈s	ADJ
ejpam-3860	380	23	〈	〈	PROPN
ejpam-3860	380	24	n	n	PRON
ejpam-3860	380	25	[	[	X
ejpam-3860	380	26	v	v	NOUN
ejpam-3860	380	27	]	]	X
ejpam-3860	380	28	〉	〉	PROPN
ejpam-3860	380	29	6=	6=	SYM
ejpam-3860	380	30	pk	pk	NOUN
ejpam-3860	380	31	�	�	PROPN
ejpam-3860	380	32	cenn	cenn	NOUN
ejpam-3860	380	33	.	.	PUNCT
ejpam-3860	381	1	then	then	ADV
ejpam-3860	381	2	there	there	PRON
ejpam-3860	381	3	exists	exist	VERB
ejpam-3860	381	4	xy	xy	PROPN
ejpam-3860	381	5	∈	∈	PROPN
ejpam-3860	381	6	e(pk	e(pk	PROPN
ejpam-3860	381	7	�	�	NOUN
ejpam-3860	381	8	cn	cn	NOUN
ejpam-3860	381	9	)	)	PUNCT
ejpam-3860	381	10	such	such	ADJ
ejpam-3860	381	11	that	that	PRON
ejpam-3860	381	12	xy	xy	PROPN
ejpam-3860	381	13	/∈	/∈	PUNCT
ejpam-3860	382	1	e	e	X
ejpam-3860	382	2	(	(	PUNCT
ejpam-3860	382	3	⋃	⋃	ADP
ejpam-3860	382	4	v∈s	v∈s	ADJ
ejpam-3860	382	5	〈	〈	PROPN
ejpam-3860	382	6	n	n	PRON
ejpam-3860	382	7	[	[	X
ejpam-3860	382	8	v	v	NOUN
ejpam-3860	382	9	]	]	X
ejpam-3860	382	10	〉	〉	NUM
ejpam-3860	382	11	)	)	PUNCT
ejpam-3860	382	12	.	.	PUNCT
ejpam-3860	383	1	this	this	PRON
ejpam-3860	383	2	implies	imply	VERB
ejpam-3860	383	3	both	both	DET
ejpam-3860	383	4	x	x	PROPN
ejpam-3860	383	5	,	,	PUNCT
ejpam-3860	383	6	y	y	PROPN
ejpam-3860	383	7	/∈	/∈	PUNCT
ejpam-3860	383	8	s.	s.	PROPN
ejpam-3860	383	9	case	case	NOUN
ejpam-3860	383	10	1	1	NUM
ejpam-3860	383	11	:	:	PUNCT
ejpam-3860	383	12	x	x	SYM
ejpam-3860	383	13	=	=	SYM
ejpam-3860	383	14	(	(	PUNCT
ejpam-3860	383	15	i1	i1	PROPN
ejpam-3860	383	16	,	,	PUNCT
ejpam-3860	383	17	j1a	j1a	PROPN
ejpam-3860	383	18	)	)	PUNCT
ejpam-3860	383	19	and	and	CCONJ
ejpam-3860	383	20	y	y	PROPN
ejpam-3860	383	21	=	=	SYM
ejpam-3860	383	22	(	(	PUNCT
ejpam-3860	383	23	i2	i2	PROPN
ejpam-3860	383	24	,	,	PUNCT
ejpam-3860	383	25	j2b	j2b	PROPN
ejpam-3860	383	26	)	)	PUNCT
ejpam-3860	383	27	since	since	SCONJ
ejpam-3860	383	28	(	(	PUNCT
ejpam-3860	383	29	i1	i1	PROPN
ejpam-3860	383	30	,	,	PUNCT
ejpam-3860	383	31	j1a	j1a	PROPN
ejpam-3860	383	32	)	)	PUNCT
ejpam-3860	383	33	/∈	/∈	PUNCT
ejpam-3860	384	1	s	s	X
ejpam-3860	384	2	,	,	PUNCT
ejpam-3860	384	3	either	either	CCONJ
ejpam-3860	384	4	i1	i1	PROPN
ejpam-3860	384	5	is	be	AUX
ejpam-3860	384	6	even	even	ADV
ejpam-3860	384	7	and	and	CCONJ
ejpam-3860	384	8	j1	j1	PROPN
ejpam-3860	384	9	is	be	AUX
ejpam-3860	384	10	odd	odd	ADJ
ejpam-3860	384	11	or	or	CCONJ
ejpam-3860	384	12	i1	i1	PROPN
ejpam-3860	384	13	is	be	AUX
ejpam-3860	384	14	odd	odd	ADJ
ejpam-3860	384	15	and	and	CCONJ
ejpam-3860	384	16	j1	j1	PROPN
ejpam-3860	384	17	is	be	AUX
ejpam-3860	384	18	even	even	ADV
ejpam-3860	384	19	.	.	PUNCT
ejpam-3860	385	1	if	if	SCONJ
ejpam-3860	385	2	i1	i1	PROPN
ejpam-3860	385	3	is	be	AUX
ejpam-3860	385	4	even	even	ADV
ejpam-3860	385	5	,	,	PUNCT
ejpam-3860	385	6	j1	j1	PROPN
ejpam-3860	385	7	is	be	AUX
ejpam-3860	385	8	odd	odd	ADJ
ejpam-3860	385	9	,	,	PUNCT
ejpam-3860	385	10	then	then	ADV
ejpam-3860	385	11	i2	i2	PROPN
ejpam-3860	385	12	is	be	AUX
ejpam-3860	385	13	even	even	ADV
ejpam-3860	385	14	and	and	CCONJ
ejpam-3860	385	15	j2	j2	PROPN
ejpam-3860	385	16	is	be	AUX
ejpam-3860	385	17	odd	odd	ADJ
ejpam-3860	385	18	.	.	PUNCT
ejpam-3860	386	1	but	but	CCONJ
ejpam-3860	386	2	(	(	PUNCT
ejpam-3860	386	3	i2	i2	PROPN
ejpam-3860	386	4	,	,	PUNCT
ejpam-3860	386	5	j2b	j2b	PROPN
ejpam-3860	386	6	)	)	PUNCT
ejpam-3860	386	7	∈	∈	PROPN
ejpam-3860	386	8	s.	s.	PROPN
ejpam-3860	387	1	this	this	PRON
ejpam-3860	387	2	is	be	AUX
ejpam-3860	387	3	a	a	DET
ejpam-3860	387	4	contradiction	contradiction	NOUN
ejpam-3860	387	5	.	.	PUNCT
ejpam-3860	388	1	for	for	ADP
ejpam-3860	388	2	i1	i1	PROPN
ejpam-3860	388	3	odd	odd	ADJ
ejpam-3860	388	4	and	and	CCONJ
ejpam-3860	388	5	j1	j1	PROPN
ejpam-3860	388	6	even	even	ADV
ejpam-3860	388	7	,	,	PUNCT
ejpam-3860	388	8	i2	i2	PROPN
ejpam-3860	388	9	is	be	AUX
ejpam-3860	388	10	odd	odd	ADJ
ejpam-3860	388	11	and	and	CCONJ
ejpam-3860	388	12	j2	j2	PROPN
ejpam-3860	388	13	is	be	AUX
ejpam-3860	388	14	even	even	ADV
ejpam-3860	388	15	.	.	PUNCT
ejpam-3860	389	1	similarly	similarly	ADV
ejpam-3860	389	2	,	,	PUNCT
ejpam-3860	389	3	(	(	PUNCT
ejpam-3860	389	4	i2	i2	PROPN
ejpam-3860	389	5	,	,	PUNCT
ejpam-3860	389	6	j2b	j2b	PROPN
ejpam-3860	389	7	)	)	PUNCT
ejpam-3860	389	8	∈	∈	PROPN
ejpam-3860	389	9	s	s	PART
ejpam-3860	389	10	which	which	PRON
ejpam-3860	389	11	is	be	AUX
ejpam-3860	389	12	a	a	DET
ejpam-3860	389	13	contradiction	contradiction	NOUN
ejpam-3860	389	14	.	.	PUNCT
ejpam-3860	390	1	case	case	NOUN
ejpam-3860	390	2	2	2	NUM
ejpam-3860	390	3	:	:	PUNCT
ejpam-3860	390	4	x	x	SYM
ejpam-3860	390	5	=	=	SYM
ejpam-3860	390	6	(	(	PUNCT
ejpam-3860	390	7	i1	i1	PROPN
ejpam-3860	390	8	,	,	PUNCT
ejpam-3860	390	9	j1a	j1a	PROPN
ejpam-3860	390	10	)	)	PUNCT
ejpam-3860	390	11	and	and	CCONJ
ejpam-3860	390	12	y	y	PROPN
ejpam-3860	390	13	=	=	SYM
ejpam-3860	390	14	(	(	PUNCT
ejpam-3860	390	15	i2	i2	PROPN
ejpam-3860	390	16	,	,	PUNCT
ejpam-3860	390	17	j2a	j2a	PROPN
ejpam-3860	390	18	)	)	PUNCT
ejpam-3860	390	19	when	when	SCONJ
ejpam-3860	390	20	(	(	PUNCT
ejpam-3860	390	21	i1	i1	PROPN
ejpam-3860	390	22	,	,	PUNCT
ejpam-3860	390	23	j1a	j1a	PROPN
ejpam-3860	390	24	)	)	PUNCT
ejpam-3860	390	25	/∈	/∈	PUNCT
ejpam-3860	391	1	s	s	X
ejpam-3860	391	2	,	,	PUNCT
ejpam-3860	391	3	it	it	PRON
ejpam-3860	391	4	follows	follow	VERB
ejpam-3860	391	5	that	that	SCONJ
ejpam-3860	391	6	either	either	CCONJ
ejpam-3860	391	7	i1	i1	PROPN
ejpam-3860	391	8	is	be	AUX
ejpam-3860	391	9	even	even	ADV
ejpam-3860	391	10	and	and	CCONJ
ejpam-3860	391	11	j1	j1	PROPN
ejpam-3860	391	12	is	be	AUX
ejpam-3860	391	13	odd	odd	ADJ
ejpam-3860	391	14	or	or	CCONJ
ejpam-3860	391	15	i1	i1	PROPN
ejpam-3860	391	16	is	be	AUX
ejpam-3860	391	17	odd	odd	ADJ
ejpam-3860	391	18	and	and	CCONJ
ejpam-3860	391	19	j1	j1	PROPN
ejpam-3860	391	20	is	be	AUX
ejpam-3860	391	21	even	even	ADV
ejpam-3860	391	22	.	.	PUNCT
ejpam-3860	392	1	consider	consider	VERB
ejpam-3860	392	2	i1	i1	PROPN
ejpam-3860	392	3	to	to	PART
ejpam-3860	392	4	be	be	AUX
ejpam-3860	392	5	even	even	ADV
ejpam-3860	392	6	and	and	CCONJ
ejpam-3860	392	7	j1	j1	PROPN
ejpam-3860	392	8	to	to	PART
ejpam-3860	392	9	be	be	AUX
ejpam-3860	392	10	odd	odd	ADJ
ejpam-3860	392	11	.	.	PUNCT
ejpam-3860	393	1	since	since	SCONJ
ejpam-3860	393	2	(	(	PUNCT
ejpam-3860	393	3	i1	i1	PROPN
ejpam-3860	393	4	,	,	PUNCT
ejpam-3860	393	5	j1a)(i2	j1a)(i2	NOUN
ejpam-3860	393	6	,	,	PUNCT
ejpam-3860	393	7	j2a	j2a	NOUN
ejpam-3860	393	8	)	)	PUNCT
ejpam-3860	393	9	∈	∈	PROPN
ejpam-3860	393	10	e(pk	e(pk	PROPN
ejpam-3860	393	11	�	�	NOUN
ejpam-3860	393	12	cenn	cenn	NOUN
ejpam-3860	393	13	)	)	PUNCT
ejpam-3860	393	14	n.	n.	PROPN
ejpam-3860	393	15	abdulcarim	abdulcarim	PROPN
ejpam-3860	393	16	,	,	PUNCT
ejpam-3860	393	17	s.	s.	PROPN
ejpam-3860	393	18	dagondon	dagondon	PROPN
ejpam-3860	393	19	,	,	PUNCT
ejpam-3860	393	20	e.	e.	PROPN
ejpam-3860	393	21	chacon	chacon	PROPN
ejpam-3860	393	22	/	/	SYM
ejpam-3860	393	23	eur	eur	PROPN
ejpam-3860	393	24	.	.	PUNCT
ejpam-3860	394	1	j.	j.	PROPN
ejpam-3860	394	2	pure	pure	PROPN
ejpam-3860	394	3	appl	appl	PROPN
ejpam-3860	394	4	.	.	PROPN
ejpam-3860	394	5	math	math	PROPN
ejpam-3860	394	6	,	,	PUNCT
ejpam-3860	394	7	14	14	NUM
ejpam-3860	394	8	(	(	PUNCT
ejpam-3860	394	9	1	1	NUM
ejpam-3860	394	10	)	)	PUNCT
ejpam-3860	394	11	(	(	PUNCT
ejpam-3860	394	12	2021	2021	NUM
ejpam-3860	394	13	)	)	PUNCT
ejpam-3860	394	14	,	,	PUNCT
ejpam-3860	394	15	173	173	NUM
ejpam-3860	394	16	-	-	SYM
ejpam-3860	394	17	191	191	NUM
ejpam-3860	394	18	190	190	NUM
ejpam-3860	394	19	if	if	SCONJ
ejpam-3860	394	20	i1	i1	PROPN
ejpam-3860	394	21	=	=	PROPN
ejpam-3860	394	22	i2	i2	PROPN
ejpam-3860	394	23	+	+	CCONJ
ejpam-3860	394	24	1	1	NUM
ejpam-3860	394	25	and	and	CCONJ
ejpam-3860	394	26	j1	j1	PROPN
ejpam-3860	394	27	=	=	SYM
ejpam-3860	394	28	j2	j2	PROPN
ejpam-3860	395	1	,	,	PUNCT
ejpam-3860	395	2	it	it	PRON
ejpam-3860	395	3	follows	follow	VERB
ejpam-3860	395	4	that	that	SCONJ
ejpam-3860	395	5	i2	i2	PROPN
ejpam-3860	395	6	and	and	CCONJ
ejpam-3860	395	7	j2	j2	PROPN
ejpam-3860	395	8	are	be	AUX
ejpam-3860	395	9	odd	odd	ADJ
ejpam-3860	395	10	and	and	CCONJ
ejpam-3860	395	11	this	this	PRON
ejpam-3860	395	12	is	be	AUX
ejpam-3860	395	13	a	a	DET
ejpam-3860	395	14	contradiction	contradiction	NOUN
ejpam-3860	395	15	for	for	ADP
ejpam-3860	395	16	(	(	PUNCT
ejpam-3860	395	17	i2	i2	PROPN
ejpam-3860	395	18	,	,	PUNCT
ejpam-3860	395	19	j2a	j2a	PROPN
ejpam-3860	395	20	)	)	PUNCT
ejpam-3860	395	21	∈	∈	PROPN
ejpam-3860	395	22	s.	s.	PROPN
ejpam-3860	395	23	similarly	similarly	ADV
ejpam-3860	395	24	,	,	PUNCT
ejpam-3860	395	25	when	when	SCONJ
ejpam-3860	395	26	i1	i1	PROPN
ejpam-3860	395	27	is	be	AUX
ejpam-3860	395	28	odd	odd	ADJ
ejpam-3860	395	29	and	and	CCONJ
ejpam-3860	395	30	j1	j1	PROPN
ejpam-3860	395	31	is	be	AUX
ejpam-3860	395	32	even	even	ADV
ejpam-3860	395	33	,	,	PUNCT
ejpam-3860	395	34	i2	i2	PROPN
ejpam-3860	395	35	and	and	CCONJ
ejpam-3860	395	36	j2	j2	PROPN
ejpam-3860	395	37	are	be	AUX
ejpam-3860	395	38	even	even	ADV
ejpam-3860	395	39	and	and	CCONJ
ejpam-3860	395	40	this	this	PRON
ejpam-3860	395	41	is	be	AUX
ejpam-3860	395	42	a	a	DET
ejpam-3860	395	43	contradiction	contradiction	NOUN
ejpam-3860	395	44	since	since	SCONJ
ejpam-3860	395	45	(	(	PUNCT
ejpam-3860	395	46	i2	i2	PROPN
ejpam-3860	395	47	,	,	PUNCT
ejpam-3860	395	48	j2a	j2a	PROPN
ejpam-3860	395	49	)	)	PUNCT
ejpam-3860	395	50	∈	∈	PROPN
ejpam-3860	395	51	s.	s.	PROPN
ejpam-3860	395	52	case	case	NOUN
ejpam-3860	395	53	3	3	NUM
ejpam-3860	395	54	:	:	PUNCT
ejpam-3860	395	55	x	x	SYM
ejpam-3860	395	56	=	=	SYM
ejpam-3860	395	57	(	(	PUNCT
ejpam-3860	395	58	i1	i1	PROPN
ejpam-3860	395	59	,	,	PUNCT
ejpam-3860	395	60	j1b	j1b	PROPN
ejpam-3860	395	61	)	)	PUNCT
ejpam-3860	395	62	and	and	CCONJ
ejpam-3860	395	63	y	y	PROPN
ejpam-3860	395	64	=	=	SYM
ejpam-3860	395	65	(	(	PUNCT
ejpam-3860	395	66	i2	i2	PROPN
ejpam-3860	395	67	,	,	PUNCT
ejpam-3860	395	68	j2b	j2b	PROPN
ejpam-3860	395	69	)	)	PUNCT
ejpam-3860	395	70	since	since	SCONJ
ejpam-3860	395	71	(	(	PUNCT
ejpam-3860	395	72	i1	i1	PROPN
ejpam-3860	395	73	,	,	PUNCT
ejpam-3860	395	74	j1b	j1b	PROPN
ejpam-3860	395	75	)	)	PUNCT
ejpam-3860	395	76	/∈	/∈	PUNCT
ejpam-3860	396	1	s	s	X
ejpam-3860	396	2	,	,	PUNCT
ejpam-3860	396	3	either	either	CCONJ
ejpam-3860	396	4	i1	i1	PROPN
ejpam-3860	396	5	and	and	CCONJ
ejpam-3860	396	6	j1	j1	PROPN
ejpam-3860	396	7	are	be	AUX
ejpam-3860	396	8	odd	odd	ADJ
ejpam-3860	396	9	or	or	CCONJ
ejpam-3860	396	10	even	even	ADV
ejpam-3860	396	11	.	.	PUNCT
ejpam-3860	397	1	similarly	similarly	ADV
ejpam-3860	397	2	,	,	PUNCT
ejpam-3860	397	3	(	(	PUNCT
ejpam-3860	397	4	i2	i2	PROPN
ejpam-3860	397	5	,	,	PUNCT
ejpam-3860	397	6	j2b	j2b	PROPN
ejpam-3860	397	7	)	)	PUNCT
ejpam-3860	397	8	/∈	/∈	PUNCT
ejpam-3860	398	1	s	s	PROPN
ejpam-3860	398	2	implies	imply	VERB
ejpam-3860	398	3	i2	i2	PROPN
ejpam-3860	398	4	and	and	CCONJ
ejpam-3860	398	5	j2	j2	PROPN
ejpam-3860	398	6	are	be	AUX
ejpam-3860	398	7	odd	odd	ADJ
ejpam-3860	398	8	or	or	CCONJ
ejpam-3860	398	9	even	even	ADV
ejpam-3860	398	10	.	.	PUNCT
ejpam-3860	399	1	but	but	CCONJ
ejpam-3860	399	2	if	if	SCONJ
ejpam-3860	399	3	i1	i1	PROPN
ejpam-3860	399	4	,	,	PUNCT
ejpam-3860	399	5	j1	j1	PROPN
ejpam-3860	399	6	,	,	PUNCT
ejpam-3860	399	7	i2	i2	PROPN
ejpam-3860	399	8	,	,	PUNCT
ejpam-3860	399	9	j2	j2	PROPN
ejpam-3860	399	10	are	be	AUX
ejpam-3860	399	11	all	all	PRON
ejpam-3860	399	12	odd	odd	ADJ
ejpam-3860	399	13	,	,	PUNCT
ejpam-3860	399	14	(	(	PUNCT
ejpam-3860	399	15	i1	i1	PROPN
ejpam-3860	399	16	,	,	PUNCT
ejpam-3860	399	17	j1b)(i2	j1b)(i2	NOUN
ejpam-3860	399	18	,	,	PUNCT
ejpam-3860	399	19	j2b	j2b	PROPN
ejpam-3860	399	20	)	)	PUNCT
ejpam-3860	399	21	/∈	/∈	PUNCT
ejpam-3860	400	1	e(pk	e(pk	NOUN
ejpam-3860	400	2	�	�	NOUN
ejpam-3860	400	3	cenn	cenn	NOUN
ejpam-3860	400	4	)	)	PUNCT
ejpam-3860	400	5	.	.	PUNCT
ejpam-3860	401	1	also	also	ADV
ejpam-3860	401	2	,	,	PUNCT
ejpam-3860	401	3	when	when	SCONJ
ejpam-3860	401	4	i1	i1	PROPN
ejpam-3860	401	5	,	,	PUNCT
ejpam-3860	401	6	i2	i2	PROPN
ejpam-3860	401	7	,	,	PUNCT
ejpam-3860	401	8	j1	j1	PROPN
ejpam-3860	401	9	,	,	PUNCT
ejpam-3860	401	10	j2	j2	PROPN
ejpam-3860	401	11	are	be	AUX
ejpam-3860	401	12	all	all	ADV
ejpam-3860	401	13	even	even	ADV
ejpam-3860	401	14	,	,	PUNCT
ejpam-3860	401	15	(	(	PUNCT
ejpam-3860	401	16	i1	i1	PROPN
ejpam-3860	401	17	,	,	PUNCT
ejpam-3860	401	18	j1b)(i2	j1b)(i2	NOUN
ejpam-3860	401	19	,	,	PUNCT
ejpam-3860	401	20	j2b	j2b	PROPN
ejpam-3860	401	21	)	)	PUNCT
ejpam-3860	401	22	/∈	/∈	PUNCT
ejpam-3860	402	1	e(pk	e(pk	NOUN
ejpam-3860	402	2	�	�	NOUN
ejpam-3860	402	3	cenn	cenn	NOUN
ejpam-3860	402	4	)	)	PUNCT
ejpam-3860	402	5	.	.	PUNCT
ejpam-3860	403	1	if	if	SCONJ
ejpam-3860	403	2	we	we	PRON
ejpam-3860	403	3	consider	consider	VERB
ejpam-3860	403	4	i1	i1	PROPN
ejpam-3860	403	5	,	,	PUNCT
ejpam-3860	403	6	j1	j1	PROPN
ejpam-3860	403	7	to	to	PART
ejpam-3860	403	8	be	be	AUX
ejpam-3860	403	9	odd	odd	ADJ
ejpam-3860	403	10	and	and	CCONJ
ejpam-3860	403	11	i2	i2	PROPN
ejpam-3860	403	12	,	,	PUNCT
ejpam-3860	403	13	j2	j2	PROPN
ejpam-3860	403	14	to	to	PART
ejpam-3860	403	15	be	be	AUX
ejpam-3860	403	16	even	even	ADV
ejpam-3860	403	17	,	,	PUNCT
ejpam-3860	403	18	clearly	clearly	ADV
ejpam-3860	403	19	,	,	PUNCT
ejpam-3860	403	20	(	(	PUNCT
ejpam-3860	403	21	i1	i1	PROPN
ejpam-3860	403	22	,	,	PUNCT
ejpam-3860	403	23	j1b)(i2	j1b)(i2	NOUN
ejpam-3860	403	24	,	,	PUNCT
ejpam-3860	403	25	j2b	j2b	PROPN
ejpam-3860	403	26	)	)	PUNCT
ejpam-3860	403	27	/∈	/∈	PUNCT
ejpam-3860	404	1	e(pk	e(pk	NOUN
ejpam-3860	404	2	�	�	NOUN
ejpam-3860	404	3	cenn	cenn	NOUN
ejpam-3860	404	4	)	)	PUNCT
ejpam-3860	404	5	.	.	PUNCT
ejpam-3860	405	1	hence	hence	ADV
ejpam-3860	405	2	,	,	PUNCT
ejpam-3860	405	3	all	all	DET
ejpam-3860	405	4	possibilities	possibility	NOUN
ejpam-3860	405	5	yield	yield	VERB
ejpam-3860	405	6	a	a	DET
ejpam-3860	405	7	contradiction	contradiction	NOUN
ejpam-3860	405	8	.	.	PUNCT
ejpam-3860	406	1	thus	thus	ADV
ejpam-3860	406	2	,	,	PUNCT
ejpam-3860	406	3	xy	xy	PROPN
ejpam-3860	406	4	∈	∈	PROPN
ejpam-3860	406	5	e	e	X
ejpam-3860	406	6	(	(	PUNCT
ejpam-3860	406	7	⋃	⋃	ADP
ejpam-3860	406	8	v∈s	v∈s	ADJ
ejpam-3860	406	9	〈	〈	PROPN
ejpam-3860	406	10	n	n	PRON
ejpam-3860	406	11	[	[	X
ejpam-3860	406	12	v	v	NOUN
ejpam-3860	406	13	]	]	X
ejpam-3860	406	14	〉	〉	NUM
ejpam-3860	406	15	)	)	PUNCT
ejpam-3860	406	16	.	.	PUNCT
ejpam-3860	407	1	consequently	consequently	ADV
ejpam-3860	407	2	,	,	PUNCT
ejpam-3860	407	3	⋃	⋃	PUNCT
ejpam-3860	407	4	v∈s	v∈s	ADJ
ejpam-3860	407	5	〈	〈	PROPN
ejpam-3860	407	6	n	n	PRON
ejpam-3860	407	7	[	[	X
ejpam-3860	407	8	v	v	NOUN
ejpam-3860	407	9	]	]	X
ejpam-3860	407	10	〉	〉	NOUN
ejpam-3860	407	11	=	=	SYM
ejpam-3860	407	12	pk	pk	NOUN
ejpam-3860	407	13	�	�	NOUN
ejpam-3860	407	14	cenn	cenn	NOUN
ejpam-3860	407	15	.	.	PUNCT
ejpam-3860	408	1	thus	thus	ADV
ejpam-3860	408	2	,	,	PUNCT
ejpam-3860	408	3	s	s	VERB
ejpam-3860	408	4	is	be	AUX
ejpam-3860	408	5	an	an	DET
ejpam-3860	408	6	independent	independent	ADJ
ejpam-3860	408	7	neighborhood	neighborhood	NOUN
ejpam-3860	408	8	set	set	NOUN
ejpam-3860	408	9	of	of	ADP
ejpam-3860	408	10	pk	pk	NOUN
ejpam-3860	408	11	�	�	NOUN
ejpam-3860	408	12	cenn	cenn	NOUN
ejpam-3860	408	13	.	.	PUNCT
ejpam-3860	409	1	we	we	PRON
ejpam-3860	409	2	can	can	AUX
ejpam-3860	409	3	also	also	ADV
ejpam-3860	409	4	verify	verify	VERB
ejpam-3860	409	5	that	that	SCONJ
ejpam-3860	409	6	t	t	PROPN
ejpam-3860	409	7	is	be	AUX
ejpam-3860	409	8	an	an	DET
ejpam-3860	409	9	independent	independent	ADJ
ejpam-3860	409	10	neighborhood	neighborhood	NOUN
ejpam-3860	409	11	set	set	NOUN
ejpam-3860	409	12	of	of	ADP
ejpam-3860	409	13	pk	pk	NOUN
ejpam-3860	409	14	�	�	NOUN
ejpam-3860	409	15	cenn	cenn	NOUN
ejpam-3860	409	16	by	by	ADP
ejpam-3860	409	17	following	follow	VERB
ejpam-3860	409	18	the	the	DET
ejpam-3860	409	19	same	same	ADJ
ejpam-3860	409	20	argument	argument	NOUN
ejpam-3860	409	21	in	in	ADP
ejpam-3860	409	22	s.	s.	PROPN
ejpam-3860	409	23	lastly	lastly	ADV
ejpam-3860	409	24	,	,	PUNCT
ejpam-3860	409	25	observe	observe	VERB
ejpam-3860	409	26	that	that	SCONJ
ejpam-3860	409	27	|ap|	|ap|	PRON
ejpam-3860	409	28	=	=	SYM
ejpam-3860	409	29	⌈	⌈	NOUN
ejpam-3860	409	30	k	k	PROPN
ejpam-3860	409	31	2	2	NUM
ejpam-3860	409	32	⌉	⌉	NOUN
ejpam-3860	409	33	⌈	⌈	NOUN
ejpam-3860	409	34	n	n	PRON
ejpam-3860	409	35	2	2	NUM
ejpam-3860	409	36	⌉	⌉	NOUN
ejpam-3860	409	37	,	,	PUNCT
ejpam-3860	409	38	|dp|	|dp|	PROPN
ejpam-3860	409	39	=	=	SYM
ejpam-3860	409	40	⌈	⌈	NOUN
ejpam-3860	409	41	k	k	X
ejpam-3860	409	42	2	2	NUM
ejpam-3860	409	43	⌉	⌉	X
ejpam-3860	409	44	⌊	⌊	VERB
ejpam-3860	409	45	n	n	DET
ejpam-3860	409	46	2	2	NUM
ejpam-3860	409	47	⌋	⌋	NOUN
ejpam-3860	409	48	,	,	PUNCT
ejpam-3860	409	49	|bq|	|bq|	PROPN
ejpam-3860	409	50	=	=	PUNCT
ejpam-3860	410	1	⌊	⌊	VERB
ejpam-3860	410	2	k	k	X
ejpam-3860	410	3	2	2	NUM
ejpam-3860	410	4	⌋	⌋	NOUN
ejpam-3860	410	5	⌊	⌊	VERB
ejpam-3860	410	6	n	n	ADV
ejpam-3860	410	7	2	2	NUM
ejpam-3860	410	8	⌋	⌋	NOUN
ejpam-3860	410	9	,	,	PUNCT
ejpam-3860	410	10	|cq|	|cq|	PROPN
ejpam-3860	410	11	=	=	PUNCT
ejpam-3860	411	1	⌊	⌊	VERB
ejpam-3860	411	2	k	k	X
ejpam-3860	411	3	2	2	NUM
ejpam-3860	411	4	⌋	⌋	NOUN
ejpam-3860	411	5	⌊	⌊	VERB
ejpam-3860	411	6	n	n	ADV
ejpam-3860	411	7	2	2	NUM
ejpam-3860	411	8	⌋	⌋	NOUN
ejpam-3860	411	9	,	,	PUNCT
ejpam-3860	411	10	|aq|	|aq|	NOUN
ejpam-3860	411	11	=	=	ADJ
ejpam-3860	411	12	⌊	⌊	NOUN
ejpam-3860	411	13	k	k	X
ejpam-3860	411	14	2	2	NUM
ejpam-3860	411	15	⌋	⌋	NOUN
ejpam-3860	411	16	⌈	⌈	NOUN
ejpam-3860	411	17	n	n	PRON
ejpam-3860	411	18	2	2	NUM
ejpam-3860	411	19	⌉	⌉	NOUN
ejpam-3860	411	20	,	,	PUNCT
ejpam-3860	411	21	|dq|	|dq|	NOUN
ejpam-3860	411	22	=	=	SYM
ejpam-3860	412	1	⌊	⌊	VERB
ejpam-3860	412	2	k	k	X
ejpam-3860	412	3	2	2	NUM
ejpam-3860	412	4	⌋	⌋	NOUN
ejpam-3860	412	5	⌊	⌊	VERB
ejpam-3860	412	6	n	n	ADV
ejpam-3860	412	7	2	2	NUM
ejpam-3860	412	8	⌋	⌋	NOUN
ejpam-3860	412	9	,	,	PUNCT
ejpam-3860	412	10	|bp|	|bp|	PROPN
ejpam-3860	412	11	=	=	PUNCT
ejpam-3860	413	1	⌈	⌈	PROPN
ejpam-3860	413	2	k	k	X
ejpam-3860	413	3	2	2	NUM
ejpam-3860	413	4	⌉	⌉	X
ejpam-3860	413	5	⌊	⌊	VERB
ejpam-3860	413	6	n	n	ADV
ejpam-3860	413	7	2	2	NUM
ejpam-3860	413	8	⌋	⌋	NOUN
ejpam-3860	413	9	and	and	CCONJ
ejpam-3860	413	10	|cp|	|cp|	NOUN
ejpam-3860	413	11	=	=	SYM
ejpam-3860	413	12	⌈	⌈	SYM
ejpam-3860	413	13	k	k	X
ejpam-3860	413	14	2	2	NUM
ejpam-3860	413	15	⌉	⌉	NOUN
ejpam-3860	413	16	⌈	⌈	NOUN
ejpam-3860	413	17	n	n	CCONJ
ejpam-3860	413	18	2	2	NUM
ejpam-3860	413	19	⌉	⌉	X
ejpam-3860	413	20	.	.	PUNCT
ejpam-3860	414	1	hence	hence	ADV
ejpam-3860	414	2	,	,	PUNCT
ejpam-3860	414	3	|s|	|s|	PROPN
ejpam-3860	414	4	=	=	SYM
ejpam-3860	414	5	|ap|+	|ap|+	PROPN
ejpam-3860	414	6	|dp|+	|dp|+	PROPN
ejpam-3860	414	7	|bq|+	|bq|+	PROPN
ejpam-3860	414	8	|cq|	|cq|	NOUN
ejpam-3860	414	9	=	=	PUNCT
ejpam-3860	414	10	⌈	⌈	SYM
ejpam-3860	414	11	k	k	X
ejpam-3860	414	12	2	2	NUM
ejpam-3860	414	13	⌉	⌉	X
ejpam-3860	414	14	⌈n	⌈n	NOUN
ejpam-3860	414	15	2	2	NUM
ejpam-3860	414	16	⌉	⌉	NOUN
ejpam-3860	414	17	+	+	CCONJ
ejpam-3860	414	18	⌈	⌈	SYM
ejpam-3860	414	19	k	k	X
ejpam-3860	414	20	2	2	NUM
ejpam-3860	414	21	⌉	⌉	NOUN
ejpam-3860	414	22	⌊n	⌊n	ADP
ejpam-3860	414	23	2	2	NUM
ejpam-3860	414	24	⌋	⌋	NOUN
ejpam-3860	414	25	+	+	CCONJ
ejpam-3860	414	26	⌊	⌊	X
ejpam-3860	414	27	k	k	PROPN
ejpam-3860	414	28	2	2	NUM
ejpam-3860	414	29	⌋⌊n	⌋⌊n	NOUN
ejpam-3860	414	30	2	2	NUM
ejpam-3860	414	31	⌋	⌋	NOUN
ejpam-3860	415	1	+	+	CCONJ
ejpam-3860	415	2	⌊	⌊	X
ejpam-3860	415	3	k	k	ADJ
ejpam-3860	415	4	2	2	NUM
ejpam-3860	415	5	⌋	⌋	NOUN
ejpam-3860	415	6	⌈n	⌈n	NOUN
ejpam-3860	415	7	2	2	NUM
ejpam-3860	415	8	⌉	⌉	SCONJ
ejpam-3860	415	9	=	=	SYM
ejpam-3860	415	10	⌈	⌈	SYM
ejpam-3860	415	11	k	k	PROPN
ejpam-3860	415	12	2	2	NUM
ejpam-3860	415	13	⌉(⌈n	⌉(⌈n	NUM
ejpam-3860	415	14	2	2	NUM
ejpam-3860	415	15	⌉	⌉	NOUN
ejpam-3860	415	16	+	+	CCONJ
ejpam-3860	415	17	⌊n	⌊n	ADJ
ejpam-3860	415	18	2	2	NUM
ejpam-3860	415	19	⌋	⌋	NOUN
ejpam-3860	415	20	)	)	PUNCT
ejpam-3860	416	1	+	+	CCONJ
ejpam-3860	416	2	⌊	⌊	X
ejpam-3860	416	3	k	k	ADJ
ejpam-3860	416	4	2	2	NUM
ejpam-3860	416	5	⌋(⌈n	⌋(⌈n	SYM
ejpam-3860	416	6	2	2	NUM
ejpam-3860	416	7	⌉	⌉	NOUN
ejpam-3860	416	8	+	+	CCONJ
ejpam-3860	416	9	⌊n	⌊n	ADJ
ejpam-3860	416	10	2	2	NUM
ejpam-3860	416	11	⌋	⌋	NOUN
ejpam-3860	416	12	)	)	PUNCT
ejpam-3860	416	13	=	=	PRON
ejpam-3860	417	1	(	(	PUNCT
ejpam-3860	417	2	⌈n	⌈n	NOUN
ejpam-3860	417	3	2	2	NUM
ejpam-3860	417	4	⌉	⌉	NOUN
ejpam-3860	417	5	+	+	CCONJ
ejpam-3860	417	6	⌊n	⌊n	ADJ
ejpam-3860	417	7	2	2	NUM
ejpam-3860	417	8	⌋)(⌈k	⌋)(⌈k	NUM
ejpam-3860	417	9	2	2	NUM
ejpam-3860	417	10	⌉	⌉	NOUN
ejpam-3860	417	11	+	+	CCONJ
ejpam-3860	418	1	⌊	⌊	PROPN
ejpam-3860	418	2	k	k	X
ejpam-3860	418	3	2	2	NUM
ejpam-3860	418	4	⌋	⌋	NOUN
ejpam-3860	418	5	)	)	PUNCT
ejpam-3860	419	1	=	=	SYM
ejpam-3860	419	2	nk	nk	PROPN
ejpam-3860	419	3	and	and	CCONJ
ejpam-3860	419	4	|t	|t	VERB
ejpam-3860	420	1	|	|	ADV
ejpam-3860	420	2	=	=	NOUN
ejpam-3860	420	3	|aq|+	|aq|+	NOUN
ejpam-3860	420	4	|dq|+	|dq|+	NOUN
ejpam-3860	420	5	|bp|+	|bp|+	NOUN
ejpam-3860	420	6	|cp|	|cp|	PROPN
ejpam-3860	420	7	=	=	SYM
ejpam-3860	420	8	⌊	⌊	VERB
ejpam-3860	420	9	k	k	X
ejpam-3860	420	10	2	2	NUM
ejpam-3860	420	11	⌋	⌋	NOUN
ejpam-3860	420	12	⌈n	⌈n	NOUN
ejpam-3860	420	13	2	2	NUM
ejpam-3860	420	14	⌉	⌉	PUNCT
ejpam-3860	420	15	+	+	CCONJ
ejpam-3860	420	16	⌊	⌊	PROPN
ejpam-3860	420	17	k	k	ADJ
ejpam-3860	420	18	2	2	NUM
ejpam-3860	420	19	⌋	⌋	NOUN
ejpam-3860	420	20	⌊n	⌊n	PUNCT
ejpam-3860	420	21	2	2	NUM
ejpam-3860	420	22	⌋	⌋	NOUN
ejpam-3860	420	23	+	+	CCONJ
ejpam-3860	420	24	⌈	⌈	PROPN
ejpam-3860	420	25	k	k	PROPN
ejpam-3860	420	26	2	2	NUM
ejpam-3860	420	27	⌉⌊n	⌉⌊n	NOUN
ejpam-3860	420	28	2	2	NUM
ejpam-3860	420	29	⌋	⌋	NOUN
ejpam-3860	420	30	+	+	CCONJ
ejpam-3860	420	31	⌈	⌈	SYM
ejpam-3860	420	32	k	k	PROPN
ejpam-3860	420	33	2	2	NUM
ejpam-3860	420	34	⌉	⌉	X
ejpam-3860	420	35	⌈n	⌈n	NOUN
ejpam-3860	420	36	2	2	NUM
ejpam-3860	420	37	⌉	⌉	NOUN
ejpam-3860	420	38	=	=	SYM
ejpam-3860	420	39	(	(	PUNCT
ejpam-3860	420	40	⌈n	⌈n	NOUN
ejpam-3860	420	41	2	2	NUM
ejpam-3860	420	42	⌉	⌉	NOUN
ejpam-3860	420	43	+	+	CCONJ
ejpam-3860	420	44	⌊n	⌊n	ADJ
ejpam-3860	420	45	2	2	NUM
ejpam-3860	420	46	⌋)(⌈k	⌋)(⌈k	NUM
ejpam-3860	420	47	2	2	NUM
ejpam-3860	420	48	⌋	⌋	NOUN
ejpam-3860	420	49	+	+	CCONJ
ejpam-3860	420	50	⌊	⌊	X
ejpam-3860	420	51	k	k	ADJ
ejpam-3860	420	52	2	2	NUM
ejpam-3860	420	53	⌋	⌋	NOUN
ejpam-3860	420	54	)	)	PUNCT
ejpam-3860	421	1	=	=	SYM
ejpam-3860	421	2	nk	nk	PROPN
ejpam-3860	421	3	.	.	PUNCT
ejpam-3860	421	4	therefore	therefore	ADV
ejpam-3860	421	5	,	,	PUNCT
ejpam-3860	421	6	ni(pk	ni(pk	PROPN
ejpam-3860	421	7	�	�	PROPN
ejpam-3860	421	8	cn	cn	PROPN
ejpam-3860	421	9	,	,	PUNCT
ejpam-3860	421	10	x	x	X
ejpam-3860	421	11	)	)	PUNCT
ejpam-3860	421	12	=	=	SYM
ejpam-3860	421	13	2xnk	2xnk	PROPN
ejpam-3860	421	14	.	.	PUNCT
ejpam-3860	421	15	remark	remark	PROPN
ejpam-3860	421	16	1	1	NUM
ejpam-3860	421	17	.	.	PUNCT
ejpam-3860	422	1	when	when	SCONJ
ejpam-3860	422	2	m	m	VERB
ejpam-3860	422	3	=	=	SYM
ejpam-3860	422	4	2	2	NUM
ejpam-3860	422	5	in	in	ADP
ejpam-3860	422	6	theorem	theorem	ADJ
ejpam-3860	422	7	3.4	3.4	NUM
ejpam-3860	422	8	,	,	PUNCT
ejpam-3860	422	9	ni(pk	ni(pk	PROPN
ejpam-3860	422	10	�	�	NOUN
ejpam-3860	422	11	f2,n	f2,n	PROPN
ejpam-3860	422	12	,	,	PUNCT
ejpam-3860	422	13	x	x	NOUN
ejpam-3860	422	14	)	)	PUNCT
ejpam-3860	423	1	=	=	PUNCT
ejpam-3860	423	2	xd	xd	NUM
ejpam-3860	424	1	k	k	PROPN
ejpam-3860	424	2	2e(d	2e(d	PROPN
ejpam-3860	424	3	22e(n−1)+b	22e(n−1)+b	ADJ
ejpam-3860	425	1	22c)+b	22c)+b	NUM
ejpam-3860	425	2	k2c(d	k2c(d	PROPN
ejpam-3860	425	3	22e+b	22e+b	PROPN
ejpam-3860	425	4	22c(n−1	22c(n−1	NUM
ejpam-3860	425	5	)	)	PUNCT
ejpam-3860	425	6	)	)	PUNCT
ejpam-3860	426	1	+	+	CCONJ
ejpam-3860	426	2	xb	xb	PROPN
ejpam-3860	427	1	k	k	PROPN
ejpam-3860	427	2	2c(d	2c(d	NUM
ejpam-3860	427	3	22e(n−1)+b	22e(n−1)+b	ADJ
ejpam-3860	427	4	22c)+d	22c)+d	NUM
ejpam-3860	427	5	k2e(d	k2e(d	PROPN
ejpam-3860	427	6	22e+b	22e+b	PROPN
ejpam-3860	427	7	22c(n−1	22c(n−1	NUM
ejpam-3860	427	8	)	)	PUNCT
ejpam-3860	427	9	)	)	PUNCT
ejpam-3860	428	1	=	=	PUNCT
ejpam-3860	428	2	xd	xd	INTJ
ejpam-3860	428	3	k	k	PROPN
ejpam-3860	428	4	2en+b	2en+b	PROPN
ejpam-3860	428	5	k2cn	k2cn	VERB
ejpam-3860	429	1	+	+	CCONJ
ejpam-3860	429	2	xb	xb	PROPN
ejpam-3860	429	3	k	k	PROPN
ejpam-3860	429	4	2cn+d	2cn+d	PROPN
ejpam-3860	429	5	k2en	k2en	PUNCT
ejpam-3860	429	6	references	reference	VERB
ejpam-3860	429	7	191	191	NUM
ejpam-3860	429	8	=	=	SYM
ejpam-3860	429	9	2xn(d	2xn(d	NUM
ejpam-3860	429	10	k	k	PROPN
ejpam-3860	429	11	2c+b	2c+b	NUM
ejpam-3860	429	12	k2c	k2c	NOUN
ejpam-3860	429	13	)	)	PUNCT
ejpam-3860	429	14	=	=	PUNCT
ejpam-3860	430	1	2xnk	2xnk	NUM
ejpam-3860	430	2	=	=	SYM
ejpam-3860	430	3	ni(pk	ni(pk	PROPN
ejpam-3860	430	4	�	�	PROPN
ejpam-3860	430	5	cenn	cenn	NOUN
ejpam-3860	430	6	,	,	PUNCT
ejpam-3860	430	7	x	x	NOUN
ejpam-3860	430	8	)	)	PUNCT
ejpam-3860	430	9	.	.	PUNCT
ejpam-3860	431	1	acknowledgements	acknowledgement	NOUN
ejpam-3860	431	2	this	this	DET
ejpam-3860	431	3	research	research	NOUN
ejpam-3860	431	4	is	be	AUX
ejpam-3860	431	5	funded	fund	VERB
ejpam-3860	431	6	by	by	ADP
ejpam-3860	431	7	the	the	DET
ejpam-3860	431	8	department	department	PROPN
ejpam-3860	431	9	of	of	ADP
ejpam-3860	431	10	science	science	NOUN
ejpam-3860	431	11	and	and	CCONJ
ejpam-3860	431	12	technology	technology	NOUN
ejpam-3860	431	13	(	(	PUNCT
ejpam-3860	431	14	dost	dost	NOUN
ejpam-3860	431	15	)	)	PUNCT
ejpam-3860	431	16	,	,	PUNCT
ejpam-3860	431	17	mindanao	mindanao	PROPN
ejpam-3860	431	18	state	state	PROPN
ejpam-3860	431	19	university	university	PROPN
ejpam-3860	431	20	iit	iit	PROPN
ejpam-3860	431	21	,	,	PUNCT
ejpam-3860	431	22	department	department	NOUN
ejpam-3860	431	23	of	of	ADP
ejpam-3860	431	24	research	research	NOUN
ejpam-3860	431	25	,	,	PUNCT
ejpam-3860	431	26	office	office	NOUN
ejpam-3860	431	27	of	of	ADP
ejpam-3860	431	28	the	the	DET
ejpam-3860	431	29	vice	vice	NOUN
ejpam-3860	431	30	chancellor	chancellor	NOUN
ejpam-3860	431	31	for	for	ADP
ejpam-3860	431	32	research	research	NOUN
ejpam-3860	431	33	and	and	CCONJ
ejpam-3860	431	34	extension(ovcre	extension(ovcre	PROPN
ejpam-3860	431	35	)	)	PUNCT
ejpam-3860	431	36	,	,	PUNCT
ejpam-3860	431	37	and	and	CCONJ
ejpam-3860	431	38	mindanao	mindanao	PROPN
ejpam-3860	431	39	state	state	PROPN
ejpam-3860	431	40	university	university	PROPN
ejpam-3860	431	41	main	main	ADJ
ejpam-3860	431	42	campus	campus	NOUN
ejpam-3860	431	43	(	(	PUNCT
ejpam-3860	431	44	msu	msu	NOUN
ejpam-3860	431	45	main	main	ADJ
ejpam-3860	431	46	)	)	PUNCT
ejpam-3860	431	47	.	.	PUNCT
ejpam-3860	432	1	references	reference	NOUN
ejpam-3860	432	2	[	[	X
ejpam-3860	432	3	1	1	NUM
ejpam-3860	432	4	]	]	PUNCT
ejpam-3860	432	5	a.	a.	NOUN
ejpam-3860	432	6	alwardi	alwardi	PROPN
ejpam-3860	432	7	and	and	CCONJ
ejpam-3860	432	8	p.m.	p.m.	NOUN
ejpam-3860	432	9	shivaswamy	shivaswamy	ADJ
ejpam-3860	432	10	.	.	PUNCT
ejpam-3860	433	1	on	on	ADP
ejpam-3860	433	2	the	the	DET
ejpam-3860	433	3	neighbourhood	neighbourhood	NOUN
ejpam-3860	433	4	polynomial	polynomial	NOUN
ejpam-3860	433	5	of	of	ADP
ejpam-3860	433	6	graphs	graph	NOUN
ejpam-3860	433	7	.	.	PUNCT
ejpam-3860	434	1	bulletin	bulletin	NOUN
ejpam-3860	434	2	of	of	ADP
ejpam-3860	434	3	the	the	DET
ejpam-3860	434	4	society	society	NOUN
ejpam-3860	434	5	of	of	ADP
ejpam-3860	434	6	mathematicians	mathematician	NOUN
ejpam-3860	434	7	banja	banja	PROPN
ejpam-3860	434	8	luka	luka	PROPN
ejpam-3860	434	9	,	,	PUNCT
ejpam-3860	434	10	6:13–24	6:13–24	NOUN
ejpam-3860	434	11	.	.	PUNCT
ejpam-3860	435	1	[	[	X
ejpam-3860	435	2	2	2	NUM
ejpam-3860	435	3	]	]	X
ejpam-3860	435	4	f.	f.	PROPN
ejpam-3860	435	5	buckley	buckley	PROPN
ejpam-3860	435	6	and	and	CCONJ
ejpam-3860	435	7	f.	f.	PROPN
ejpam-3860	435	8	harary	harary	PROPN
ejpam-3860	435	9	.	.	PUNCT
ejpam-3860	436	1	distance	distance	NOUN
ejpam-3860	436	2	in	in	ADP
ejpam-3860	436	3	graphs	graph	NOUN
ejpam-3860	436	4	.	.	PUNCT
ejpam-3860	437	1	addison	addison	PROPN
ejpam-3860	437	2	-	-	PUNCT
ejpam-3860	437	3	wesley	wesley	PROPN
ejpam-3860	437	4	series	series	PROPN
ejpam-3860	437	5	in	in	ADP
ejpam-3860	437	6	mathematics	mathematic	NOUN
ejpam-3860	437	7	,	,	PUNCT
ejpam-3860	437	8	1990	1990	NUM
ejpam-3860	437	9	.	.	PUNCT
ejpam-3860	438	1	[	[	X
ejpam-3860	438	2	3	3	X
ejpam-3860	438	3	]	]	X
ejpam-3860	438	4	r.	r.	PROPN
ejpam-3860	438	5	diestel	diestel	PROPN
ejpam-3860	438	6	.	.	PUNCT
ejpam-3860	439	1	graph	graph	NOUN
ejpam-3860	439	2	theory	theory	NOUN
ejpam-3860	439	3	.	.	PUNCT
ejpam-3860	440	1	springer	springer	NOUN
ejpam-3860	440	2	nature	nature	NOUN
ejpam-3860	440	3	,	,	PUNCT
ejpam-3860	440	4	2017	2017	NUM
ejpam-3860	440	5	.	.	PUNCT
ejpam-3860	441	1	[	[	X
ejpam-3860	441	2	4	4	NUM
ejpam-3860	441	3	]	]	X
ejpam-3860	441	4	m.s	m.s	PROPN
ejpam-3860	441	5	.	.	PROPN
ejpam-3860	441	6	sardar	sardar	PROPN
ejpam-3860	441	7	et.al	et.al	PROPN
ejpam-3860	441	8	.	.	PUNCT
ejpam-3860	442	1	computing	compute	VERB
ejpam-3860	442	2	topological	topological	ADJ
ejpam-3860	442	3	indices	index	NOUN
ejpam-3860	442	4	of	of	ADP
ejpam-3860	442	5	the	the	DET
ejpam-3860	442	6	line	line	NOUN
ejpam-3860	442	7	graphs	graph	NOUN
ejpam-3860	442	8	of	of	ADP
ejpam-3860	442	9	banana	banana	NOUN
ejpam-3860	442	10	tree	tree	NOUN
ejpam-3860	442	11	graph	graph	NOUN
ejpam-3860	442	12	and	and	CCONJ
ejpam-3860	442	13	firecracker	firecracker	NOUN
ejpam-3860	442	14	graph	graph	NOUN
ejpam-3860	442	15	.	.	PUNCT
ejpam-3860	443	1	applied	apply	VERB
ejpam-3860	443	2	mathematics	mathematic	NOUN
ejpam-3860	443	3	and	and	CCONJ
ejpam-3860	443	4	nonlinear	nonlinear	ADJ
ejpam-3860	443	5	sciences	science	NOUN
ejpam-3860	443	6	,	,	PUNCT
ejpam-3860	443	7	2:83–92	2:83–92	NUM
ejpam-3860	443	8	,	,	PUNCT
ejpam-3860	443	9	2017	2017	NUM
ejpam-3860	443	10	.	.	PUNCT
ejpam-3860	444	1	[	[	X
ejpam-3860	444	2	5	5	NUM
ejpam-3860	444	3	]	]	PUNCT
ejpam-3860	444	4	r.	r.	PROPN
ejpam-3860	444	5	hammack	hammack	PROPN
ejpam-3860	444	6	et.al	et.al	PROPN
ejpam-3860	444	7	.	.	PUNCT
ejpam-3860	445	1	handbook	handbook	NOUN
ejpam-3860	445	2	of	of	ADP
ejpam-3860	445	3	product	product	NOUN
ejpam-3860	445	4	of	of	ADP
ejpam-3860	445	5	graphs	graph	NOUN
ejpam-3860	445	6	.	.	PUNCT
ejpam-3860	446	1	crc	crc	PROPN
ejpam-3860	446	2	press	press	PROPN
ejpam-3860	446	3	taylor	taylor	PROPN
ejpam-3860	446	4	and	and	CCONJ
ejpam-3860	446	5	francis	francis	PROPN
ejpam-3860	446	6	group	group	PROPN
ejpam-3860	446	7	,	,	PUNCT
ejpam-3860	446	8	london	london	PROPN
ejpam-3860	446	9	and	and	CCONJ
ejpam-3860	446	10	new	new	PROPN
ejpam-3860	446	11	york	york	PROPN
ejpam-3860	446	12	,	,	PUNCT
ejpam-3860	446	13	2011	2011	NUM
ejpam-3860	446	14	.	.	PUNCT
ejpam-3860	447	1	[	[	X
ejpam-3860	447	2	6	6	NUM
ejpam-3860	447	3	]	]	PUNCT
ejpam-3860	447	4	s.	s.	PROPN
ejpam-3860	447	5	ganesh	ganesh	PROPN
ejpam-3860	447	6	and	and	CCONJ
ejpam-3860	447	7	r.	r.	PROPN
ejpam-3860	447	8	revathi	revathi	PROPN
ejpam-3860	447	9	.	.	PUNCT
ejpam-3860	448	1	analysis	analysis	NOUN
ejpam-3860	448	2	of	of	ADP
ejpam-3860	448	3	some	some	DET
ejpam-3860	448	4	bistar	bistar	NOUN
ejpam-3860	448	5	related	relate	VERB
ejpam-3860	448	6	mmd	mmd	NOUN
ejpam-3860	448	7	graphs	graph	NOUN
ejpam-3860	448	8	.	.	PUNCT
ejpam-3860	449	1	international	international	ADJ
ejpam-3860	449	2	journal	journal	NOUN
ejpam-3860	449	3	of	of	ADP
ejpam-3860	449	4	pure	pure	ADJ
ejpam-3860	449	5	and	and	CCONJ
ejpam-3860	449	6	applied	applied	ADJ
ejpam-3860	449	7	mathematics	mathematic	NOUN
ejpam-3860	449	8	,	,	PUNCT
ejpam-3860	449	9	118(10):407–413	118(10):407–413	PROPN
ejpam-3860	449	10	,	,	PUNCT
ejpam-3860	449	11	2018	2018	NUM
ejpam-3860	449	12	.	.	PUNCT
ejpam-3860	450	1	[	[	X
ejpam-3860	450	2	7	7	X
ejpam-3860	450	3	]	]	X
ejpam-3860	450	4	f.	f.	PROPN
ejpam-3860	450	5	harary	harary	PROPN
ejpam-3860	450	6	.	.	PUNCT
ejpam-3860	451	1	graph	graph	NOUN
ejpam-3860	451	2	theory	theory	NOUN
ejpam-3860	451	3	.	.	PUNCT
ejpam-3860	452	1	addison	addison	PROPN
ejpam-3860	452	2	-	-	PUNCT
ejpam-3860	452	3	wesley	wesley	PROPN
ejpam-3860	452	4	publishing	publishing	PROPN
ejpam-3860	452	5	company	company	NOUN
ejpam-3860	452	6	,	,	PUNCT
ejpam-3860	452	7	1969	1969	NUM
ejpam-3860	452	8	.	.	PUNCT
ejpam-3860	453	1	[	[	X
ejpam-3860	453	2	8	8	NUM
ejpam-3860	453	3	]	]	PUNCT
ejpam-3860	453	4	m.	m.	NOUN
ejpam-3860	453	5	khasif	khasif	NOUN
ejpam-3860	453	6	.	.	PUNCT
ejpam-3860	454	1	chromatic	chromatic	ADJ
ejpam-3860	454	2	polynomials	polynomial	NOUN
ejpam-3860	454	3	and	and	CCONJ
ejpam-3860	454	4	chromaticity	chromaticity	NOUN
ejpam-3860	454	5	of	of	ADP
ejpam-3860	454	6	some	some	DET
ejpam-3860	454	7	linear	linear	ADJ
ejpam-3860	454	8	h	h	NOUN
ejpam-3860	454	9	-	-	PUNCT
ejpam-3860	454	10	hypergraphs	hypergraph	NOUN
ejpam-3860	454	11	.	.	PUNCT
ejpam-3860	455	1	1969	1969	NUM
ejpam-3860	455	2	.	.	PUNCT
ejpam-3860	456	1	[	[	X
ejpam-3860	456	2	9	9	NUM
ejpam-3860	456	3	]	]	SYM
ejpam-3860	456	4	v.r	v.r	PROPN
ejpam-3860	456	5	.	.	PROPN
ejpam-3860	456	6	kulli	kulli	PROPN
ejpam-3860	456	7	.	.	PUNCT
ejpam-3860	457	1	the	the	DET
ejpam-3860	457	2	neighborhood	neighborhood	NOUN
ejpam-3860	457	3	graph	graph	NOUN
ejpam-3860	457	4	of	of	ADP
ejpam-3860	457	5	a	a	DET
ejpam-3860	457	6	graph	graph	NOUN
ejpam-3860	457	7	.	.	PUNCT
ejpam-3860	458	1	international	international	ADJ
ejpam-3860	458	2	journal	journal	NOUN
ejpam-3860	458	3	of	of	ADP
ejpam-3860	458	4	fuzzy	fuzzy	ADJ
ejpam-3860	458	5	mathematical	mathematical	ADJ
ejpam-3860	458	6	archive	archive	NOUN
ejpam-3860	458	7	,	,	PUNCT
ejpam-3860	458	8	8(2):93–99	8(2):93–99	NUM
ejpam-3860	458	9	,	,	PUNCT
ejpam-3860	458	10	2015	2015	NUM
ejpam-3860	458	11	.	.	PUNCT
ejpam-3860	459	1	[	[	X
ejpam-3860	459	2	10	10	NUM
ejpam-3860	459	3	]	]	X
ejpam-3860	459	4	v.	v.	PROPN
ejpam-3860	459	5	e.	e.	PROPN
ejpam-3860	459	6	levit	levit	PROPN
ejpam-3860	459	7	and	and	CCONJ
ejpam-3860	459	8	e.	e.	PROPN
ejpam-3860	459	9	mandrescui	mandrescui	PROPN
ejpam-3860	459	10	.	.	PUNCT
ejpam-3860	460	1	the	the	DET
ejpam-3860	460	2	independence	independence	NOUN
ejpam-3860	460	3	polynomial	polynomial	NOUN
ejpam-3860	460	4	of	of	ADP
ejpam-3860	460	5	a	a	DET
ejpam-3860	460	6	graph	graph	NOUN
ejpam-3860	460	7	-	-	PUNCT
ejpam-3860	460	8	a	a	DET
ejpam-3860	460	9	survey	survey	NOUN
ejpam-3860	460	10	.	.	PUNCT
ejpam-3860	461	1	in	in	ADP
ejpam-3860	461	2	proceedings	proceeding	NOUN
ejpam-3860	461	3	of	of	ADP
ejpam-3860	461	4	the	the	DET
ejpam-3860	461	5	1st	1st	ADJ
ejpam-3860	461	6	international	international	ADJ
ejpam-3860	461	7	conference	conference	NOUN
ejpam-3860	461	8	on	on	ADP
ejpam-3860	461	9	algebraic	algebraic	PROPN
ejpam-3860	461	10	informatics	informatic	NOUN
ejpam-3860	461	11	,	,	PUNCT
ejpam-3860	461	12	pages	page	NOUN
ejpam-3860	461	13	233–254	233–254	NUM
ejpam-3860	461	14	,	,	PUNCT
ejpam-3860	461	15	2005	2005	NUM
ejpam-3860	461	16	.	.	PUNCT
ejpam-3860	462	1	[	[	X
ejpam-3860	462	2	11	11	NUM
ejpam-3860	462	3	]	]	X
ejpam-3860	462	4	k.b	k.b	PROPN
ejpam-3860	462	5	.	.	PROPN
ejpam-3860	462	6	murthy	murthy	PROPN
ejpam-3860	462	7	and	and	CCONJ
ejpam-3860	462	8	puttaswamy	puttaswamy	ADJ
ejpam-3860	462	9	.	.	PUNCT
ejpam-3860	463	1	on	on	ADP
ejpam-3860	463	2	the	the	DET
ejpam-3860	463	3	independent	independent	ADJ
ejpam-3860	463	4	neighbourhood	neighbourhood	NOUN
ejpam-3860	463	5	polynomial	polynomial	NOUN
ejpam-3860	463	6	of	of	ADP
ejpam-3860	463	7	graphs	graph	NOUN
ejpam-3860	463	8	.	.	PUNCT
ejpam-3860	464	1	indian	indian	ADJ
ejpam-3860	464	2	streams	streams	PROPN
ejpam-3860	464	3	research	research	NOUN
ejpam-3860	464	4	journal	journal	NOUN
ejpam-3860	464	5	,	,	PUNCT
ejpam-3860	464	6	5(12):1–7	5(12):1–7	NUM
ejpam-3860	464	7	,	,	PUNCT
ejpam-3860	464	8	2015	2015	NUM
ejpam-3860	464	9	.	.	PUNCT