id	sid	tid	token	lemma	pos
ejpam-4520	1	1	european	european	PROPN
ejpam-4520	1	2	journal	journal	PROPN
ejpam-4520	1	3	of	of	ADP
ejpam-4520	1	4	pure	pure	ADJ
ejpam-4520	1	5	and	and	CCONJ
ejpam-4520	1	6	applied	apply	VERB
ejpam-4520	1	7	mathematics	mathematic	NOUN
ejpam-4520	1	8	vol	vol	NOUN
ejpam-4520	1	9	.	.	PUNCT
ejpam-4520	2	1	16	16	NUM
ejpam-4520	2	2	,	,	PUNCT
ejpam-4520	2	3	no	no	INTJ
ejpam-4520	2	4	.	.	NOUN
ejpam-4520	2	5	1	1	NUM
ejpam-4520	2	6	,	,	PUNCT
ejpam-4520	2	7	2023	2023	NUM
ejpam-4520	2	8	,	,	PUNCT
ejpam-4520	2	9	271	271	NUM
ejpam-4520	2	10	-	-	SYM
ejpam-4520	2	11	285	285	NUM
ejpam-4520	2	12	issn	issn	PROPN
ejpam-4520	2	13	1307	1307	NUM
ejpam-4520	2	14	-	-	SYM
ejpam-4520	2	15	5543	5543	NUM
ejpam-4520	2	16	–	–	PUNCT
ejpam-4520	2	17	ejpam.com	ejpam.com	X
ejpam-4520	2	18	published	publish	VERB
ejpam-4520	2	19	by	by	ADP
ejpam-4520	2	20	new	new	PROPN
ejpam-4520	2	21	york	york	PROPN
ejpam-4520	2	22	business	business	PROPN
ejpam-4520	2	23	global	global	PROPN
ejpam-4520	2	24	on	on	ADP
ejpam-4520	2	25	the	the	DET
ejpam-4520	2	26	study	study	NOUN
ejpam-4520	2	27	of	of	ADP
ejpam-4520	2	28	rainbow	rainbow	NOUN
ejpam-4520	2	29	antimagic	antimagic	ADJ
ejpam-4520	2	30	connection	connection	NOUN
ejpam-4520	2	31	number	number	NOUN
ejpam-4520	2	32	of	of	ADP
ejpam-4520	2	33	corona	corona	NOUN
ejpam-4520	2	34	product	product	NOUN
ejpam-4520	2	35	of	of	ADP
ejpam-4520	2	36	graphs	graph	NOUN
ejpam-4520	2	37	brian	brian	PROPN
ejpam-4520	2	38	juned	juned	PROPN
ejpam-4520	2	39	septory1,3	septory1,3	PROPN
ejpam-4520	2	40	,	,	PUNCT
ejpam-4520	2	41	liliek	liliek	NOUN
ejpam-4520	2	42	susilowati1,∗	susilowati1,∗	NOUN
ejpam-4520	2	43	,	,	PUNCT
ejpam-4520	2	44	dafik2,3	dafik2,3	PROPN
ejpam-4520	2	45	,	,	PUNCT
ejpam-4520	2	46	veerabhadraiah	veerabhadraiah	NOUN
ejpam-4520	2	47	lokesha4	lokesha4	NOUN
ejpam-4520	2	48	,	,	PUNCT
ejpam-4520	2	49	gnaneswaran	gnaneswaran	NOUN
ejpam-4520	2	50	nagamani5	nagamani5	NOUN
ejpam-4520	2	51	1	1	NUM
ejpam-4520	2	52	mathematics	mathematic	NOUN
ejpam-4520	2	53	department	department	NOUN
ejpam-4520	2	54	,	,	PUNCT
ejpam-4520	2	55	faculty	faculty	NOUN
ejpam-4520	2	56	of	of	ADP
ejpam-4520	2	57	science	science	NOUN
ejpam-4520	2	58	and	and	CCONJ
ejpam-4520	2	59	technology	technology	NOUN
ejpam-4520	2	60	,	,	PUNCT
ejpam-4520	2	61	airlangga	airlangga	PROPN
ejpam-4520	2	62	university	university	PROPN
ejpam-4520	2	63	,	,	PUNCT
ejpam-4520	2	64	surabaya	surabaya	PROPN
ejpam-4520	2	65	,	,	PUNCT
ejpam-4520	2	66	indonesia	indonesia	PROPN
ejpam-4520	2	67	2	2	NUM
ejpam-4520	2	68	mathematics	mathematics	PROPN
ejpam-4520	2	69	education	education	NOUN
ejpam-4520	2	70	study	study	NOUN
ejpam-4520	2	71	program	program	NOUN
ejpam-4520	2	72	,	,	PUNCT
ejpam-4520	2	73	faculty	faculty	NOUN
ejpam-4520	2	74	of	of	ADP
ejpam-4520	2	75	teacher	teacher	NOUN
ejpam-4520	2	76	training	training	NOUN
ejpam-4520	2	77	and	and	CCONJ
ejpam-4520	2	78	education	education	NOUN
ejpam-4520	2	79	,	,	PUNCT
ejpam-4520	2	80	university	university	NOUN
ejpam-4520	2	81	of	of	ADP
ejpam-4520	2	82	jember	jember	PROPN
ejpam-4520	2	83	,	,	PUNCT
ejpam-4520	2	84	jember	jember	PROPN
ejpam-4520	2	85	,	,	PUNCT
ejpam-4520	2	86	indonesia	indonesia	PROPN
ejpam-4520	2	87	3	3	NUM
ejpam-4520	2	88	pusat	pusat	PROPN
ejpam-4520	2	89	unggulan	unggulan	PROPN
ejpam-4520	2	90	ipteks	ipteks	PROPN
ejpam-4520	2	91	-	-	PUNCT
ejpam-4520	2	92	perguruan	perguruan	PROPN
ejpam-4520	2	93	tinggi	tinggi	PROPN
ejpam-4520	2	94	,	,	PUNCT
ejpam-4520	2	95	combinatorics	combinatoric	NOUN
ejpam-4520	2	96	and	and	CCONJ
ejpam-4520	2	97	graph	graph	NOUN
ejpam-4520	2	98	,	,	PUNCT
ejpam-4520	2	99	cgant	cgant	ADJ
ejpam-4520	2	100	,	,	PUNCT
ejpam-4520	2	101	university	university	NOUN
ejpam-4520	2	102	of	of	ADP
ejpam-4520	2	103	jember	jember	PROPN
ejpam-4520	2	104	,	,	PUNCT
ejpam-4520	2	105	jember	jember	PROPN
ejpam-4520	2	106	,	,	PUNCT
ejpam-4520	2	107	indonesia	indonesia	PROPN
ejpam-4520	2	108	4	4	NUM
ejpam-4520	2	109	mathematics	mathematics	PROPN
ejpam-4520	2	110	department	department	NOUN
ejpam-4520	2	111	,	,	PUNCT
ejpam-4520	2	112	vijayanagara	vijayanagara	PROPN
ejpam-4520	2	113	sri	sri	PROPN
ejpam-4520	2	114	krishnadevaraya	krishnadevaraya	PROPN
ejpam-4520	2	115	university	university	PROPN
ejpam-4520	2	116	,	,	PUNCT
ejpam-4520	2	117	bellary	bellary	PROPN
ejpam-4520	2	118	,	,	PUNCT
ejpam-4520	2	119	india	india	PROPN
ejpam-4520	2	120	5	5	NUM
ejpam-4520	2	121	department	department	PROPN
ejpam-4520	2	122	of	of	ADP
ejpam-4520	2	123	mathematic	mathematic	ADJ
ejpam-4520	2	124	the	the	DET
ejpam-4520	2	125	gandhigram	gandhigram	PROPN
ejpam-4520	2	126	rural	rural	PROPN
ejpam-4520	2	127	institute	institute	PROPN
ejpam-4520	2	128	,	,	PUNCT
ejpam-4520	2	129	tamil	tamil	PROPN
ejpam-4520	2	130	nadu	nadu	PROPN
ejpam-4520	2	131	,	,	PUNCT
ejpam-4520	2	132	india	india	PROPN
ejpam-4520	2	133	abstract	abstract	NOUN
ejpam-4520	2	134	.	.	PUNCT
ejpam-4520	3	1	given	give	VERB
ejpam-4520	3	2	that	that	SCONJ
ejpam-4520	3	3	a	a	DET
ejpam-4520	3	4	graph	graph	NOUN
ejpam-4520	3	5	g	g	NOUN
ejpam-4520	3	6	=	=	SYM
ejpam-4520	3	7	(	(	PUNCT
ejpam-4520	3	8	v	v	NOUN
ejpam-4520	3	9	,	,	PUNCT
ejpam-4520	3	10	e	e	NOUN
ejpam-4520	3	11	)	)	PUNCT
ejpam-4520	3	12	.	.	PUNCT
ejpam-4520	4	1	by	by	ADP
ejpam-4520	4	2	an	an	DET
ejpam-4520	4	3	edge	edge	NOUN
ejpam-4520	4	4	-	-	PUNCT
ejpam-4520	4	5	antimagic	antimagic	NOUN
ejpam-4520	4	6	vertex	vertex	NOUN
ejpam-4520	4	7	labeling	labeling	NOUN
ejpam-4520	4	8	of	of	ADP
ejpam-4520	4	9	graph	graph	NOUN
ejpam-4520	4	10	,	,	PUNCT
ejpam-4520	4	11	we	we	PRON
ejpam-4520	4	12	mean	mean	VERB
ejpam-4520	4	13	assigning	assign	VERB
ejpam-4520	4	14	labels	label	NOUN
ejpam-4520	4	15	on	on	ADP
ejpam-4520	4	16	each	each	DET
ejpam-4520	4	17	vertex	vertex	NOUN
ejpam-4520	4	18	under	under	ADP
ejpam-4520	4	19	the	the	DET
ejpam-4520	4	20	label	label	NOUN
ejpam-4520	4	21	function	function	NOUN
ejpam-4520	4	22	f	f	NOUN
ejpam-4520	4	23	:	:	PUNCT
ejpam-4520	4	24	v	v	X
ejpam-4520	4	25	→	→	SYM
ejpam-4520	4	26	{	{	PUNCT
ejpam-4520	4	27	1	1	NUM
ejpam-4520	4	28	,	,	PUNCT
ejpam-4520	4	29	2	2	NUM
ejpam-4520	4	30	,	,	PUNCT
ejpam-4520	4	31	.	.	PUNCT
ejpam-4520	4	32	.	.	PUNCT
ejpam-4520	4	33	.	.	PUNCT
ejpam-4520	5	1	,	,	PUNCT
ejpam-4520	5	2	|v	|v	PROPN
ejpam-4520	5	3	(	(	PUNCT
ejpam-4520	5	4	g)|	g)|	PROPN
ejpam-4520	5	5	}	}	PUNCT
ejpam-4520	5	6	such	such	ADJ
ejpam-4520	5	7	that	that	SCONJ
ejpam-4520	5	8	the	the	DET
ejpam-4520	5	9	associated	associated	ADJ
ejpam-4520	5	10	weight	weight	NOUN
ejpam-4520	5	11	of	of	ADP
ejpam-4520	5	12	an	an	DET
ejpam-4520	5	13	edge	edge	NOUN
ejpam-4520	5	14	uv	uv	PROPN
ejpam-4520	5	15	∈	∈	PROPN
ejpam-4520	5	16	e(g	e(g	PROPN
ejpam-4520	5	17	)	)	PUNCT
ejpam-4520	5	18	,	,	PUNCT
ejpam-4520	5	19	namely	namely	ADV
ejpam-4520	5	20	w(xy	w(xy	PROPN
ejpam-4520	5	21	)	)	PUNCT
ejpam-4520	5	22	=	=	SYM
ejpam-4520	5	23	f(x	f(x	PROPN
ejpam-4520	5	24	)	)	PUNCT
ejpam-4520	5	25	+	+	SYM
ejpam-4520	5	26	f(y	f(y	NOUN
ejpam-4520	5	27	)	)	PUNCT
ejpam-4520	5	28	,	,	PUNCT
ejpam-4520	5	29	has	have	VERB
ejpam-4520	5	30	distinct	distinct	ADJ
ejpam-4520	5	31	weight	weight	NOUN
ejpam-4520	5	32	.	.	PUNCT
ejpam-4520	6	1	a	a	DET
ejpam-4520	6	2	path	path	NOUN
ejpam-4520	6	3	p	p	NOUN
ejpam-4520	6	4	in	in	ADP
ejpam-4520	6	5	the	the	DET
ejpam-4520	6	6	vertex	vertex	NOUN
ejpam-4520	6	7	-	-	PUNCT
ejpam-4520	6	8	labeled	label	VERB
ejpam-4520	6	9	graph	graph	NOUN
ejpam-4520	6	10	g	g	PROPN
ejpam-4520	6	11	is	be	AUX
ejpam-4520	6	12	said	say	VERB
ejpam-4520	6	13	to	to	PART
ejpam-4520	6	14	be	be	AUX
ejpam-4520	6	15	a	a	DET
ejpam-4520	6	16	rainbow	rainbow	NOUN
ejpam-4520	6	17	path	path	NOUN
ejpam-4520	6	18	if	if	SCONJ
ejpam-4520	6	19	for	for	ADP
ejpam-4520	6	20	every	every	DET
ejpam-4520	6	21	two	two	NUM
ejpam-4520	6	22	edges	edge	NOUN
ejpam-4520	6	23	xy	xy	PRON
ejpam-4520	6	24	,	,	PUNCT
ejpam-4520	6	25	x′y′	x′y′	PROPN
ejpam-4520	6	26	∈	∈	PROPN
ejpam-4520	6	27	e(p	e(p	PROPN
ejpam-4520	6	28	)	)	PUNCT
ejpam-4520	6	29	satisfies	satisfy	VERB
ejpam-4520	6	30	w(xy	w(xy	PROPN
ejpam-4520	6	31	)	)	PUNCT
ejpam-4520	6	32	̸=	̸=	PROPN
ejpam-4520	6	33	w(x′y′	w(x′y′	ADJ
ejpam-4520	6	34	)	)	PUNCT
ejpam-4520	6	35	.	.	PUNCT
ejpam-4520	7	1	the	the	DET
ejpam-4520	7	2	function	function	NOUN
ejpam-4520	7	3	f	f	PROPN
ejpam-4520	7	4	is	be	AUX
ejpam-4520	7	5	called	call	VERB
ejpam-4520	7	6	a	a	DET
ejpam-4520	7	7	rainbow	rainbow	NOUN
ejpam-4520	7	8	antimagic	antimagic	ADJ
ejpam-4520	7	9	labeling	labeling	NOUN
ejpam-4520	7	10	of	of	ADP
ejpam-4520	7	11	g	g	PROPN
ejpam-4520	7	12	if	if	SCONJ
ejpam-4520	7	13	for	for	ADP
ejpam-4520	7	14	every	every	DET
ejpam-4520	7	15	two	two	NUM
ejpam-4520	7	16	vertices	vertex	NOUN
ejpam-4520	7	17	x	x	PUNCT
ejpam-4520	7	18	and	and	CCONJ
ejpam-4520	7	19	y	y	PROPN
ejpam-4520	7	20	of	of	ADP
ejpam-4520	7	21	g	g	PROPN
ejpam-4520	7	22	,	,	PUNCT
ejpam-4520	7	23	there	there	PRON
ejpam-4520	7	24	exists	exist	VERB
ejpam-4520	7	25	a	a	DET
ejpam-4520	7	26	rainbow	rainbow	NOUN
ejpam-4520	7	27	x	x	PUNCT
ejpam-4520	7	28	−	−	PROPN
ejpam-4520	7	29	y	y	PROPN
ejpam-4520	7	30	path	path	NOUN
ejpam-4520	7	31	.	.	PUNCT
ejpam-4520	8	1	when	when	SCONJ
ejpam-4520	8	2	we	we	PRON
ejpam-4520	8	3	assign	assign	VERB
ejpam-4520	8	4	each	each	DET
ejpam-4520	8	5	edge	edge	NOUN
ejpam-4520	8	6	xy	xy	NOUN
ejpam-4520	8	7	with	with	ADP
ejpam-4520	8	8	the	the	DET
ejpam-4520	8	9	color	color	NOUN
ejpam-4520	8	10	of	of	ADP
ejpam-4520	8	11	the	the	DET
ejpam-4520	8	12	edge	edge	NOUN
ejpam-4520	8	13	weight	weight	NOUN
ejpam-4520	8	14	w(xy	w(xy	PROPN
ejpam-4520	8	15	)	)	PUNCT
ejpam-4520	8	16	,	,	PUNCT
ejpam-4520	8	17	thus	thus	ADV
ejpam-4520	8	18	we	we	PRON
ejpam-4520	8	19	say	say	VERB
ejpam-4520	8	20	the	the	DET
ejpam-4520	8	21	graph	graph	NOUN
ejpam-4520	8	22	g	g	PROPN
ejpam-4520	8	23	admits	admit	VERB
ejpam-4520	8	24	a	a	DET
ejpam-4520	8	25	rainbow	rainbow	NOUN
ejpam-4520	8	26	antimagic	antimagic	ADJ
ejpam-4520	8	27	coloring	coloring	NOUN
ejpam-4520	8	28	.	.	PUNCT
ejpam-4520	9	1	the	the	DET
ejpam-4520	9	2	rainbow	rainbow	NOUN
ejpam-4520	9	3	antimagic	antimagic	ADJ
ejpam-4520	9	4	connection	connection	NOUN
ejpam-4520	9	5	number	number	NOUN
ejpam-4520	9	6	of	of	ADP
ejpam-4520	9	7	g	g	NOUN
ejpam-4520	9	8	,	,	PUNCT
ejpam-4520	9	9	denoted	denote	VERB
ejpam-4520	9	10	by	by	ADP
ejpam-4520	9	11	rac(g	rac(g	NOUN
ejpam-4520	9	12	)	)	PUNCT
ejpam-4520	9	13	,	,	PUNCT
ejpam-4520	9	14	is	be	AUX
ejpam-4520	9	15	the	the	DET
ejpam-4520	9	16	smallest	small	ADJ
ejpam-4520	9	17	number	number	NOUN
ejpam-4520	9	18	of	of	ADP
ejpam-4520	9	19	colors	color	NOUN
ejpam-4520	9	20	induced	induce	VERB
ejpam-4520	9	21	from	from	ADP
ejpam-4520	9	22	all	all	DET
ejpam-4520	9	23	edge	edge	NOUN
ejpam-4520	9	24	weight	weight	NOUN
ejpam-4520	9	25	of	of	ADP
ejpam-4520	9	26	antimagic	antimagic	ADJ
ejpam-4520	9	27	labeling	labeling	NOUN
ejpam-4520	9	28	.	.	PUNCT
ejpam-4520	10	1	in	in	ADP
ejpam-4520	10	2	this	this	DET
ejpam-4520	10	3	paper	paper	NOUN
ejpam-4520	10	4	,	,	PUNCT
ejpam-4520	10	5	we	we	PRON
ejpam-4520	10	6	will	will	AUX
ejpam-4520	10	7	study	study	VERB
ejpam-4520	10	8	the	the	DET
ejpam-4520	10	9	rac(g	rac(g	NOUN
ejpam-4520	10	10	)	)	PUNCT
ejpam-4520	10	11	of	of	ADP
ejpam-4520	10	12	the	the	DET
ejpam-4520	10	13	corona	corona	NOUN
ejpam-4520	10	14	product	product	NOUN
ejpam-4520	10	15	of	of	ADP
ejpam-4520	10	16	graphs	graph	NOUN
ejpam-4520	10	17	.	.	PUNCT
ejpam-4520	11	1	by	by	ADP
ejpam-4520	11	2	the	the	DET
ejpam-4520	11	3	corona	corona	NOUN
ejpam-4520	11	4	product	product	NOUN
ejpam-4520	11	5	of	of	ADP
ejpam-4520	11	6	graphs	graph	NOUN
ejpam-4520	11	7	g	g	PROPN
ejpam-4520	11	8	and	and	CCONJ
ejpam-4520	11	9	h	h	NOUN
ejpam-4520	11	10	,	,	PUNCT
ejpam-4520	11	11	denoted	denote	VERB
ejpam-4520	11	12	by	by	ADP
ejpam-4520	11	13	g⊙h	g⊙h	NOUN
ejpam-4520	11	14	,	,	PUNCT
ejpam-4520	11	15	we	we	PRON
ejpam-4520	11	16	mean	mean	VERB
ejpam-4520	11	17	a	a	DET
ejpam-4520	11	18	graph	graph	NOUN
ejpam-4520	11	19	obtained	obtain	VERB
ejpam-4520	11	20	by	by	ADP
ejpam-4520	11	21	taking	take	VERB
ejpam-4520	11	22	a	a	DET
ejpam-4520	11	23	copy	copy	NOUN
ejpam-4520	11	24	of	of	ADP
ejpam-4520	11	25	graph	graph	NOUN
ejpam-4520	11	26	g	g	PROPN
ejpam-4520	11	27	and	and	CCONJ
ejpam-4520	11	28	n	n	PROPN
ejpam-4520	11	29	copies	copy	NOUN
ejpam-4520	11	30	of	of	ADP
ejpam-4520	11	31	graph	graph	NOUN
ejpam-4520	11	32	h	h	NOUN
ejpam-4520	11	33	,	,	PUNCT
ejpam-4520	11	34	namely	namely	ADV
ejpam-4520	11	35	h1,h2	h1,h2	PROPN
ejpam-4520	11	36	,	,	PUNCT
ejpam-4520	11	37	...	...	PUNCT
ejpam-4520	11	38	,	,	PUNCT
ejpam-4520	11	39	hn	hn	PROPN
ejpam-4520	11	40	,	,	PUNCT
ejpam-4520	11	41	then	then	ADV
ejpam-4520	11	42	connecting	connect	VERB
ejpam-4520	11	43	vertex	vertex	NOUN
ejpam-4520	11	44	vi	vi	NOUN
ejpam-4520	11	45	from	from	ADP
ejpam-4520	11	46	the	the	DET
ejpam-4520	11	47	copy	copy	NOUN
ejpam-4520	11	48	of	of	ADP
ejpam-4520	11	49	graph	graph	NOUN
ejpam-4520	11	50	g	g	PROPN
ejpam-4520	11	51	to	to	ADP
ejpam-4520	11	52	every	every	DET
ejpam-4520	11	53	vertex	vertex	NOUN
ejpam-4520	11	54	on	on	ADP
ejpam-4520	11	55	graph	graph	NOUN
ejpam-4520	11	56	hi	hi	INTJ
ejpam-4520	11	57	,	,	PUNCT
ejpam-4520	11	58	i	i	PRON
ejpam-4520	11	59	=	=	NOUN
ejpam-4520	11	60	1	1	NUM
ejpam-4520	11	61	,	,	PUNCT
ejpam-4520	11	62	2	2	NUM
ejpam-4520	11	63	,	,	PUNCT
ejpam-4520	11	64	3	3	NUM
ejpam-4520	11	65	,	,	PUNCT
ejpam-4520	11	66	.	.	PUNCT
ejpam-4520	11	67	.	.	PUNCT
ejpam-4520	12	1	.	.	PUNCT
ejpam-4520	13	1	,	,	PUNCT
ejpam-4520	13	2	n.	n.	NOUN
ejpam-4520	13	3	in	in	ADP
ejpam-4520	13	4	this	this	DET
ejpam-4520	13	5	paper	paper	NOUN
ejpam-4520	13	6	,	,	PUNCT
ejpam-4520	13	7	we	we	PRON
ejpam-4520	13	8	show	show	VERB
ejpam-4520	13	9	the	the	DET
ejpam-4520	13	10	exact	exact	ADJ
ejpam-4520	13	11	value	value	NOUN
ejpam-4520	13	12	of	of	ADP
ejpam-4520	13	13	the	the	DET
ejpam-4520	13	14	rainbow	rainbow	NOUN
ejpam-4520	13	15	antimagic	antimagic	ADJ
ejpam-4520	13	16	connection	connection	NOUN
ejpam-4520	13	17	number	number	NOUN
ejpam-4520	13	18	of	of	ADP
ejpam-4520	13	19	tn	tn	PROPN
ejpam-4520	13	20	⊙	⊙	PROPN
ejpam-4520	13	21	sm	sm	PROPN
ejpam-4520	13	22	where	where	SCONJ
ejpam-4520	13	23	tn	tn	PROPN
ejpam-4520	13	24	∈	∈	PROPN
ejpam-4520	13	25	{	{	PUNCT
ejpam-4520	13	26	pn	pn	PROPN
ejpam-4520	13	27	,	,	PUNCT
ejpam-4520	13	28	sn	sn	PROPN
ejpam-4520	13	29	,	,	PUNCT
ejpam-4520	13	30	sn	sn	PROPN
ejpam-4520	13	31	,	,	PUNCT
ejpam-4520	13	32	p	p	X
ejpam-4520	13	33	,	,	PUNCT
ejpam-4520	13	34	fn,3	fn,3	NOUN
ejpam-4520	13	35	}	}	PUNCT
ejpam-4520	13	36	.	.	PUNCT
ejpam-4520	13	37	2020	2020	NUM
ejpam-4520	13	38	mathematics	mathematic	NOUN
ejpam-4520	13	39	subject	subject	NOUN
ejpam-4520	13	40	classifications	classification	NOUN
ejpam-4520	13	41	:	:	PUNCT
ejpam-4520	13	42	05c15	05c15	NUM
ejpam-4520	13	43	,	,	PUNCT
ejpam-4520	13	44	05c78	05c78	NUM
ejpam-4520	13	45	key	key	ADJ
ejpam-4520	13	46	words	word	NOUN
ejpam-4520	13	47	and	and	CCONJ
ejpam-4520	13	48	phrases	phrase	NOUN
ejpam-4520	13	49	:	:	PUNCT
ejpam-4520	13	50	antimagic	antimagic	ADJ
ejpam-4520	13	51	labeling	labeling	NOUN
ejpam-4520	13	52	,	,	PUNCT
ejpam-4520	13	53	rainbow	rainbow	NOUN
ejpam-4520	13	54	connection	connection	NOUN
ejpam-4520	13	55	,	,	PUNCT
ejpam-4520	13	56	rainbow	rainbow	VERB
ejpam-4520	13	57	antimagic	antimagic	ADJ
ejpam-4520	13	58	connection	connection	NOUN
ejpam-4520	13	59	number	number	NOUN
ejpam-4520	13	60	,	,	PUNCT
ejpam-4520	13	61	corona	corona	NOUN
ejpam-4520	13	62	product	product	NOUN
ejpam-4520	13	63	of	of	ADP
ejpam-4520	13	64	graphs	graph	NOUN
ejpam-4520	13	65	.	.	PUNCT
ejpam-4520	14	1	∗corresponding	∗corresponde	VERB
ejpam-4520	14	2	author	author	NOUN
ejpam-4520	14	3	.	.	PUNCT
ejpam-4520	15	1	doi	doi	NOUN
ejpam-4520	15	2	:	:	PUNCT
ejpam-4520	15	3	https://doi.org/10.29020/nybg.ejpam.v16i1.4520	https://doi.org/10.29020/nybg.ejpam.v16i1.4520	ADJ
ejpam-4520	15	4	email	email	NOUN
ejpam-4520	15	5	addresses	address	NOUN
ejpam-4520	15	6	:	:	PUNCT
ejpam-4520	15	7	liliek-s@fst.unair.ac.id	liliek-s@fst.unair.ac.id	NOUN
ejpam-4520	15	8	(	(	PUNCT
ejpam-4520	15	9	l.	l.	PROPN
ejpam-4520	15	10	susilowati	susilowati	PROPN
ejpam-4520	15	11	)	)	PUNCT
ejpam-4520	15	12	,	,	PUNCT
ejpam-4520	15	13	brianseptory95@gmail.com	brianseptory95@gmail.com	PROPN
ejpam-4520	15	14	(	(	PUNCT
ejpam-4520	15	15	b.	b.	PROPN
ejpam-4520	15	16	j.	j.	PROPN
ejpam-4520	15	17	septory	septory	PROPN
ejpam-4520	15	18	)	)	PUNCT
ejpam-4520	15	19	,	,	PUNCT
ejpam-4520	15	20	d.dafik@unej.ac.id	d.dafik@unej.ac.id	NOUN
ejpam-4520	15	21	(	(	PUNCT
ejpam-4520	15	22	dafik	dafik	NOUN
ejpam-4520	15	23	)	)	PUNCT
ejpam-4520	15	24	,	,	PUNCT
ejpam-4520	15	25	mathematics@vskub.ac.in	mathematics@vskub.ac.in	ADV
ejpam-4520	15	26	(	(	PUNCT
ejpam-4520	15	27	v.	v.	ADP
ejpam-4520	15	28	lokesha	lokesha	PROPN
ejpam-4520	15	29	)	)	PUNCT
ejpam-4520	15	30	,	,	PUNCT
ejpam-4520	15	31	nagamanigru@gmail.com	nagamanigru@gmail.com	X
ejpam-4520	15	32	(	(	PUNCT
ejpam-4520	15	33	g.	g.	PROPN
ejpam-4520	15	34	nagamani	nagamani	PROPN
ejpam-4520	15	35	)	)	PUNCT
ejpam-4520	15	36	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-4520	16	1	271	271	NUM
ejpam-4520	16	2	©	©	PROPN
ejpam-4520	16	3	2023	2023	NUM
ejpam-4520	16	4	ejpam	ejpam	NOUN
ejpam-4520	16	5	all	all	DET
ejpam-4520	16	6	rights	right	NOUN
ejpam-4520	16	7	reserved	reserve	VERB
ejpam-4520	16	8	.	.	PUNCT
ejpam-4520	17	1	susilowati	susilowati	PROPN
ejpam-4520	17	2	et	et	PROPN
ejpam-4520	17	3	.	.	PUNCT
ejpam-4520	18	1	al	al	PROPN
ejpam-4520	18	2	/	/	PUNCT
ejpam-4520	18	3	eur	eur	PROPN
ejpam-4520	18	4	.	.	PUNCT
ejpam-4520	19	1	j.	j.	PROPN
ejpam-4520	19	2	pure	pure	PROPN
ejpam-4520	19	3	appl	appl	PROPN
ejpam-4520	19	4	.	.	PROPN
ejpam-4520	19	5	math	math	PROPN
ejpam-4520	19	6	,	,	PUNCT
ejpam-4520	19	7	16	16	NUM
ejpam-4520	19	8	(	(	PUNCT
ejpam-4520	19	9	1	1	NUM
ejpam-4520	19	10	)	)	PUNCT
ejpam-4520	19	11	(	(	PUNCT
ejpam-4520	19	12	2023	2023	NUM
ejpam-4520	19	13	)	)	PUNCT
ejpam-4520	19	14	,	,	PUNCT
ejpam-4520	19	15	271	271	NUM
ejpam-4520	19	16	-	-	SYM
ejpam-4520	19	17	285	285	NUM
ejpam-4520	19	18	272	272	NUM
ejpam-4520	19	19	1	1	NUM
ejpam-4520	19	20	.	.	PUNCT
ejpam-4520	20	1	introduction	introduction	NOUN
ejpam-4520	20	2	given	give	VERB
ejpam-4520	20	3	two	two	NUM
ejpam-4520	20	4	any	any	DET
ejpam-4520	20	5	graphs	graph	NOUN
ejpam-4520	20	6	g	g	NOUN
ejpam-4520	20	7	and	and	CCONJ
ejpam-4520	20	8	h.	h.	PROPN
ejpam-4520	20	9	the	the	DET
ejpam-4520	20	10	corona	corona	PROPN
ejpam-4520	20	11	operation	operation	NOUN
ejpam-4520	20	12	of	of	ADP
ejpam-4520	20	13	two	two	NUM
ejpam-4520	20	14	graphs	graph	NOUN
ejpam-4520	20	15	g	g	NOUN
ejpam-4520	20	16	and	and	CCONJ
ejpam-4520	20	17	h	h	NOUN
ejpam-4520	20	18	,	,	PUNCT
ejpam-4520	20	19	denoted	denote	VERB
ejpam-4520	20	20	by	by	ADP
ejpam-4520	20	21	g⊙h	g⊙h	NOUN
ejpam-4520	20	22	,	,	PUNCT
ejpam-4520	20	23	is	be	AUX
ejpam-4520	20	24	a	a	DET
ejpam-4520	20	25	graph	graph	NOUN
ejpam-4520	20	26	obtained	obtain	VERB
ejpam-4520	20	27	by	by	ADP
ejpam-4520	20	28	taking	take	VERB
ejpam-4520	20	29	a	a	DET
ejpam-4520	20	30	copy	copy	NOUN
ejpam-4520	20	31	of	of	ADP
ejpam-4520	20	32	graph	graph	NOUN
ejpam-4520	20	33	g	g	PROPN
ejpam-4520	20	34	and	and	CCONJ
ejpam-4520	20	35	n	n	PROPN
ejpam-4520	20	36	copies	copy	NOUN
ejpam-4520	20	37	of	of	ADP
ejpam-4520	20	38	graph	graph	NOUN
ejpam-4520	20	39	h	h	PROPN
ejpam-4520	20	40	namely	namely	ADV
ejpam-4520	20	41	h1,h2	h1,h2	PROPN
ejpam-4520	20	42	,	,	PUNCT
ejpam-4520	20	43	...	...	PUNCT
ejpam-4520	20	44	,	,	PUNCT
ejpam-4520	20	45	hn	hn	PROPN
ejpam-4520	20	46	then	then	ADV
ejpam-4520	20	47	connecting	connect	VERB
ejpam-4520	20	48	vertex	vertex	NOUN
ejpam-4520	20	49	vi	vi	NOUN
ejpam-4520	20	50	from	from	ADP
ejpam-4520	20	51	the	the	DET
ejpam-4520	20	52	copy	copy	NOUN
ejpam-4520	20	53	of	of	ADP
ejpam-4520	20	54	graph	graph	NOUN
ejpam-4520	20	55	g	g	PROPN
ejpam-4520	20	56	to	to	ADP
ejpam-4520	20	57	every	every	DET
ejpam-4520	20	58	vertex	vertex	NOUN
ejpam-4520	20	59	on	on	ADP
ejpam-4520	20	60	graph	graph	NOUN
ejpam-4520	20	61	hi	hi	INTJ
ejpam-4520	20	62	,	,	PUNCT
ejpam-4520	20	63	i	i	PRON
ejpam-4520	20	64	=	=	NOUN
ejpam-4520	20	65	1	1	NUM
ejpam-4520	20	66	,	,	PUNCT
ejpam-4520	20	67	2	2	NUM
ejpam-4520	20	68	,	,	PUNCT
ejpam-4520	20	69	3	3	NUM
ejpam-4520	20	70	,	,	PUNCT
ejpam-4520	20	71	.	.	PUNCT
ejpam-4520	20	72	.	.	PUNCT
ejpam-4520	20	73	.	.	PUNCT
ejpam-4520	21	1	,	,	PUNCT
ejpam-4520	21	2	n	n	CCONJ
ejpam-4520	21	3	,	,	PUNCT
ejpam-4520	21	4	see	see	VERB
ejpam-4520	21	5	[	[	X
ejpam-4520	21	6	8	8	NUM
ejpam-4520	21	7	,	,	PUNCT
ejpam-4520	21	8	12	12	NUM
ejpam-4520	21	9	]	]	PUNCT
ejpam-4520	21	10	for	for	ADP
ejpam-4520	21	11	detail	detail	NOUN
ejpam-4520	21	12	.	.	PUNCT
ejpam-4520	22	1	the	the	DET
ejpam-4520	22	2	rainbow	rainbow	NOUN
ejpam-4520	22	3	antimagic	antimagic	ADJ
ejpam-4520	22	4	coloring	coloring	NOUN
ejpam-4520	22	5	defined	define	VERB
ejpam-4520	22	6	in	in	ADP
ejpam-4520	22	7	above	above	ADP
ejpam-4520	22	8	abstract	abstract	ADJ
ejpam-4520	22	9	is	be	AUX
ejpam-4520	22	10	a	a	DET
ejpam-4520	22	11	combination	combination	NOUN
ejpam-4520	22	12	of	of	ADP
ejpam-4520	22	13	the	the	DET
ejpam-4520	22	14	rainbow	rainbow	NOUN
ejpam-4520	22	15	coloring	coloring	NOUN
ejpam-4520	22	16	and	and	CCONJ
ejpam-4520	22	17	antimagic	antimagic	ADJ
ejpam-4520	22	18	labeling	labeling	NOUN
ejpam-4520	22	19	concepts	concept	NOUN
ejpam-4520	22	20	.	.	PUNCT
ejpam-4520	23	1	rainbow	rainbow	PROPN
ejpam-4520	23	2	coloring	coloring	PROPN
ejpam-4520	23	3	was	be	AUX
ejpam-4520	23	4	first	first	ADV
ejpam-4520	23	5	introduced	introduce	VERB
ejpam-4520	23	6	by	by	ADP
ejpam-4520	23	7	chartrand	chartrand	PROPN
ejpam-4520	23	8	et	et	PROPN
ejpam-4520	23	9	al	al	PROPN
ejpam-4520	23	10	.	.	PROPN
ejpam-4520	24	1	in	in	ADP
ejpam-4520	24	2	2008	2008	NUM
ejpam-4520	24	3	[	[	X
ejpam-4520	24	4	7	7	NUM
ejpam-4520	24	5	]	]	PUNCT
ejpam-4520	24	6	.	.	PUNCT
ejpam-4520	24	7	suppose	suppose	VERB
ejpam-4520	24	8	that	that	SCONJ
ejpam-4520	24	9	g	g	PROPN
ejpam-4520	24	10	is	be	AUX
ejpam-4520	24	11	a	a	DET
ejpam-4520	24	12	nontrivially	nontrivially	ADV
ejpam-4520	24	13	connected	connect	VERB
ejpam-4520	24	14	graph	graph	NOUN
ejpam-4520	24	15	and	and	CCONJ
ejpam-4520	24	16	c	c	NOUN
ejpam-4520	24	17	is	be	AUX
ejpam-4520	24	18	the	the	DET
ejpam-4520	24	19	edge	edge	NOUN
ejpam-4520	24	20	coloring	coloring	NOUN
ejpam-4520	24	21	of	of	ADP
ejpam-4520	24	22	g.	g.	PROPN
ejpam-4520	24	23	a	a	DET
ejpam-4520	24	24	u−	u−	PROPN
ejpam-4520	24	25	v	v	ADP
ejpam-4520	24	26	path	path	NOUN
ejpam-4520	24	27	of	of	ADP
ejpam-4520	24	28	g	g	NOUN
ejpam-4520	24	29	,	,	PUNCT
ejpam-4520	24	30	if	if	SCONJ
ejpam-4520	24	31	no	no	DET
ejpam-4520	24	32	two	two	NUM
ejpam-4520	24	33	edges	edge	NOUN
ejpam-4520	24	34	of	of	ADP
ejpam-4520	24	35	the	the	DET
ejpam-4520	24	36	u−	u−	PROPN
ejpam-4520	24	37	v	v	NOUN
ejpam-4520	24	38	path	path	NOUN
ejpam-4520	24	39	are	be	AUX
ejpam-4520	24	40	the	the	DET
ejpam-4520	24	41	same	same	ADJ
ejpam-4520	24	42	color	color	NOUN
ejpam-4520	24	43	is	be	AUX
ejpam-4520	24	44	called	call	VERB
ejpam-4520	24	45	a	a	DET
ejpam-4520	24	46	rainbow	rainbow	NOUN
ejpam-4520	24	47	path	path	NOUN
ejpam-4520	24	48	.	.	PUNCT
ejpam-4520	25	1	the	the	DET
ejpam-4520	25	2	c	c	PROPN
ejpam-4520	25	3	edge	edge	NOUN
ejpam-4520	25	4	coloring	coloring	NOUN
ejpam-4520	25	5	,	,	PUNCT
ejpam-4520	25	6	if	if	SCONJ
ejpam-4520	25	7	for	for	ADP
ejpam-4520	25	8	every	every	DET
ejpam-4520	25	9	vertex	vertex	NOUN
ejpam-4520	25	10	u	u	NOUN
ejpam-4520	25	11	,	,	PUNCT
ejpam-4520	25	12	v	v	PROPN
ejpam-4520	25	13	∈	∈	PROPN
ejpam-4520	25	14	v	v	NOUN
ejpam-4520	25	15	(	(	PUNCT
ejpam-4520	25	16	g	g	NOUN
ejpam-4520	25	17	)	)	PUNCT
ejpam-4520	25	18	there	there	PRON
ejpam-4520	25	19	is	be	VERB
ejpam-4520	25	20	a	a	DET
ejpam-4520	25	21	rainbow	rainbow	NOUN
ejpam-4520	25	22	path	path	NOUN
ejpam-4520	25	23	u−	u−	PROPN
ejpam-4520	25	24	v	v	PROPN
ejpam-4520	25	25	is	be	AUX
ejpam-4520	25	26	called	call	VERB
ejpam-4520	25	27	a	a	DET
ejpam-4520	25	28	rainbow	rainbow	NOUN
ejpam-4520	25	29	connection	connection	NOUN
ejpam-4520	25	30	.	.	PUNCT
ejpam-4520	26	1	there	there	PRON
ejpam-4520	26	2	are	be	VERB
ejpam-4520	26	3	a	a	DET
ejpam-4520	26	4	lot	lot	NOUN
ejpam-4520	26	5	of	of	ADP
ejpam-4520	26	6	results	result	NOUN
ejpam-4520	26	7	related	relate	VERB
ejpam-4520	26	8	to	to	ADP
ejpam-4520	26	9	the	the	DET
ejpam-4520	26	10	rainbow	rainbow	NOUN
ejpam-4520	26	11	connection	connection	NOUN
ejpam-4520	26	12	,	,	PUNCT
ejpam-4520	26	13	see	see	VERB
ejpam-4520	26	14	[	[	X
ejpam-4520	26	15	17	17	NUM
ejpam-4520	26	16	]	]	PUNCT
ejpam-4520	26	17	and	and	CCONJ
ejpam-4520	26	18	[	[	X
ejpam-4520	26	19	18	18	NUM
ejpam-4520	26	20	]	]	PUNCT
ejpam-4520	26	21	.	.	PUNCT
ejpam-4520	27	1	proposition	proposition	NOUN
ejpam-4520	27	2	1	1	NUM
ejpam-4520	27	3	.	.	PUNCT
ejpam-4520	28	1	[	[	X
ejpam-4520	28	2	21	21	NUM
ejpam-4520	28	3	]	]	PUNCT
ejpam-4520	28	4	let	let	VERB
ejpam-4520	28	5	g	g	PRON
ejpam-4520	28	6	be	be	AUX
ejpam-4520	28	7	a	a	DET
ejpam-4520	28	8	connected	connected	ADJ
ejpam-4520	28	9	graph	graph	NOUN
ejpam-4520	28	10	of	of	ADP
ejpam-4520	28	11	size	size	NOUN
ejpam-4520	28	12	m.	m.	NOUN
ejpam-4520	28	13	the	the	DET
ejpam-4520	28	14	rainbow	rainbow	NOUN
ejpam-4520	28	15	connection	connection	NOUN
ejpam-4520	28	16	number	number	NOUN
ejpam-4520	28	17	rc(g	rc(g	PUNCT
ejpam-4520	28	18	)	)	PUNCT
ejpam-4520	29	1	=	=	PUNCT
ejpam-4520	29	2	m	m	NOUN
ejpam-4520	29	3	if	if	SCONJ
ejpam-4520	29	4	and	and	CCONJ
ejpam-4520	29	5	only	only	ADV
ejpam-4520	29	6	if	if	SCONJ
ejpam-4520	29	7	g	g	PROPN
ejpam-4520	29	8	is	be	AUX
ejpam-4520	29	9	a	a	DET
ejpam-4520	29	10	tree	tree	NOUN
ejpam-4520	29	11	.	.	PUNCT
ejpam-4520	30	1	other	other	ADJ
ejpam-4520	30	2	extension	extension	NOUN
ejpam-4520	30	3	of	of	ADP
ejpam-4520	30	4	rainbow	rainbow	NOUN
ejpam-4520	30	5	coloring	coloring	NOUN
ejpam-4520	30	6	study	study	NOUN
ejpam-4520	30	7	is	be	AUX
ejpam-4520	30	8	rainbow	rainbow	NOUN
ejpam-4520	30	9	vertex	vertex	NOUN
ejpam-4520	30	10	coloring	coloring	NOUN
ejpam-4520	30	11	introduced	introduce	VERB
ejpam-4520	30	12	in	in	ADP
ejpam-4520	30	13	[	[	X
ejpam-4520	30	14	16	16	NUM
ejpam-4520	30	15	]	]	PUNCT
ejpam-4520	30	16	.	.	PUNCT
ejpam-4520	31	1	some	some	DET
ejpam-4520	31	2	results	result	NOUN
ejpam-4520	31	3	on	on	ADP
ejpam-4520	31	4	rainbow	rainbow	NOUN
ejpam-4520	31	5	vertex	vertex	NOUN
ejpam-4520	31	6	connection	connection	NOUN
ejpam-4520	31	7	number	number	NOUN
ejpam-4520	31	8	can	can	AUX
ejpam-4520	31	9	see	see	VERB
ejpam-4520	31	10	in	in	ADP
ejpam-4520	31	11	[	[	X
ejpam-4520	31	12	19	19	NUM
ejpam-4520	31	13	]	]	PUNCT
ejpam-4520	31	14	,	,	PUNCT
ejpam-4520	31	15	[	[	X
ejpam-4520	31	16	23	23	NUM
ejpam-4520	31	17	]	]	PUNCT
ejpam-4520	31	18	.	.	PUNCT
ejpam-4520	32	1	furthermore	furthermore	ADV
ejpam-4520	32	2	,	,	PUNCT
ejpam-4520	32	3	we	we	PRON
ejpam-4520	32	4	also	also	ADV
ejpam-4520	32	5	have	have	VERB
ejpam-4520	32	6	other	other	ADJ
ejpam-4520	32	7	version	version	NOUN
ejpam-4520	32	8	of	of	ADP
ejpam-4520	32	9	rainbow	rainbow	NOUN
ejpam-4520	32	10	coloring	coloring	NOUN
ejpam-4520	32	11	study	study	NOUN
ejpam-4520	32	12	,	,	PUNCT
ejpam-4520	32	13	called	call	VERB
ejpam-4520	32	14	rainbow	rainbow	NOUN
ejpam-4520	32	15	total	total	NOUN
ejpam-4520	32	16	coloring	coloring	NOUN
ejpam-4520	32	17	,	,	PUNCT
ejpam-4520	32	18	see	see	VERB
ejpam-4520	32	19	[	[	X
ejpam-4520	32	20	14	14	NUM
ejpam-4520	32	21	]	]	PUNCT
ejpam-4520	32	22	and	and	CCONJ
ejpam-4520	32	23	[	[	X
ejpam-4520	32	24	24	24	NUM
ejpam-4520	32	25	]	]	PUNCT
ejpam-4520	32	26	.	.	PUNCT
ejpam-4520	33	1	the	the	DET
ejpam-4520	33	2	complete	complete	ADJ
ejpam-4520	33	3	survey	survey	NOUN
ejpam-4520	33	4	of	of	ADP
ejpam-4520	33	5	rainbow	rainbow	NOUN
ejpam-4520	33	6	connection	connection	NOUN
ejpam-4520	33	7	number	number	NOUN
ejpam-4520	33	8	can	can	AUX
ejpam-4520	33	9	be	be	AUX
ejpam-4520	33	10	found	find	VERB
ejpam-4520	33	11	in	in	ADP
ejpam-4520	33	12	[	[	X
ejpam-4520	33	13	20	20	NUM
ejpam-4520	33	14	]	]	PUNCT
ejpam-4520	33	15	.	.	PUNCT
ejpam-4520	34	1	meanwhile	meanwhile	ADV
ejpam-4520	34	2	,	,	PUNCT
ejpam-4520	34	3	graph	graph	NOUN
ejpam-4520	34	4	labeling	labeling	NOUN
ejpam-4520	34	5	was	be	AUX
ejpam-4520	34	6	first	first	ADV
ejpam-4520	34	7	introduced	introduce	VERB
ejpam-4520	34	8	by	by	ADP
ejpam-4520	34	9	wallis	wallis	PROPN
ejpam-4520	34	10	et	et	PROPN
ejpam-4520	34	11	al	al	PROPN
ejpam-4520	34	12	.	.	PROPN
ejpam-4520	35	1	in	in	ADP
ejpam-4520	35	2	2001	2001	NUM
ejpam-4520	35	3	[	[	X
ejpam-4520	35	4	25	25	NUM
ejpam-4520	35	5	]	]	PUNCT
ejpam-4520	35	6	.	.	PUNCT
ejpam-4520	36	1	hartsfield	hartsfield	PROPN
ejpam-4520	36	2	and	and	CCONJ
ejpam-4520	36	3	ringel	ringel	NOUN
ejpam-4520	36	4	in	in	ADP
ejpam-4520	36	5	1990	1990	NUM
ejpam-4520	36	6	[	[	SYM
ejpam-4520	36	7	13	13	NUM
ejpam-4520	36	8	]	]	PUNCT
ejpam-4520	36	9	introduced	introduce	VERB
ejpam-4520	36	10	an	an	DET
ejpam-4520	36	11	antimagic	antimagic	ADJ
ejpam-4520	36	12	labeling	labeling	NOUN
ejpam-4520	36	13	of	of	ADP
ejpam-4520	36	14	a	a	DET
ejpam-4520	36	15	graph	graph	NOUN
ejpam-4520	36	16	g	g	NOUN
ejpam-4520	36	17	with	with	ADP
ejpam-4520	36	18	edges	edge	NOUN
ejpam-4520	36	19	is	be	AUX
ejpam-4520	36	20	a	a	DET
ejpam-4520	36	21	bijection	bijection	ADJ
ejpam-4520	36	22	function	function	NOUN
ejpam-4520	36	23	f	f	NOUN
ejpam-4520	36	24	:	:	PUNCT
ejpam-4520	36	25	e(g	e(g	PROPN
ejpam-4520	36	26	)	)	PUNCT
ejpam-4520	36	27	→	→	PUNCT
ejpam-4520	36	28	{	{	PUNCT
ejpam-4520	36	29	1	1	NUM
ejpam-4520	36	30	,	,	PUNCT
ejpam-4520	36	31	2	2	NUM
ejpam-4520	36	32	,	,	PUNCT
ejpam-4520	36	33	...	...	PUNCT
ejpam-4520	36	34	,	,	PUNCT
ejpam-4520	36	35	|e(g)|	|e(g)|	ADJ
ejpam-4520	36	36	}	}	PUNCT
ejpam-4520	36	37	and	and	CCONJ
ejpam-4520	36	38	w(v	w(v	NOUN
ejpam-4520	36	39	)	)	PUNCT
ejpam-4520	36	40	=	=	SYM
ejpam-4520	36	41	σe∈e(v)f(e	σe∈e(v)f(e	NOUN
ejpam-4520	36	42	)	)	PUNCT
ejpam-4520	36	43	,	,	PUNCT
ejpam-4520	36	44	and	and	CCONJ
ejpam-4520	36	45	e(v	e(v	NOUN
ejpam-4520	36	46	)	)	PUNCT
ejpam-4520	36	47	is	be	AUX
ejpam-4520	36	48	the	the	DET
ejpam-4520	36	49	set	set	NOUN
ejpam-4520	36	50	of	of	ADP
ejpam-4520	36	51	edges	edge	NOUN
ejpam-4520	36	52	incidence	incidence	NOUN
ejpam-4520	36	53	to	to	ADP
ejpam-4520	36	54	v	v	NOUN
ejpam-4520	36	55	,	,	PUNCT
ejpam-4520	36	56	for	for	ADP
ejpam-4520	36	57	vertex	vertex	NOUN
ejpam-4520	36	58	u	u	NOUN
ejpam-4520	36	59	,	,	PUNCT
ejpam-4520	36	60	v	v	PROPN
ejpam-4520	36	61	∈	∈	PROPN
ejpam-4520	36	62	v	v	NOUN
ejpam-4520	36	63	(	(	PUNCT
ejpam-4520	36	64	g	g	NOUN
ejpam-4520	36	65	)	)	PUNCT
ejpam-4520	36	66	,	,	PUNCT
ejpam-4520	36	67	w(u	w(u	X
ejpam-4520	36	68	)	)	PUNCT
ejpam-4520	37	1	=	=	SYM
ejpam-4520	37	2	̸	̸	NUM
ejpam-4520	37	3	w(v	w(v	NOUN
ejpam-4520	37	4	)	)	PUNCT
ejpam-4520	37	5	.	.	PUNCT
ejpam-4520	38	1	some	some	DET
ejpam-4520	38	2	results	result	NOUN
ejpam-4520	38	3	of	of	ADP
ejpam-4520	38	4	antimagic	antimagic	ADJ
ejpam-4520	38	5	labeling	labeling	NOUN
ejpam-4520	38	6	have	have	AUX
ejpam-4520	38	7	been	be	AUX
ejpam-4520	38	8	extensively	extensively	ADV
ejpam-4520	38	9	studied	study	VERB
ejpam-4520	38	10	by	by	ADP
ejpam-4520	38	11	baca	baca	PROPN
ejpam-4520	38	12	et	et	PROPN
ejpam-4520	38	13	al	al	PROPN
ejpam-4520	38	14	.	.	PUNCT
ejpam-4520	39	1	in	in	ADP
ejpam-4520	39	2	[	[	X
ejpam-4520	39	3	2–4	2–4	NUM
ejpam-4520	39	4	]	]	PUNCT
ejpam-4520	39	5	.	.	PUNCT
ejpam-4520	40	1	furthermore	furthermore	ADV
ejpam-4520	40	2	,	,	PUNCT
ejpam-4520	40	3	dafik	dafik	VERB
ejpam-4520	40	4	et	et	PROPN
ejpam-4520	40	5	al	al	PROPN
ejpam-4520	40	6	.	.	PROPN
ejpam-4520	41	1	in	in	ADP
ejpam-4520	41	2	2021	2021	NUM
ejpam-4520	41	3	[	[	X
ejpam-4520	41	4	10	10	NUM
ejpam-4520	41	5	]	]	PUNCT
ejpam-4520	41	6	also	also	ADV
ejpam-4520	41	7	contributed	contribute	VERB
ejpam-4520	41	8	some	some	DET
ejpam-4520	41	9	results	result	NOUN
ejpam-4520	41	10	on	on	ADP
ejpam-4520	41	11	antimagic	antimagic	ADJ
ejpam-4520	41	12	labeling	labeling	NOUN
ejpam-4520	41	13	.	.	PUNCT
ejpam-4520	42	1	moreover	moreover	ADV
ejpam-4520	42	2	,	,	PUNCT
ejpam-4520	42	3	there	there	PRON
ejpam-4520	42	4	are	be	VERB
ejpam-4520	42	5	some	some	DET
ejpam-4520	42	6	other	other	ADJ
ejpam-4520	42	7	results	result	NOUN
ejpam-4520	42	8	related	relate	VERB
ejpam-4520	42	9	to	to	ADP
ejpam-4520	42	10	antimagic	antimagic	ADJ
ejpam-4520	42	11	labeling	labeling	NOUN
ejpam-4520	42	12	,	,	PUNCT
ejpam-4520	42	13	see	see	VERB
ejpam-4520	42	14	[	[	X
ejpam-4520	42	15	6	6	NUM
ejpam-4520	42	16	]	]	PUNCT
ejpam-4520	42	17	and	and	CCONJ
ejpam-4520	42	18	[	[	X
ejpam-4520	42	19	9	9	NUM
ejpam-4520	42	20	]	]	PUNCT
ejpam-4520	42	21	.	.	PUNCT
ejpam-4520	43	1	the	the	DET
ejpam-4520	43	2	concept	concept	NOUN
ejpam-4520	43	3	of	of	ADP
ejpam-4520	43	4	combining	combine	VERB
ejpam-4520	43	5	the	the	DET
ejpam-4520	43	6	graph	graph	NOUN
ejpam-4520	43	7	coloring	coloring	NOUN
ejpam-4520	43	8	and	and	CCONJ
ejpam-4520	43	9	the	the	DET
ejpam-4520	43	10	graph	graph	NOUN
ejpam-4520	43	11	labeling	labeling	NOUN
ejpam-4520	43	12	was	be	AUX
ejpam-4520	43	13	initiated	initiate	VERB
ejpam-4520	43	14	by	by	ADP
ejpam-4520	43	15	arumugam	arumugam	PROPN
ejpam-4520	43	16	et	et	PROPN
ejpam-4520	43	17	al	al	PROPN
ejpam-4520	43	18	.	.	PROPN
ejpam-4520	44	1	in	in	ADP
ejpam-4520	44	2	2017	2017	NUM
ejpam-4520	44	3	[	[	X
ejpam-4520	44	4	1	1	NUM
ejpam-4520	44	5	]	]	PUNCT
ejpam-4520	44	6	.	.	PUNCT
ejpam-4520	45	1	he	he	PRON
ejpam-4520	45	2	defined	define	VERB
ejpam-4520	45	3	that	that	SCONJ
ejpam-4520	45	4	for	for	ADP
ejpam-4520	45	5	a	a	DET
ejpam-4520	45	6	bijection	bijection	ADJ
ejpam-4520	45	7	f	f	NOUN
ejpam-4520	45	8	:	:	PUNCT
ejpam-4520	45	9	e(g	e(g	PROPN
ejpam-4520	45	10	)	)	PUNCT
ejpam-4520	45	11	→	→	PUNCT
ejpam-4520	45	12	{	{	PUNCT
ejpam-4520	45	13	1	1	NUM
ejpam-4520	45	14	,	,	PUNCT
ejpam-4520	45	15	2	2	NUM
ejpam-4520	45	16	,	,	PUNCT
ejpam-4520	45	17	...	...	PUNCT
ejpam-4520	46	1	|e(g)|	|e(g)|	ADJ
ejpam-4520	46	2	}	}	PUNCT
ejpam-4520	46	3	and	and	CCONJ
ejpam-4520	46	4	w(v	w(v	NOUN
ejpam-4520	46	5	)	)	PUNCT
ejpam-4520	46	6	=	=	SYM
ejpam-4520	46	7	σe∈e(v)f(e	σe∈e(v)f(e	NOUN
ejpam-4520	46	8	)	)	PUNCT
ejpam-4520	46	9	,	,	PUNCT
ejpam-4520	46	10	and	and	CCONJ
ejpam-4520	46	11	e(v	e(v	NOUN
ejpam-4520	46	12	)	)	PUNCT
ejpam-4520	46	13	is	be	AUX
ejpam-4520	46	14	the	the	DET
ejpam-4520	46	15	set	set	NOUN
ejpam-4520	46	16	of	of	ADP
ejpam-4520	46	17	edges	edge	NOUN
ejpam-4520	46	18	incidence	incidence	NOUN
ejpam-4520	46	19	to	to	ADP
ejpam-4520	46	20	v	v	NOUN
ejpam-4520	46	21	,	,	PUNCT
ejpam-4520	46	22	for	for	ADP
ejpam-4520	46	23	each	each	DET
ejpam-4520	46	24	v	v	NUM
ejpam-4520	46	25	∈	∈	PROPN
ejpam-4520	46	26	v	v	NOUN
ejpam-4520	46	27	(	(	PUNCT
ejpam-4520	46	28	g	g	NOUN
ejpam-4520	46	29	)	)	PUNCT
ejpam-4520	46	30	.	.	PUNCT
ejpam-4520	47	1	the	the	DET
ejpam-4520	47	2	bijection	bijection	NOUN
ejpam-4520	47	3	f	f	PROPN
ejpam-4520	47	4	is	be	AUX
ejpam-4520	47	5	called	call	VERB
ejpam-4520	47	6	local	local	ADJ
ejpam-4520	47	7	antimagic	antimagic	ADJ
ejpam-4520	47	8	labeling	labeling	NOUN
ejpam-4520	47	9	if	if	SCONJ
ejpam-4520	47	10	for	for	ADP
ejpam-4520	47	11	every	every	DET
ejpam-4520	47	12	two	two	NUM
ejpam-4520	47	13	adjacent	adjacent	ADJ
ejpam-4520	47	14	vertices	vertex	NOUN
ejpam-4520	47	15	u	u	NOUN
ejpam-4520	47	16	,	,	PUNCT
ejpam-4520	47	17	v	v	NOUN
ejpam-4520	47	18	∈	∈	PROPN
ejpam-4520	47	19	v	v	NOUN
ejpam-4520	47	20	(	(	PUNCT
ejpam-4520	47	21	g	g	NOUN
ejpam-4520	47	22	)	)	PUNCT
ejpam-4520	47	23	,	,	PUNCT
ejpam-4520	47	24	w(u	w(u	PROPN
ejpam-4520	47	25	)	)	PUNCT
ejpam-4520	47	26	̸=	̸=	PROPN
ejpam-4520	47	27	w(v	w(v	PROPN
ejpam-4520	47	28	)	)	PUNCT
ejpam-4520	47	29	.	.	PUNCT
ejpam-4520	48	1	thus	thus	ADV
ejpam-4520	48	2	,	,	PUNCT
ejpam-4520	48	3	each	each	DET
ejpam-4520	48	4	local	local	ADJ
ejpam-4520	48	5	antimagic	antimagic	ADJ
ejpam-4520	48	6	labeling	labeling	NOUN
ejpam-4520	48	7	is	be	AUX
ejpam-4520	48	8	a	a	DET
ejpam-4520	48	9	vertex	vertex	NOUN
ejpam-4520	48	10	coloring	coloring	NOUN
ejpam-4520	48	11	at	at	ADP
ejpam-4520	48	12	g	g	NOUN
ejpam-4520	48	13	with	with	ADP
ejpam-4520	48	14	vertex	vertex	NOUN
ejpam-4520	48	15	v	v	ADP
ejpam-4520	48	16	colored	color	VERB
ejpam-4520	48	17	with	with	ADP
ejpam-4520	48	18	w(v	w(v	PROPN
ejpam-4520	48	19	)	)	PUNCT
ejpam-4520	48	20	.	.	PUNCT
ejpam-4520	49	1	when	when	SCONJ
ejpam-4520	49	2	we	we	PRON
ejpam-4520	49	3	consider	consider	VERB
ejpam-4520	49	4	the	the	DET
ejpam-4520	49	5	chromatic	chromatic	ADJ
ejpam-4520	49	6	number	number	NOUN
ejpam-4520	49	7	of	of	ADP
ejpam-4520	49	8	the	the	DET
ejpam-4520	49	9	local	local	ADJ
ejpam-4520	49	10	antimagic	antimagic	ADJ
ejpam-4520	49	11	labeling	labeling	NOUN
ejpam-4520	49	12	,	,	PUNCT
ejpam-4520	49	13	this	this	DET
ejpam-4520	49	14	notion	notion	NOUN
ejpam-4520	49	15	is	be	AUX
ejpam-4520	49	16	called	call	VERB
ejpam-4520	49	17	a	a	DET
ejpam-4520	49	18	local	local	ADJ
ejpam-4520	49	19	antimagic	antimagic	ADJ
ejpam-4520	49	20	coloring	coloring	NOUN
ejpam-4520	49	21	.	.	PUNCT
ejpam-4520	50	1	motivated	motivate	VERB
ejpam-4520	50	2	by	by	ADP
ejpam-4520	50	3	this	this	DET
ejpam-4520	50	4	combination	combination	NOUN
ejpam-4520	50	5	,	,	PUNCT
ejpam-4520	50	6	dafik	dafik	PROPN
ejpam-4520	50	7	et	et	PROPN
ejpam-4520	50	8	al	al	PROPN
ejpam-4520	50	9	.	.	PROPN
ejpam-4520	51	1	in	in	ADP
ejpam-4520	51	2	2021	2021	NUM
ejpam-4520	51	3	[	[	X
ejpam-4520	51	4	11	11	NUM
ejpam-4520	51	5	]	]	PUNCT
ejpam-4520	51	6	initiates	initiate	VERB
ejpam-4520	51	7	to	to	PART
ejpam-4520	51	8	study	study	VERB
ejpam-4520	51	9	a	a	DET
ejpam-4520	51	10	rainbow	rainbow	NOUN
ejpam-4520	51	11	antimagic	antimagic	ADJ
ejpam-4520	51	12	coloring	coloring	NOUN
ejpam-4520	51	13	of	of	ADP
ejpam-4520	51	14	graph	graph	NOUN
ejpam-4520	51	15	.	.	PUNCT
ejpam-4520	52	1	2	2	X
ejpam-4520	52	2	.	.	X
ejpam-4520	52	3	rainbow	rainbow	VERB
ejpam-4520	52	4	antimagic	antimagic	ADJ
ejpam-4520	52	5	coloring	coloring	NOUN
ejpam-4520	52	6	based	base	VERB
ejpam-4520	52	7	on	on	ADP
ejpam-4520	52	8	the	the	DET
ejpam-4520	52	9	description	description	NOUN
ejpam-4520	52	10	above	above	ADV
ejpam-4520	52	11	,	,	PUNCT
ejpam-4520	52	12	dafik	dafik	VERB
ejpam-4520	52	13	et	et	PROPN
ejpam-4520	52	14	al	al	PROPN
ejpam-4520	52	15	.	.	PROPN
ejpam-4520	53	1	in	in	ADP
ejpam-4520	53	2	2021	2021	NUM
ejpam-4520	53	3	[	[	X
ejpam-4520	53	4	11	11	NUM
ejpam-4520	53	5	]	]	PUNCT
ejpam-4520	53	6	have	have	AUX
ejpam-4520	53	7	obtained	obtain	VERB
ejpam-4520	53	8	the	the	DET
ejpam-4520	53	9	lower	low	ADJ
ejpam-4520	53	10	bound	bind	VERB
ejpam-4520	53	11	of	of	ADP
ejpam-4520	53	12	the	the	DET
ejpam-4520	53	13	rac(g	rac(g	NOUN
ejpam-4520	53	14	)	)	PUNCT
ejpam-4520	53	15	and	and	CCONJ
ejpam-4520	53	16	given	give	VERB
ejpam-4520	53	17	some	some	DET
ejpam-4520	53	18	relevan	relevan	ADJ
ejpam-4520	53	19	results	result	NOUN
ejpam-4520	53	20	too	too	ADV
ejpam-4520	53	21	.	.	PUNCT
ejpam-4520	54	1	proposition	proposition	NOUN
ejpam-4520	54	2	2	2	NUM
ejpam-4520	54	3	.	.	PUNCT
ejpam-4520	55	1	[	[	X
ejpam-4520	55	2	11	11	NUM
ejpam-4520	55	3	]	]	PUNCT
ejpam-4520	55	4	for	for	ADP
ejpam-4520	55	5	any	any	DET
ejpam-4520	55	6	connected	connected	ADJ
ejpam-4520	55	7	graph	graph	NOUN
ejpam-4520	55	8	g	g	NOUN
ejpam-4520	55	9	,	,	PUNCT
ejpam-4520	55	10	rac(g	rac(g	PROPN
ejpam-4520	55	11	)	)	PUNCT
ejpam-4520	55	12	≥	≥	NOUN
ejpam-4520	55	13	rc(g	rc(g	NOUN
ejpam-4520	55	14	)	)	PUNCT
ejpam-4520	55	15	.	.	PUNCT
ejpam-4520	56	1	theorem	theorem	NOUN
ejpam-4520	56	2	1	1	NUM
ejpam-4520	56	3	.	.	PUNCT
ejpam-4520	57	1	[	[	X
ejpam-4520	57	2	11	11	NUM
ejpam-4520	57	3	]	]	PUNCT
ejpam-4520	57	4	let	let	VERB
ejpam-4520	57	5	g	g	NOUN
ejpam-4520	57	6	be	be	AUX
ejpam-4520	57	7	any	any	DET
ejpam-4520	57	8	connected	connected	ADJ
ejpam-4520	57	9	graph	graph	NOUN
ejpam-4520	57	10	.	.	PUNCT
ejpam-4520	58	1	let	let	VERB
ejpam-4520	58	2	rc(g	rc(g	NOUN
ejpam-4520	58	3	)	)	PUNCT
ejpam-4520	58	4	and	and	CCONJ
ejpam-4520	58	5	∆(g	∆(g	PROPN
ejpam-4520	58	6	)	)	PUNCT
ejpam-4520	58	7	be	be	VERB
ejpam-4520	58	8	the	the	DET
ejpam-4520	58	9	rainbow	rainbow	NOUN
ejpam-4520	58	10	connection	connection	NOUN
ejpam-4520	58	11	number	number	NOUN
ejpam-4520	58	12	of	of	ADP
ejpam-4520	58	13	g	g	PROPN
ejpam-4520	58	14	and	and	CCONJ
ejpam-4520	58	15	the	the	DET
ejpam-4520	58	16	maximum	maximum	ADJ
ejpam-4520	58	17	degree	degree	NOUN
ejpam-4520	58	18	of	of	ADP
ejpam-4520	58	19	g	g	NOUN
ejpam-4520	58	20	,	,	PUNCT
ejpam-4520	58	21	rac(g	rac(g	PROPN
ejpam-4520	58	22	)	)	PUNCT
ejpam-4520	58	23	≥	≥	NOUN
ejpam-4520	58	24	max{rc(g),∆(g	max{rc(g),∆(g	NOUN
ejpam-4520	58	25	)	)	PUNCT
ejpam-4520	58	26	}	}	PUNCT
ejpam-4520	58	27	.	.	PUNCT
ejpam-4520	59	1	susilowati	susilowati	PROPN
ejpam-4520	59	2	et	et	PROPN
ejpam-4520	59	3	.	.	PUNCT
ejpam-4520	60	1	al	al	PROPN
ejpam-4520	60	2	/	/	PUNCT
ejpam-4520	60	3	eur	eur	PROPN
ejpam-4520	60	4	.	.	PUNCT
ejpam-4520	61	1	j.	j.	PROPN
ejpam-4520	61	2	pure	pure	PROPN
ejpam-4520	61	3	appl	appl	PROPN
ejpam-4520	61	4	.	.	PROPN
ejpam-4520	61	5	math	math	PROPN
ejpam-4520	61	6	,	,	PUNCT
ejpam-4520	61	7	16	16	NUM
ejpam-4520	61	8	(	(	PUNCT
ejpam-4520	61	9	1	1	NUM
ejpam-4520	61	10	)	)	PUNCT
ejpam-4520	61	11	(	(	PUNCT
ejpam-4520	61	12	2023	2023	NUM
ejpam-4520	61	13	)	)	PUNCT
ejpam-4520	61	14	,	,	PUNCT
ejpam-4520	61	15	271	271	NUM
ejpam-4520	61	16	-	-	SYM
ejpam-4520	61	17	285	285	NUM
ejpam-4520	61	18	273	273	NUM
ejpam-4520	61	19	theorem	theorem	NOUN
ejpam-4520	61	20	2	2	NUM
ejpam-4520	61	21	.	.	PUNCT
ejpam-4520	62	1	[	[	X
ejpam-4520	62	2	11	11	NUM
ejpam-4520	62	3	]	]	PUNCT
ejpam-4520	62	4	let	let	VERB
ejpam-4520	62	5	g	g	PRON
ejpam-4520	62	6	be	be	AUX
ejpam-4520	62	7	a	a	DET
ejpam-4520	62	8	connected	connected	ADJ
ejpam-4520	62	9	graph	graph	NOUN
ejpam-4520	62	10	of	of	ADP
ejpam-4520	62	11	diameter	diameter	NOUN
ejpam-4520	62	12	diam(g	diam(g	PROPN
ejpam-4520	62	13	)	)	PUNCT
ejpam-4520	62	14	≤	≤	NOUN
ejpam-4520	62	15	2	2	NUM
ejpam-4520	62	16	.	.	PUNCT
ejpam-4520	63	1	let	let	VERB
ejpam-4520	63	2	f	f	PRON
ejpam-4520	63	3	be	be	AUX
ejpam-4520	63	4	any	any	DET
ejpam-4520	63	5	bijective	bijective	ADJ
ejpam-4520	63	6	function	function	NOUN
ejpam-4520	63	7	from	from	ADP
ejpam-4520	63	8	v	v	NUM
ejpam-4520	63	9	(	(	PUNCT
ejpam-4520	63	10	g	g	NOUN
ejpam-4520	63	11	)	)	PUNCT
ejpam-4520	63	12	to	to	ADP
ejpam-4520	63	13	the	the	DET
ejpam-4520	63	14	set	set	NOUN
ejpam-4520	63	15	{	{	PUNCT
ejpam-4520	63	16	1	1	NUM
ejpam-4520	63	17	,	,	PUNCT
ejpam-4520	63	18	2	2	NUM
ejpam-4520	63	19	,	,	PUNCT
ejpam-4520	63	20	.	.	PUNCT
ejpam-4520	63	21	.	.	PUNCT
ejpam-4520	64	1	.	.	PUNCT
ejpam-4520	65	1	,	,	PUNCT
ejpam-4520	65	2	|v	|v	PROPN
ejpam-4520	65	3	(	(	PUNCT
ejpam-4520	65	4	g)|	g)|	PROPN
ejpam-4520	65	5	}	}	PUNCT
ejpam-4520	65	6	,	,	PUNCT
ejpam-4520	65	7	there	there	PRON
ejpam-4520	65	8	exists	exist	VERB
ejpam-4520	65	9	a	a	DET
ejpam-4520	65	10	rainbow	rainbow	NOUN
ejpam-4520	65	11	path	path	NOUN
ejpam-4520	65	12	u−v	u−v	PROPN
ejpam-4520	65	13	.	.	PUNCT
ejpam-4520	66	1	theorem	theorem	VERB
ejpam-4520	66	2	3	3	NUM
ejpam-4520	66	3	.	.	PUNCT
ejpam-4520	67	1	[	[	X
ejpam-4520	67	2	11	11	NUM
ejpam-4520	67	3	]	]	PUNCT
ejpam-4520	67	4	for	for	ADP
ejpam-4520	67	5	tm	tm	NOUN
ejpam-4520	67	6	,	,	PUNCT
ejpam-4520	67	7	being	be	AUX
ejpam-4520	67	8	any	any	DET
ejpam-4520	67	9	tree	tree	NOUN
ejpam-4520	67	10	of	of	ADP
ejpam-4520	67	11	order	order	NOUN
ejpam-4520	67	12	m	m	VERB
ejpam-4520	67	13	≥	≥	NOUN
ejpam-4520	67	14	3	3	NUM
ejpam-4520	67	15	,	,	PUNCT
ejpam-4520	67	16	rac(tm	rac(tm	NOUN
ejpam-4520	67	17	)	)	PUNCT
ejpam-4520	67	18	=	=	SYM
ejpam-4520	67	19	m−	m−	PROPN
ejpam-4520	67	20	1	1	NUM
ejpam-4520	67	21	.	.	PUNCT
ejpam-4520	68	1	some	some	DET
ejpam-4520	68	2	initial	initial	ADJ
ejpam-4520	68	3	results	result	NOUN
ejpam-4520	68	4	for	for	ADP
ejpam-4520	68	5	rainbow	rainbow	NOUN
ejpam-4520	68	6	antimagic	antimagic	ADJ
ejpam-4520	68	7	coloring	coloring	NOUN
ejpam-4520	68	8	have	have	AUX
ejpam-4520	68	9	been	be	AUX
ejpam-4520	68	10	found	find	VERB
ejpam-4520	68	11	in	in	ADP
ejpam-4520	68	12	[	[	X
ejpam-4520	68	13	5	5	NUM
ejpam-4520	68	14	]	]	PUNCT
ejpam-4520	68	15	,	,	PUNCT
ejpam-4520	68	16	[	[	X
ejpam-4520	68	17	11	11	NUM
ejpam-4520	68	18	]	]	PUNCT
ejpam-4520	68	19	,	,	PUNCT
ejpam-4520	68	20	[	[	X
ejpam-4520	68	21	15	15	NUM
ejpam-4520	68	22	]	]	PUNCT
ejpam-4520	68	23	and	and	CCONJ
ejpam-4520	68	24	[	[	X
ejpam-4520	68	25	22	22	NUM
ejpam-4520	68	26	]	]	PUNCT
ejpam-4520	68	27	.	.	PUNCT
ejpam-4520	69	1	theorem	theorem	ADJ
ejpam-4520	69	2	4	4	NUM
ejpam-4520	69	3	.	.	PUNCT
ejpam-4520	70	1	[	[	X
ejpam-4520	70	2	22]for	22]for	NUM
ejpam-4520	70	3	any	any	DET
ejpam-4520	70	4	integer	integer	NOUN
ejpam-4520	70	5	m	m	VERB
ejpam-4520	70	6	≥	≥	NOUN
ejpam-4520	70	7	3	3	NUM
ejpam-4520	70	8	,	,	PUNCT
ejpam-4520	70	9	rac(k2,m	rac(k2,m	PROPN
ejpam-4520	70	10	)	)	PUNCT
ejpam-4520	71	1	=	=	PUNCT
ejpam-4520	71	2	m+	m+	NUM
ejpam-4520	72	1	1	1	NUM
ejpam-4520	72	2	.	.	X
ejpam-4520	72	3	3	3	X
ejpam-4520	72	4	.	.	NOUN
ejpam-4520	72	5	results	result	NOUN
ejpam-4520	72	6	in	in	ADP
ejpam-4520	72	7	this	this	DET
ejpam-4520	72	8	section	section	NOUN
ejpam-4520	72	9	,	,	PUNCT
ejpam-4520	72	10	we	we	PRON
ejpam-4520	72	11	will	will	AUX
ejpam-4520	72	12	show	show	VERB
ejpam-4520	72	13	the	the	DET
ejpam-4520	72	14	rainbow	rainbow	NOUN
ejpam-4520	72	15	antimagic	antimagic	ADJ
ejpam-4520	72	16	connection	connection	NOUN
ejpam-4520	72	17	number	number	NOUN
ejpam-4520	72	18	of	of	ADP
ejpam-4520	72	19	tn	tn	PROPN
ejpam-4520	72	20	⊙	⊙	PROPN
ejpam-4520	72	21	sm	sm	PROPN
ejpam-4520	72	22	where	where	SCONJ
ejpam-4520	72	23	tn	tn	PROPN
ejpam-4520	72	24	∈	∈	PROPN
ejpam-4520	72	25	{	{	PUNCT
ejpam-4520	72	26	pn	pn	PROPN
ejpam-4520	72	27	,	,	PUNCT
ejpam-4520	72	28	sn	sn	PROPN
ejpam-4520	72	29	,	,	PUNCT
ejpam-4520	72	30	sn	sn	PROPN
ejpam-4520	72	31	,	,	PUNCT
ejpam-4520	72	32	p	p	X
ejpam-4520	72	33	,	,	PUNCT
ejpam-4520	72	34	fn,3	fn,3	NOUN
ejpam-4520	72	35	}	}	PUNCT
ejpam-4520	72	36	.	.	PUNCT
ejpam-4520	73	1	our	our	PRON
ejpam-4520	73	2	strategy	strategy	NOUN
ejpam-4520	73	3	is	be	AUX
ejpam-4520	73	4	firstly	firstly	ADV
ejpam-4520	73	5	determined	determine	VERB
ejpam-4520	73	6	the	the	DET
ejpam-4520	73	7	rainbow	rainbow	NOUN
ejpam-4520	73	8	antimagic	antimagic	ADJ
ejpam-4520	73	9	connection	connection	NOUN
ejpam-4520	73	10	number	number	NOUN
ejpam-4520	73	11	of	of	ADP
ejpam-4520	73	12	k1	k1	PROPN
ejpam-4520	73	13	+	+	CCONJ
ejpam-4520	73	14	sm	sm	NOUN
ejpam-4520	73	15	.	.	PUNCT
ejpam-4520	74	1	secondly	secondly	ADV
ejpam-4520	74	2	,	,	PUNCT
ejpam-4520	74	3	establish	establish	VERB
ejpam-4520	74	4	the	the	DET
ejpam-4520	74	5	lower	low	ADJ
ejpam-4520	74	6	bound	bind	VERB
ejpam-4520	74	7	of	of	ADP
ejpam-4520	74	8	rac(tn	rac(tn	X
ejpam-4520	74	9	⊙	⊙	X
ejpam-4520	74	10	sm	sm	PROPN
ejpam-4520	74	11	)	)	PUNCT
ejpam-4520	74	12	.	.	PUNCT
ejpam-4520	75	1	finally	finally	ADV
ejpam-4520	75	2	,	,	PUNCT
ejpam-4520	75	3	we	we	PRON
ejpam-4520	75	4	show	show	VERB
ejpam-4520	75	5	the	the	DET
ejpam-4520	75	6	exact	exact	ADJ
ejpam-4520	75	7	values	value	NOUN
ejpam-4520	75	8	of	of	ADP
ejpam-4520	75	9	rac(pn	rac(pn	NOUN
ejpam-4520	75	10	⊙	⊙	X
ejpam-4520	75	11	sm	sm	PROPN
ejpam-4520	75	12	)	)	PUNCT
ejpam-4520	75	13	,	,	PUNCT
ejpam-4520	75	14	rac(sn	rac(sn	VERB
ejpam-4520	75	15	⊙	⊙	PROPN
ejpam-4520	75	16	sm	sm	PROPN
ejpam-4520	75	17	)	)	PUNCT
ejpam-4520	75	18	,	,	PUNCT
ejpam-4520	75	19	rac(sn	rac(sn	ADJ
ejpam-4520	75	20	,	,	PUNCT
ejpam-4520	75	21	p	p	PROPN
ejpam-4520	75	22	⊙	⊙	PROPN
ejpam-4520	75	23	sm	sm	PROPN
ejpam-4520	75	24	)	)	PUNCT
ejpam-4520	75	25	and	and	CCONJ
ejpam-4520	75	26	rac(fn,3	rac(fn,3	NUM
ejpam-4520	75	27	⊙	⊙	NOUN
ejpam-4520	75	28	sm	sm	PROPN
ejpam-4520	75	29	)	)	PUNCT
ejpam-4520	75	30	.	.	PUNCT
ejpam-4520	76	1	theorem	theorem	ADJ
ejpam-4520	76	2	5	5	NUM
ejpam-4520	76	3	.	.	PUNCT
ejpam-4520	77	1	for	for	ADP
ejpam-4520	77	2	m	m	PROPN
ejpam-4520	77	3	≥	≥	NOUN
ejpam-4520	77	4	3	3	NUM
ejpam-4520	77	5	,	,	PUNCT
ejpam-4520	77	6	rac(k1	rac(k1	NOUN
ejpam-4520	77	7	+	+	CCONJ
ejpam-4520	77	8	sm	sm	NOUN
ejpam-4520	77	9	)	)	PUNCT
ejpam-4520	77	10	=	=	PUNCT
ejpam-4520	77	11	m+	m+	NUM
ejpam-4520	77	12	2	2	NUM
ejpam-4520	77	13	.	.	PUNCT
ejpam-4520	77	14	proof	proof	NOUN
ejpam-4520	77	15	.	.	PUNCT
ejpam-4520	78	1	the	the	DET
ejpam-4520	78	2	graph	graph	NOUN
ejpam-4520	78	3	k1+sm	k1+sm	ADV
ejpam-4520	78	4	is	be	AUX
ejpam-4520	78	5	a	a	DET
ejpam-4520	78	6	connected	connected	ADJ
ejpam-4520	78	7	graph	graph	NOUN
ejpam-4520	78	8	with	with	ADP
ejpam-4520	78	9	vertex	vertex	NOUN
ejpam-4520	78	10	set	set	VERB
ejpam-4520	78	11	v	v	NOUN
ejpam-4520	78	12	(	(	PUNCT
ejpam-4520	78	13	k1+sm	k1+sm	NOUN
ejpam-4520	78	14	)	)	PUNCT
ejpam-4520	78	15	=	=	PRON
ejpam-4520	78	16	{	{	PUNCT
ejpam-4520	78	17	a1}∪	a1}∪	X
ejpam-4520	78	18	{	{	PUNCT
ejpam-4520	78	19	b1	b1	PROPN
ejpam-4520	78	20	}	}	PUNCT
ejpam-4520	78	21	∪	∪	NOUN
ejpam-4520	78	22	{	{	PUNCT
ejpam-4520	78	23	xj	xj	PROPN
ejpam-4520	78	24	,	,	PUNCT
ejpam-4520	78	25	1	1	NUM
ejpam-4520	78	26	≤	≤	NUM
ejpam-4520	78	27	j	j	PROPN
ejpam-4520	78	28	≤	≤	PROPN
ejpam-4520	78	29	m	m	PROPN
ejpam-4520	78	30	}	}	PUNCT
ejpam-4520	78	31	,	,	PUNCT
ejpam-4520	78	32	and	and	CCONJ
ejpam-4520	78	33	the	the	DET
ejpam-4520	78	34	edge	edge	NOUN
ejpam-4520	78	35	set	set	VERB
ejpam-4520	78	36	e(k1	e(k1	NOUN
ejpam-4520	78	37	+	+	X
ejpam-4520	78	38	sm	sm	NOUN
ejpam-4520	78	39	)	)	PUNCT
ejpam-4520	78	40	=	=	PRON
ejpam-4520	79	1	{	{	PUNCT
ejpam-4520	79	2	a1b1	a1b1	ADJ
ejpam-4520	79	3	}	}	PUNCT
ejpam-4520	79	4	∪	∪	X
ejpam-4520	79	5	{	{	PUNCT
ejpam-4520	79	6	a1xj	a1xj	NOUN
ejpam-4520	79	7	,	,	PUNCT
ejpam-4520	79	8	b1xj	b1xj	X
ejpam-4520	79	9	,	,	PUNCT
ejpam-4520	79	10	1	1	NUM
ejpam-4520	79	11	≤	≤	NUM
ejpam-4520	79	12	j	j	PROPN
ejpam-4520	79	13	≤	≤	PROPN
ejpam-4520	79	14	m	m	PROPN
ejpam-4520	79	15	}	}	PUNCT
ejpam-4520	79	16	.	.	PUNCT
ejpam-4520	80	1	the	the	DET
ejpam-4520	80	2	cardinality	cardinality	NOUN
ejpam-4520	80	3	of	of	ADP
ejpam-4520	80	4	|v	|v	PROPN
ejpam-4520	80	5	(	(	PUNCT
ejpam-4520	80	6	k1	k1	NOUN
ejpam-4520	80	7	+	+	PROPN
ejpam-4520	80	8	sm)|	sm)|	PROPN
ejpam-4520	80	9	=	=	SYM
ejpam-4520	80	10	m+2	m+2	NOUN
ejpam-4520	80	11	and	and	CCONJ
ejpam-4520	80	12	the	the	DET
ejpam-4520	80	13	cardinality	cardinality	NOUN
ejpam-4520	80	14	of	of	ADP
ejpam-4520	80	15	|e(k1	|e(k1	PROPN
ejpam-4520	81	1	+	+	PROPN
ejpam-4520	81	2	sm)|	sm)|	X
ejpam-4520	81	3	=	=	SYM
ejpam-4520	81	4	2nm+1	2nm+1	NUM
ejpam-4520	81	5	.	.	NOUN
ejpam-4520	81	6	based	base	VERB
ejpam-4520	81	7	on	on	ADP
ejpam-4520	81	8	this	this	DET
ejpam-4520	81	9	definition	definition	NOUN
ejpam-4520	81	10	,	,	PUNCT
ejpam-4520	81	11	the	the	DET
ejpam-4520	81	12	graph	graph	NOUN
ejpam-4520	81	13	k1	k1	NOUN
ejpam-4520	81	14	+	+	CCONJ
ejpam-4520	81	15	sm	sm	PROPN
ejpam-4520	81	16	has	have	VERB
ejpam-4520	81	17	∆(k1	∆(k1	NUM
ejpam-4520	81	18	+	+	NUM
ejpam-4520	81	19	sm	sm	NOUN
ejpam-4520	81	20	)	)	PUNCT
ejpam-4520	82	1	=	=	PUNCT
ejpam-4520	82	2	m+	m+	NUM
ejpam-4520	83	1	1	1	NUM
ejpam-4520	83	2	.	.	PUNCT
ejpam-4520	83	3	to	to	PART
ejpam-4520	83	4	prove	prove	VERB
ejpam-4520	83	5	rac(k1+sm	rac(k1+sm	NOUN
ejpam-4520	83	6	)	)	PUNCT
ejpam-4520	83	7	,	,	PUNCT
ejpam-4520	83	8	first	first	ADV
ejpam-4520	83	9	we	we	PRON
ejpam-4520	83	10	have	have	VERB
ejpam-4520	83	11	to	to	PART
ejpam-4520	83	12	show	show	VERB
ejpam-4520	83	13	the	the	DET
ejpam-4520	83	14	lower	low	ADJ
ejpam-4520	83	15	bound	bind	VERB
ejpam-4520	83	16	of	of	ADP
ejpam-4520	83	17	rac(k1+sm	rac(k1+sm	PROPN
ejpam-4520	83	18	)	)	PUNCT
ejpam-4520	83	19	.	.	PUNCT
ejpam-4520	84	1	based	base	VERB
ejpam-4520	84	2	on	on	ADP
ejpam-4520	84	3	theorem	theorem	NOUN
ejpam-4520	84	4	1	1	NUM
ejpam-4520	84	5	,	,	PUNCT
ejpam-4520	84	6	we	we	PRON
ejpam-4520	84	7	have	have	VERB
ejpam-4520	84	8	rac(g	rac(g	VERB
ejpam-4520	84	9	)	)	PUNCT
ejpam-4520	84	10	≥	≥	NOUN
ejpam-4520	84	11	max{rc(g),∆(g	max{rc(g),∆(g	NOUN
ejpam-4520	84	12	)	)	PUNCT
ejpam-4520	84	13	}	}	PUNCT
ejpam-4520	84	14	=	=	PUNCT
ejpam-4520	85	1	m+	m+	NUM
ejpam-4520	85	2	1	1	NUM
ejpam-4520	85	3	.	.	PUNCT
ejpam-4520	86	1	since	since	ADV
ejpam-4520	86	2	,	,	PUNCT
ejpam-4520	86	3	the	the	DET
ejpam-4520	86	4	construction	construction	NOUN
ejpam-4520	86	5	of	of	ADP
ejpam-4520	86	6	vertex	vertex	NOUN
ejpam-4520	86	7	labeling	labeling	NOUN
ejpam-4520	86	8	with	with	ADP
ejpam-4520	86	9	the	the	DET
ejpam-4520	86	10	function	function	NOUN
ejpam-4520	86	11	f	f	NOUN
ejpam-4520	86	12	:	:	PUNCT
ejpam-4520	86	13	v	v	NOUN
ejpam-4520	86	14	(	(	PUNCT
ejpam-4520	86	15	k1	k1	NOUN
ejpam-4520	86	16	+	+	CCONJ
ejpam-4520	86	17	sm	sm	NOUN
ejpam-4520	86	18	)	)	PUNCT
ejpam-4520	86	19	→	→	SYM
ejpam-4520	86	20	{	{	PUNCT
ejpam-4520	86	21	1	1	NUM
ejpam-4520	86	22	,	,	PUNCT
ejpam-4520	86	23	2	2	NUM
ejpam-4520	86	24	,	,	PUNCT
ejpam-4520	86	25	.	.	PUNCT
ejpam-4520	86	26	.	.	PUNCT
ejpam-4520	86	27	.	.	PUNCT
ejpam-4520	87	1	|v	|v	PROPN
ejpam-4520	87	2	(	(	PUNCT
ejpam-4520	87	3	k1	k1	NOUN
ejpam-4520	87	4	+	+	CCONJ
ejpam-4520	87	5	sm)|	sm)|	PROPN
ejpam-4520	87	6	}	}	PUNCT
ejpam-4520	87	7	is	be	AUX
ejpam-4520	87	8	a	a	DET
ejpam-4520	87	9	bijective	bijective	ADJ
ejpam-4520	87	10	function	function	NOUN
ejpam-4520	87	11	,	,	PUNCT
ejpam-4520	87	12	assigning	assign	VERB
ejpam-4520	87	13	the	the	DET
ejpam-4520	87	14	most	most	ADV
ejpam-4520	87	15	possible	possible	ADJ
ejpam-4520	87	16	label	label	NOUN
ejpam-4520	87	17	for	for	ADP
ejpam-4520	87	18	a1	a1	NOUN
ejpam-4520	87	19	,	,	PUNCT
ejpam-4520	87	20	b1	b1	NOUN
ejpam-4520	87	21	gives	give	VERB
ejpam-4520	87	22	w(a1b1	w(a1b1	NOUN
ejpam-4520	87	23	)	)	PUNCT
ejpam-4520	87	24	must	must	AUX
ejpam-4520	87	25	be	be	AUX
ejpam-4520	87	26	different	different	ADJ
ejpam-4520	87	27	with	with	ADP
ejpam-4520	87	28	other	other	ADJ
ejpam-4520	87	29	edge	edge	NOUN
ejpam-4520	87	30	weights	weight	NOUN
ejpam-4520	87	31	.	.	PUNCT
ejpam-4520	88	1	the	the	DET
ejpam-4520	88	2	rest	rest	NOUN
ejpam-4520	88	3	of	of	ADP
ejpam-4520	88	4	the	the	DET
ejpam-4520	88	5	labels	label	NOUN
ejpam-4520	88	6	are	be	AUX
ejpam-4520	88	7	considered	consider	VERB
ejpam-4520	88	8	to	to	PART
ejpam-4520	88	9	be	be	AUX
ejpam-4520	88	10	a	a	DET
ejpam-4520	88	11	rainbow	rainbow	NOUN
ejpam-4520	88	12	antimagic	antimagic	ADJ
ejpam-4520	88	13	coloring	coloring	NOUN
ejpam-4520	88	14	of	of	ADP
ejpam-4520	88	15	complete	complete	ADJ
ejpam-4520	88	16	bipartite	bipartite	PROPN
ejpam-4520	88	17	graph	graph	NOUN
ejpam-4520	88	18	k2,m	k2,m	PROPN
ejpam-4520	88	19	.	.	PROPN
ejpam-4520	88	20	refer	refer	VERB
ejpam-4520	88	21	to	to	ADP
ejpam-4520	88	22	theorem	theorem	ADJ
ejpam-4520	88	23	4	4	NUM
ejpam-4520	88	24	,	,	PUNCT
ejpam-4520	88	25	rac(k2,m	rac(k2,m	PROPN
ejpam-4520	88	26	)	)	PUNCT
ejpam-4520	88	27	=	=	SYM
ejpam-4520	88	28	∆(k2,m	∆(k2,m	NOUN
ejpam-4520	88	29	)	)	PUNCT
ejpam-4520	89	1	+	+	CCONJ
ejpam-4520	89	2	1	1	NUM
ejpam-4520	89	3	=	=	SYM
ejpam-4520	89	4	m	m	VERB
ejpam-4520	89	5	+	+	ADJ
ejpam-4520	89	6	1	1	X
ejpam-4520	89	7	.	.	PUNCT
ejpam-4520	89	8	since	since	SCONJ
ejpam-4520	89	9	∆(k1	∆(k1	SYM
ejpam-4520	89	10	+	+	NUM
ejpam-4520	89	11	sm	sm	NOUN
ejpam-4520	89	12	)	)	PUNCT
ejpam-4520	89	13	=	=	SYM
ejpam-4520	89	14	rac(k2,m	rac(k2,m	PROPN
ejpam-4520	89	15	)	)	PUNCT
ejpam-4520	89	16	,	,	PUNCT
ejpam-4520	89	17	and	and	CCONJ
ejpam-4520	89	18	apart	apart	ADV
ejpam-4520	89	19	from	from	ADP
ejpam-4520	89	20	edge	edge	NOUN
ejpam-4520	89	21	a1b1	a1b1	ADV
ejpam-4520	89	22	,	,	PUNCT
ejpam-4520	89	23	the	the	DET
ejpam-4520	89	24	graph	graph	NOUN
ejpam-4520	89	25	k1	k1	NOUN
ejpam-4520	89	26	+	+	CCONJ
ejpam-4520	89	27	s1	s1	NOUN
ejpam-4520	89	28	is	be	AUX
ejpam-4520	89	29	k2,m	k2,m	PROPN
ejpam-4520	89	30	,	,	PUNCT
ejpam-4520	89	31	it	it	PRON
ejpam-4520	89	32	implies	imply	VERB
ejpam-4520	89	33	that	that	SCONJ
ejpam-4520	89	34	rac(k1	rac(k1	PROPN
ejpam-4520	89	35	+	+	CCONJ
ejpam-4520	89	36	sm	sm	PROPN
ejpam-4520	89	37	)	)	PUNCT
ejpam-4520	89	38	≥	≥	NOUN
ejpam-4520	89	39	max{rc(g),∆(g	max{rc(g),∆(g	NOUN
ejpam-4520	89	40	)	)	PUNCT
ejpam-4520	89	41	}	}	PUNCT
ejpam-4520	89	42	=	=	SYM
ejpam-4520	89	43	∆(k1	∆(k1	SYM
ejpam-4520	89	44	+	+	NUM
ejpam-4520	89	45	sm	sm	NOUN
ejpam-4520	89	46	)	)	PUNCT
ejpam-4520	89	47	.	.	PUNCT
ejpam-4520	90	1	however	however	ADV
ejpam-4520	90	2	,	,	PUNCT
ejpam-4520	90	3	if	if	SCONJ
ejpam-4520	90	4	rac(k1	rac(k1	PROPN
ejpam-4520	90	5	+	+	PROPN
ejpam-4520	90	6	sm	sm	PROPN
ejpam-4520	90	7	)	)	PUNCT
ejpam-4520	90	8	≥	≥	NOUN
ejpam-4520	90	9	∆(k1	∆(k1	NUM
ejpam-4520	90	10	+	+	NUM
ejpam-4520	90	11	sm	sm	NOUN
ejpam-4520	90	12	)	)	PUNCT
ejpam-4520	90	13	then	then	ADV
ejpam-4520	90	14	there	there	PRON
ejpam-4520	90	15	is	be	VERB
ejpam-4520	90	16	a	a	DET
ejpam-4520	90	17	conflict	conflict	NOUN
ejpam-4520	90	18	,	,	PUNCT
ejpam-4520	90	19	since	since	SCONJ
ejpam-4520	90	20	we	we	PRON
ejpam-4520	90	21	need	need	VERB
ejpam-4520	90	22	to	to	PART
ejpam-4520	90	23	include	include	VERB
ejpam-4520	90	24	the	the	DET
ejpam-4520	90	25	edge	edge	NOUN
ejpam-4520	90	26	a1b1	a1b1	PUNCT
ejpam-4520	90	27	,	,	PUNCT
ejpam-4520	90	28	thus	thus	ADV
ejpam-4520	90	29	it	it	PRON
ejpam-4520	90	30	must	must	AUX
ejpam-4520	90	31	be	be	AUX
ejpam-4520	90	32	m	m	PROPN
ejpam-4520	90	33	+	+	ADJ
ejpam-4520	90	34	1	1	NUM
ejpam-4520	90	35	+	+	SYM
ejpam-4520	90	36	1	1	NUM
ejpam-4520	90	37	=	=	SYM
ejpam-4520	90	38	∆(k1	∆(k1	SYM
ejpam-4520	90	39	+	+	NUM
ejpam-4520	90	40	sm	sm	NOUN
ejpam-4520	90	41	)	)	PUNCT
ejpam-4520	91	1	+	+	NOUN
ejpam-4520	91	2	1	1	X
ejpam-4520	91	3	.	.	PUNCT
ejpam-4520	91	4	it	it	PRON
ejpam-4520	91	5	concludes	conclude	VERB
ejpam-4520	91	6	that	that	SCONJ
ejpam-4520	91	7	rac(k1	rac(k1	PROPN
ejpam-4520	91	8	+	+	CCONJ
ejpam-4520	91	9	sm	sm	PROPN
ejpam-4520	91	10	)	)	PUNCT
ejpam-4520	91	11	≥	≥	NOUN
ejpam-4520	91	12	∆(k1	∆(k1	NUM
ejpam-4520	92	1	+	+	NUM
ejpam-4520	92	2	sm	sm	NOUN
ejpam-4520	92	3	)	)	PUNCT
ejpam-4520	93	1	+	+	CCONJ
ejpam-4520	93	2	1	1	NUM
ejpam-4520	93	3	=	=	SYM
ejpam-4520	93	4	m+	m+	NUM
ejpam-4520	93	5	2	2	NUM
ejpam-4520	93	6	.	.	PUNCT
ejpam-4520	94	1	secondly	secondly	ADV
ejpam-4520	94	2	,	,	PUNCT
ejpam-4520	94	3	we	we	PRON
ejpam-4520	94	4	have	have	VERB
ejpam-4520	94	5	to	to	PART
ejpam-4520	94	6	show	show	VERB
ejpam-4520	94	7	the	the	DET
ejpam-4520	94	8	upper	upper	ADJ
ejpam-4520	94	9	bound	bound	NOUN
ejpam-4520	94	10	of	of	ADP
ejpam-4520	94	11	rac(k1+sm	rac(k1+sm	PROPN
ejpam-4520	94	12	)	)	PUNCT
ejpam-4520	94	13	.	.	PUNCT
ejpam-4520	95	1	define	define	VERB
ejpam-4520	95	2	the	the	DET
ejpam-4520	95	3	vertex	vertex	NOUN
ejpam-4520	95	4	labeling	labeling	NOUN
ejpam-4520	96	1	f	f	NOUN
ejpam-4520	96	2	:	:	PUNCT
ejpam-4520	96	3	v	v	X
ejpam-4520	96	4	(	(	PUNCT
ejpam-4520	96	5	k1	k1	NOUN
ejpam-4520	96	6	+	+	CCONJ
ejpam-4520	96	7	sm	sm	NOUN
ejpam-4520	96	8	)	)	PUNCT
ejpam-4520	96	9	→	→	SYM
ejpam-4520	96	10	{	{	PUNCT
ejpam-4520	96	11	1	1	NUM
ejpam-4520	96	12	,	,	PUNCT
ejpam-4520	96	13	2	2	NUM
ejpam-4520	96	14	,	,	PUNCT
ejpam-4520	96	15	...	...	PUNCT
ejpam-4520	96	16	,	,	PUNCT
ejpam-4520	96	17	m+	m+	NOUN
ejpam-4520	96	18	2	2	NUM
ejpam-4520	96	19	}	}	PUNCT
ejpam-4520	96	20	as	as	SCONJ
ejpam-4520	96	21	follows	follow	VERB
ejpam-4520	96	22	.	.	PUNCT
ejpam-4520	97	1	f(a1	f(a1	NOUN
ejpam-4520	97	2	)	)	PUNCT
ejpam-4520	97	3	=	=	SYM
ejpam-4520	97	4	1	1	NUM
ejpam-4520	97	5	,	,	PUNCT
ejpam-4520	97	6	f(b1	f(b1	NOUN
ejpam-4520	97	7	)	)	PUNCT
ejpam-4520	98	1	=	=	SYM
ejpam-4520	98	2	2	2	NUM
ejpam-4520	98	3	,	,	PUNCT
ejpam-4520	98	4	f(xi	f(xi	NUM
ejpam-4520	98	5	)	)	PUNCT
ejpam-4520	98	6	=	=	NOUN
ejpam-4520	99	1	i+	i+	NUM
ejpam-4520	99	2	2	2	NUM
ejpam-4520	99	3	,	,	PUNCT
ejpam-4520	99	4	for	for	ADP
ejpam-4520	99	5	1	1	NUM
ejpam-4520	99	6	≤	≤	NUM
ejpam-4520	99	7	i	i	PRON
ejpam-4520	99	8	≤	≤	NUM
ejpam-4520	99	9	m.	m.	NOUN
ejpam-4520	99	10	the	the	DET
ejpam-4520	99	11	edge	edge	NOUN
ejpam-4520	99	12	weights	weight	NOUN
ejpam-4520	99	13	of	of	ADP
ejpam-4520	99	14	the	the	DET
ejpam-4520	99	15	above	above	ADJ
ejpam-4520	99	16	vertex	vertex	NOUN
ejpam-4520	99	17	labeling	labeling	NOUN
ejpam-4520	99	18	f	f	PROPN
ejpam-4520	99	19	can	can	AUX
ejpam-4520	99	20	be	be	AUX
ejpam-4520	99	21	presented	present	VERB
ejpam-4520	99	22	as	as	ADP
ejpam-4520	99	23	w(a1b1	w(a1b1	NOUN
ejpam-4520	99	24	)	)	PUNCT
ejpam-4520	99	25	=	=	SYM
ejpam-4520	99	26	3	3	NUM
ejpam-4520	99	27	,	,	PUNCT
ejpam-4520	99	28	susilowati	susilowati	PROPN
ejpam-4520	99	29	et	et	NOUN
ejpam-4520	99	30	.	.	PUNCT
ejpam-4520	100	1	al	al	PROPN
ejpam-4520	100	2	/	/	PUNCT
ejpam-4520	100	3	eur	eur	PROPN
ejpam-4520	100	4	.	.	PUNCT
ejpam-4520	101	1	j.	j.	PROPN
ejpam-4520	101	2	pure	pure	PROPN
ejpam-4520	101	3	appl	appl	PROPN
ejpam-4520	101	4	.	.	PROPN
ejpam-4520	101	5	math	math	PROPN
ejpam-4520	101	6	,	,	PUNCT
ejpam-4520	101	7	16	16	NUM
ejpam-4520	101	8	(	(	PUNCT
ejpam-4520	101	9	1	1	NUM
ejpam-4520	101	10	)	)	PUNCT
ejpam-4520	101	11	(	(	PUNCT
ejpam-4520	101	12	2023	2023	NUM
ejpam-4520	101	13	)	)	PUNCT
ejpam-4520	101	14	,	,	PUNCT
ejpam-4520	101	15	271	271	NUM
ejpam-4520	101	16	-	-	SYM
ejpam-4520	101	17	285	285	NUM
ejpam-4520	101	18	274	274	NUM
ejpam-4520	101	19	w(a1xi	w(a1xi	NOUN
ejpam-4520	101	20	)	)	PUNCT
ejpam-4520	102	1	=	=	PUNCT
ejpam-4520	102	2	i+	i+	NUM
ejpam-4520	102	3	3	3	NUM
ejpam-4520	102	4	,	,	PUNCT
ejpam-4520	102	5	for	for	ADP
ejpam-4520	102	6	1	1	NUM
ejpam-4520	102	7	≤	≤	NUM
ejpam-4520	102	8	i	i	PRON
ejpam-4520	102	9	≤	≤	NOUN
ejpam-4520	102	10	m	m	VERB
ejpam-4520	102	11	w(b1xi	w(b1xi	NUM
ejpam-4520	102	12	)	)	PUNCT
ejpam-4520	103	1	=	=	NOUN
ejpam-4520	103	2	i+	i+	PUNCT
ejpam-4520	103	3	4	4	NUM
ejpam-4520	103	4	for	for	ADP
ejpam-4520	103	5	1	1	NUM
ejpam-4520	103	6	≤	≤	NUM
ejpam-4520	103	7	i	i	PRON
ejpam-4520	103	8	≤	≤	NUM
ejpam-4520	103	9	m.	m.	NOUN
ejpam-4520	103	10	it	it	PRON
ejpam-4520	103	11	is	be	AUX
ejpam-4520	103	12	easy	easy	ADJ
ejpam-4520	103	13	to	to	PART
ejpam-4520	103	14	see	see	VERB
ejpam-4520	103	15	that	that	SCONJ
ejpam-4520	103	16	the	the	DET
ejpam-4520	103	17	above	above	ADJ
ejpam-4520	103	18	edge	edge	NOUN
ejpam-4520	103	19	weight	weight	NOUN
ejpam-4520	103	20	will	will	AUX
ejpam-4520	103	21	induce	induce	VERB
ejpam-4520	103	22	a	a	DET
ejpam-4520	103	23	rainbow	rainbow	NOUN
ejpam-4520	103	24	antimagic	antimagic	ADJ
ejpam-4520	103	25	coloring	coloring	NOUN
ejpam-4520	103	26	of	of	ADP
ejpam-4520	103	27	graph	graph	NOUN
ejpam-4520	103	28	k1+sm	k1+sm	PROPN
ejpam-4520	103	29	.	.	PUNCT
ejpam-4520	104	1	by	by	ADP
ejpam-4520	104	2	this	this	DET
ejpam-4520	104	3	set	set	NOUN
ejpam-4520	104	4	of	of	ADP
ejpam-4520	104	5	edge	edge	NOUN
ejpam-4520	104	6	weight	weight	NOUN
ejpam-4520	104	7	,	,	PUNCT
ejpam-4520	104	8	we	we	PRON
ejpam-4520	104	9	can	can	AUX
ejpam-4520	104	10	easily	easily	ADV
ejpam-4520	104	11	calculate	calculate	VERB
ejpam-4520	104	12	that	that	SCONJ
ejpam-4520	104	13	the	the	DET
ejpam-4520	104	14	number	number	NOUN
ejpam-4520	104	15	of	of	ADP
ejpam-4520	104	16	color	color	NOUN
ejpam-4520	104	17	w(a1b1	w(a1b1	NOUN
ejpam-4520	104	18	)	)	PUNCT
ejpam-4520	104	19	is	be	AUX
ejpam-4520	104	20	1	1	NUM
ejpam-4520	104	21	.	.	PUNCT
ejpam-4520	105	1	the	the	DET
ejpam-4520	105	2	sets	set	NOUN
ejpam-4520	105	3	w(a1xi	w(a1xi	ADV
ejpam-4520	105	4	)	)	PUNCT
ejpam-4520	105	5	=	=	SYM
ejpam-4520	105	6	{	{	PUNCT
ejpam-4520	105	7	4	4	NUM
ejpam-4520	105	8	,	,	PUNCT
ejpam-4520	105	9	5	5	NUM
ejpam-4520	105	10	,	,	PUNCT
ejpam-4520	105	11	6	6	NUM
ejpam-4520	105	12	,	,	PUNCT
ejpam-4520	105	13	7	7	NUM
ejpam-4520	105	14	,	,	PUNCT
ejpam-4520	105	15	.	.	PUNCT
ejpam-4520	105	16	.	.	PUNCT
ejpam-4520	105	17	.	.	PUNCT
ejpam-4520	106	1	,	,	PUNCT
ejpam-4520	106	2	m+	m+	NOUN
ejpam-4520	106	3	3	3	NUM
ejpam-4520	106	4	}	}	PUNCT
ejpam-4520	106	5	and	and	CCONJ
ejpam-4520	106	6	w(b1xi	w(b1xi	NUM
ejpam-4520	106	7	)	)	PUNCT
ejpam-4520	107	1	=	=	PRON
ejpam-4520	107	2	{	{	PUNCT
ejpam-4520	107	3	5	5	NUM
ejpam-4520	107	4	,	,	PUNCT
ejpam-4520	107	5	6	6	NUM
ejpam-4520	107	6	,	,	PUNCT
ejpam-4520	107	7	7	7	NUM
ejpam-4520	107	8	,	,	PUNCT
ejpam-4520	107	9	.	.	PUNCT
ejpam-4520	107	10	.	.	PUNCT
ejpam-4520	107	11	.	.	PUNCT
ejpam-4520	108	1	,	,	PUNCT
ejpam-4520	108	2	m+	m+	NOUN
ejpam-4520	108	3	4	4	NUM
ejpam-4520	108	4	}	}	PUNCT
ejpam-4520	108	5	,	,	PUNCT
ejpam-4520	108	6	thus	thus	ADV
ejpam-4520	108	7	the	the	DET
ejpam-4520	108	8	number	number	NOUN
ejpam-4520	108	9	of	of	ADP
ejpam-4520	108	10	distinct	distinct	ADJ
ejpam-4520	108	11	colors	color	NOUN
ejpam-4520	108	12	of	of	ADP
ejpam-4520	108	13	w(a1xi)∪w(b1xi	w(a1xi)∪w(b1xi	PROPN
ejpam-4520	108	14	)	)	PUNCT
ejpam-4520	108	15	is	be	AUX
ejpam-4520	108	16	m+1	m+1	PRON
ejpam-4520	108	17	.	.	PUNCT
ejpam-4520	109	1	it	it	PRON
ejpam-4520	109	2	implies	imply	VERB
ejpam-4520	109	3	the	the	DET
ejpam-4520	109	4	edge	edge	NOUN
ejpam-4520	109	5	weights	weight	NOUN
ejpam-4520	109	6	of	of	ADP
ejpam-4520	109	7	f	f	NOUN
ejpam-4520	109	8	:	:	PUNCT
ejpam-4520	109	9	v	v	X
ejpam-4520	109	10	(	(	PUNCT
ejpam-4520	109	11	k1	k1	NOUN
ejpam-4520	109	12	+	+	CCONJ
ejpam-4520	109	13	sm	sm	NOUN
ejpam-4520	109	14	)	)	PUNCT
ejpam-4520	109	15	→	→	SYM
ejpam-4520	109	16	{	{	PUNCT
ejpam-4520	109	17	1	1	NUM
ejpam-4520	109	18	,	,	PUNCT
ejpam-4520	109	19	2	2	NUM
ejpam-4520	109	20	,	,	PUNCT
ejpam-4520	109	21	...	...	PUNCT
ejpam-4520	109	22	,	,	PUNCT
ejpam-4520	109	23	m	m	VERB
ejpam-4520	109	24	+	+	ADJ
ejpam-4520	109	25	2	2	NUM
ejpam-4520	109	26	}	}	PUNCT
ejpam-4520	109	27	induces	induce	VERB
ejpam-4520	109	28	a	a	DET
ejpam-4520	109	29	rainbow	rainbow	NOUN
ejpam-4520	109	30	antimagic	antimagic	ADJ
ejpam-4520	109	31	coloring	coloring	NOUN
ejpam-4520	109	32	of	of	ADP
ejpam-4520	109	33	1	1	NUM
ejpam-4520	109	34	+	+	NUM
ejpam-4520	109	35	m+	m+	NUM
ejpam-4520	109	36	1	1	NUM
ejpam-4520	109	37	colors	color	NOUN
ejpam-4520	109	38	.	.	PUNCT
ejpam-4520	110	1	therefore	therefore	ADV
ejpam-4520	110	2	rac(k1	rac(k1	PROPN
ejpam-4520	110	3	+	+	CCONJ
ejpam-4520	110	4	sm	sm	PROPN
ejpam-4520	110	5	)	)	PUNCT
ejpam-4520	110	6	≤	≤	NOUN
ejpam-4520	110	7	m+	m+	NUM
ejpam-4520	110	8	2	2	NUM
ejpam-4520	110	9	.	.	PUNCT
ejpam-4520	110	10	combining	combine	VERB
ejpam-4520	110	11	the	the	DET
ejpam-4520	110	12	two	two	NUM
ejpam-4520	110	13	bounds	bound	NOUN
ejpam-4520	110	14	,	,	PUNCT
ejpam-4520	110	15	we	we	PRON
ejpam-4520	110	16	have	have	VERB
ejpam-4520	110	17	the	the	DET
ejpam-4520	110	18	exact	exact	ADJ
ejpam-4520	110	19	value	value	NOUN
ejpam-4520	110	20	of	of	ADP
ejpam-4520	110	21	rac(k1	rac(k1	PROPN
ejpam-4520	110	22	+	+	CCONJ
ejpam-4520	110	23	sm	sm	PROPN
ejpam-4520	110	24	)	)	PUNCT
ejpam-4520	110	25	=	=	PUNCT
ejpam-4520	111	1	m+	m+	NUM
ejpam-4520	111	2	2	2	NUM
ejpam-4520	111	3	.	.	PUNCT
ejpam-4520	112	1	the	the	DET
ejpam-4520	112	2	next	next	ADJ
ejpam-4520	112	3	step	step	NOUN
ejpam-4520	112	4	,	,	PUNCT
ejpam-4520	112	5	we	we	PRON
ejpam-4520	112	6	need	need	VERB
ejpam-4520	112	7	to	to	PART
ejpam-4520	112	8	evaluate	evaluate	VERB
ejpam-4520	112	9	the	the	DET
ejpam-4520	112	10	existence	existence	NOUN
ejpam-4520	112	11	of	of	ADP
ejpam-4520	112	12	rainbow	rainbow	NOUN
ejpam-4520	112	13	path	path	NOUN
ejpam-4520	112	14	of	of	ADP
ejpam-4520	112	15	k1	k1	PROPN
ejpam-4520	112	16	+	+	CCONJ
ejpam-4520	112	17	sm	sm	PROPN
ejpam-4520	112	18	.	.	PUNCT
ejpam-4520	113	1	since	since	SCONJ
ejpam-4520	113	2	diam(k1	diam(k1	PROPN
ejpam-4520	113	3	+	+	CCONJ
ejpam-4520	113	4	sm	sm	NOUN
ejpam-4520	113	5	)	)	PUNCT
ejpam-4520	113	6	=	=	SYM
ejpam-4520	113	7	2	2	NUM
ejpam-4520	113	8	,	,	PUNCT
ejpam-4520	113	9	based	base	VERB
ejpam-4520	113	10	on	on	ADP
ejpam-4520	113	11	theorem	theorem	NOUN
ejpam-4520	113	12	2	2	NUM
ejpam-4520	113	13	,	,	PUNCT
ejpam-4520	113	14	there	there	PRON
ejpam-4520	113	15	exists	exist	VERB
ejpam-4520	113	16	a	a	DET
ejpam-4520	113	17	rainbow	rainbow	NOUN
ejpam-4520	113	18	u−	u−	NOUN
ejpam-4520	113	19	v	v	NUM
ejpam-4520	113	20	path	path	NOUN
ejpam-4520	113	21	for	for	ADP
ejpam-4520	113	22	any	any	DET
ejpam-4520	113	23	two	two	NUM
ejpam-4520	113	24	vertices	vertex	NOUN
ejpam-4520	113	25	u	u	NOUN
ejpam-4520	113	26	,	,	PUNCT
ejpam-4520	113	27	v	v	NOUN
ejpam-4520	113	28	∈	∈	PROPN
ejpam-4520	113	29	v	v	NOUN
ejpam-4520	113	30	(	(	PUNCT
ejpam-4520	113	31	k1	k1	NOUN
ejpam-4520	113	32	+	+	CCONJ
ejpam-4520	113	33	sm	sm	NOUN
ejpam-4520	113	34	)	)	PUNCT
ejpam-4520	113	35	.	.	PUNCT
ejpam-4520	114	1	it	it	PRON
ejpam-4520	114	2	completes	complete	VERB
ejpam-4520	114	3	the	the	DET
ejpam-4520	114	4	proof	proof	NOUN
ejpam-4520	114	5	.	.	PUNCT
ejpam-4520	115	1	lemma	lemma	PROPN
ejpam-4520	115	2	1	1	X
ejpam-4520	115	3	.	.	PUNCT
ejpam-4520	116	1	let	let	VERB
ejpam-4520	116	2	tn	tn	PROPN
ejpam-4520	116	3	⊙	⊙	PROPN
ejpam-4520	117	1	sm	sm	PROPN
ejpam-4520	117	2	be	be	AUX
ejpam-4520	117	3	a	a	DET
ejpam-4520	117	4	coronation	coronation	NOUN
ejpam-4520	117	5	of	of	ADP
ejpam-4520	117	6	tree	tree	NOUN
ejpam-4520	117	7	with	with	ADP
ejpam-4520	117	8	order	order	NOUN
ejpam-4520	117	9	n	n	NOUN
ejpam-4520	117	10	and	and	CCONJ
ejpam-4520	117	11	star	star	NOUN
ejpam-4520	117	12	graph	graph	NOUN
ejpam-4520	117	13	with	with	ADP
ejpam-4520	117	14	m	m	PROPN
ejpam-4520	117	15	≥	≥	PROPN
ejpam-4520	117	16	3	3	NUM
ejpam-4520	117	17	.	.	PUNCT
ejpam-4520	118	1	the	the	DET
ejpam-4520	118	2	lower	lower	ADV
ejpam-4520	118	3	bound	bind	VERB
ejpam-4520	118	4	of	of	ADP
ejpam-4520	118	5	rac(tn	rac(tn	X
ejpam-4520	118	6	⊙	⊙	X
ejpam-4520	118	7	sm	sm	PROPN
ejpam-4520	118	8	)	)	PUNCT
ejpam-4520	118	9	≥	≥	NOUN
ejpam-4520	118	10	rac(tn	rac(tn	NOUN
ejpam-4520	118	11	)	)	PUNCT
ejpam-4520	119	1	+	+	NOUN
ejpam-4520	119	2	m+	m+	NUM
ejpam-4520	119	3	2	2	NUM
ejpam-4520	119	4	.	.	PUNCT
ejpam-4520	120	1	proof	proof	NOUN
ejpam-4520	120	2	.	.	PUNCT
ejpam-4520	121	1	the	the	DET
ejpam-4520	121	2	graph	graph	NOUN
ejpam-4520	121	3	tn⊙sm	tn⊙sm	NOUN
ejpam-4520	121	4	is	be	AUX
ejpam-4520	121	5	the	the	DET
ejpam-4520	121	6	corona	corona	NOUN
ejpam-4520	121	7	product	product	NOUN
ejpam-4520	121	8	of	of	ADP
ejpam-4520	121	9	two	two	NUM
ejpam-4520	121	10	graphs	graph	NOUN
ejpam-4520	121	11	tn	tn	PROPN
ejpam-4520	121	12	and	and	CCONJ
ejpam-4520	121	13	sm	sm	INTJ
ejpam-4520	121	14	.	.	PUNCT
ejpam-4520	122	1	it	it	PRON
ejpam-4520	122	2	is	be	AUX
ejpam-4520	122	3	obtained	obtain	VERB
ejpam-4520	122	4	by	by	ADP
ejpam-4520	122	5	taking	take	VERB
ejpam-4520	122	6	one	one	NUM
ejpam-4520	122	7	copy	copy	NOUN
ejpam-4520	122	8	of	of	ADP
ejpam-4520	122	9	tn	tn	PROPN
ejpam-4520	122	10	and	and	CCONJ
ejpam-4520	122	11	|v	|v	PROPN
ejpam-4520	122	12	(	(	PUNCT
ejpam-4520	122	13	tn)|	tn)|	X
ejpam-4520	122	14	copies	copy	NOUN
ejpam-4520	122	15	of	of	ADP
ejpam-4520	122	16	sm	sm	PROPN
ejpam-4520	122	17	and	and	CCONJ
ejpam-4520	122	18	joining	join	VERB
ejpam-4520	122	19	the	the	DET
ejpam-4520	122	20	i	i	PROPN
ejpam-4520	122	21	-	-	PUNCT
ejpam-4520	122	22	th	th	X
ejpam-4520	122	23	vertex	vertex	NOUN
ejpam-4520	122	24	of	of	ADP
ejpam-4520	122	25	tn	tn	NOUN
ejpam-4520	122	26	to	to	ADP
ejpam-4520	122	27	every	every	DET
ejpam-4520	122	28	vertex	vertex	NOUN
ejpam-4520	122	29	in	in	ADP
ejpam-4520	122	30	the	the	DET
ejpam-4520	122	31	i	i	PROPN
ejpam-4520	122	32	-	-	PUNCT
ejpam-4520	122	33	th	th	PROPN
ejpam-4520	122	34	copy	copy	NOUN
ejpam-4520	122	35	of	of	ADP
ejpam-4520	122	36	sm	sm	PROPN
ejpam-4520	122	37	.	.	PUNCT
ejpam-4520	123	1	by	by	ADP
ejpam-4520	123	2	this	this	DET
ejpam-4520	123	3	definition	definition	NOUN
ejpam-4520	123	4	,	,	PUNCT
ejpam-4520	123	5	it	it	PRON
ejpam-4520	123	6	implies	imply	VERB
ejpam-4520	123	7	the	the	DET
ejpam-4520	123	8	graph	graph	NOUN
ejpam-4520	123	9	tn	tn	PROPN
ejpam-4520	123	10	⊙	⊙	PROPN
ejpam-4520	123	11	sm	sm	PROPN
ejpam-4520	123	12	contains	contain	VERB
ejpam-4520	123	13	|v	|v	PROPN
ejpam-4520	123	14	(	(	PUNCT
ejpam-4520	123	15	tn)|	tn)|	X
ejpam-4520	123	16	copies	copy	NOUN
ejpam-4520	123	17	of	of	ADP
ejpam-4520	123	18	k1	k1	PROPN
ejpam-4520	123	19	+	+	CCONJ
ejpam-4520	123	20	sm	sm	PROPN
ejpam-4520	123	21	,	,	PUNCT
ejpam-4520	123	22	see	see	VERB
ejpam-4520	123	23	figure	figure	NOUN
ejpam-4520	123	24	1	1	NUM
ejpam-4520	123	25	.	.	PUNCT
ejpam-4520	124	1	thus	thus	ADV
ejpam-4520	124	2	,	,	PUNCT
ejpam-4520	124	3	to	to	PART
ejpam-4520	124	4	obtain	obtain	VERB
ejpam-4520	124	5	the	the	DET
ejpam-4520	124	6	rac(tn	rac(tn	NUM
ejpam-4520	124	7	⊙	⊙	X
ejpam-4520	124	8	sm	sm	PROPN
ejpam-4520	124	9	)	)	PUNCT
ejpam-4520	124	10	,	,	PUNCT
ejpam-4520	124	11	we	we	PRON
ejpam-4520	124	12	need	need	VERB
ejpam-4520	124	13	to	to	PART
ejpam-4520	124	14	consider	consider	VERB
ejpam-4520	124	15	the	the	DET
ejpam-4520	124	16	rac(k1+sm	rac(k1+sm	NOUN
ejpam-4520	124	17	)	)	PUNCT
ejpam-4520	124	18	and	and	CCONJ
ejpam-4520	124	19	rac(tn	rac(tn	NOUN
ejpam-4520	124	20	)	)	PUNCT
ejpam-4520	124	21	.	.	PUNCT
ejpam-4520	125	1	based	base	VERB
ejpam-4520	125	2	on	on	ADP
ejpam-4520	125	3	theorem	theorem	NOUN
ejpam-4520	125	4	5	5	NUM
ejpam-4520	125	5	,	,	PUNCT
ejpam-4520	125	6	we	we	PRON
ejpam-4520	125	7	have	have	VERB
ejpam-4520	125	8	rac(k1+sm	rac(k1+sm	PUNCT
ejpam-4520	125	9	)	)	PUNCT
ejpam-4520	126	1	=	=	PUNCT
ejpam-4520	126	2	m+	m+	NUM
ejpam-4520	127	1	2	2	NUM
ejpam-4520	127	2	.	.	PUNCT
ejpam-4520	127	3	based	base	VERB
ejpam-4520	127	4	on	on	ADP
ejpam-4520	127	5	theorem	theorem	NOUN
ejpam-4520	127	6	3	3	NUM
ejpam-4520	127	7	,	,	PUNCT
ejpam-4520	127	8	we	we	PRON
ejpam-4520	127	9	have	have	VERB
ejpam-4520	127	10	rac(tn	rac(tn	NOUN
ejpam-4520	127	11	)	)	PUNCT
ejpam-4520	128	1	=	=	SYM
ejpam-4520	128	2	n−	n−	NOUN
ejpam-4520	128	3	1	1	NUM
ejpam-4520	128	4	,	,	PUNCT
ejpam-4520	128	5	since	since	SCONJ
ejpam-4520	128	6	e(tn	e(tn	NUM
ejpam-4520	128	7	)	)	PUNCT
ejpam-4520	128	8	=	=	SYM
ejpam-4520	128	9	−1	−1	NOUN
ejpam-4520	128	10	,	,	PUNCT
ejpam-4520	128	11	for	for	ADP
ejpam-4520	128	12	uv	uv	NOUN
ejpam-4520	128	13	,	,	PUNCT
ejpam-4520	128	14	u′v′	u′v′	PROPN
ejpam-4520	128	15	∈	∈	PROPN
ejpam-4520	128	16	e(tn	e(tn	PROPN
ejpam-4520	128	17	)	)	PUNCT
ejpam-4520	128	18	has	have	VERB
ejpam-4520	128	19	a	a	DET
ejpam-4520	128	20	different	different	ADJ
ejpam-4520	128	21	colors	color	NOUN
ejpam-4520	128	22	.	.	PUNCT
ejpam-4520	129	1	thus	thus	ADV
ejpam-4520	129	2	,	,	PUNCT
ejpam-4520	129	3	it	it	PRON
ejpam-4520	129	4	implies	imply	VERB
ejpam-4520	129	5	that	that	SCONJ
ejpam-4520	129	6	rac(tn	rac(tn	PROPN
ejpam-4520	129	7	⊙	⊙	PROPN
ejpam-4520	129	8	sm	sm	PROPN
ejpam-4520	129	9	)	)	PUNCT
ejpam-4520	129	10	≥	≥	NOUN
ejpam-4520	129	11	rac(tn	rac(tn	NOUN
ejpam-4520	129	12	)	)	PUNCT
ejpam-4520	130	1	+	+	NOUN
ejpam-4520	130	2	m+	m+	NUM
ejpam-4520	130	3	2	2	NUM
ejpam-4520	130	4	.	.	PUNCT
ejpam-4520	130	5	theorem	theorem	VERB
ejpam-4520	130	6	6	6	NUM
ejpam-4520	130	7	.	.	PUNCT
ejpam-4520	130	8	for	for	ADP
ejpam-4520	130	9	odd	odd	ADJ
ejpam-4520	130	10	integers	integer	NOUN
ejpam-4520	130	11	n	n	PRON
ejpam-4520	130	12	≥	≥	NOUN
ejpam-4520	130	13	3	3	NUM
ejpam-4520	130	14	and	and	CCONJ
ejpam-4520	130	15	m	m	PROPN
ejpam-4520	130	16	≥	≥	NOUN
ejpam-4520	130	17	3	3	NUM
ejpam-4520	130	18	,	,	PUNCT
ejpam-4520	130	19	rac(pn	rac(pn	NOUN
ejpam-4520	130	20	⊙	⊙	NOUN
ejpam-4520	130	21	sm	sm	PROPN
ejpam-4520	130	22	)	)	PUNCT
ejpam-4520	130	23	=	=	PUNCT
ejpam-4520	130	24	n+m+	n+m+	X
ejpam-4520	130	25	1	1	X
ejpam-4520	130	26	.	.	PUNCT
ejpam-4520	130	27	proof	proof	NOUN
ejpam-4520	130	28	.	.	PUNCT
ejpam-4520	131	1	the	the	DET
ejpam-4520	131	2	graph	graph	NOUN
ejpam-4520	131	3	pn	pn	PROPN
ejpam-4520	131	4	⊙	⊙	PROPN
ejpam-4520	131	5	sm	sm	PROPN
ejpam-4520	131	6	is	be	AUX
ejpam-4520	131	7	a	a	DET
ejpam-4520	131	8	connected	connected	ADJ
ejpam-4520	131	9	graph	graph	NOUN
ejpam-4520	131	10	with	with	ADP
ejpam-4520	131	11	vertex	vertex	NOUN
ejpam-4520	131	12	set	set	VERB
ejpam-4520	131	13	v	v	NOUN
ejpam-4520	131	14	(	(	PUNCT
ejpam-4520	131	15	pn	pn	PROPN
ejpam-4520	131	16	⊙	⊙	PROPN
ejpam-4520	131	17	sm	sm	PROPN
ejpam-4520	131	18	)	)	PUNCT
ejpam-4520	131	19	=	=	PRON
ejpam-4520	131	20	{	{	PUNCT
ejpam-4520	131	21	x0i	x0i	PROPN
ejpam-4520	131	22	,	,	PUNCT
ejpam-4520	131	23	yi	yi	PROPN
ejpam-4520	131	24	,	,	PUNCT
ejpam-4520	131	25	1	1	NUM
ejpam-4520	131	26	≤	≤	NUM
ejpam-4520	131	27	i	i	PRON
ejpam-4520	131	28	≤	≤	NUM
ejpam-4520	131	29	n}∪{yij	n}∪{yij	NOUN
ejpam-4520	131	30	,	,	PUNCT
ejpam-4520	131	31	1	1	NUM
ejpam-4520	131	32	≤	≤	NUM
ejpam-4520	131	33	i	i	PRON
ejpam-4520	131	34	≤	≤	ADJ
ejpam-4520	131	35	n	n	CCONJ
ejpam-4520	131	36	,	,	PUNCT
ejpam-4520	131	37	1	1	NUM
ejpam-4520	131	38	≤	≤	NUM
ejpam-4520	131	39	j	j	PROPN
ejpam-4520	131	40	≤	≤	PROPN
ejpam-4520	131	41	m	m	PROPN
ejpam-4520	131	42	}	}	PUNCT
ejpam-4520	131	43	and	and	CCONJ
ejpam-4520	131	44	edge	edge	VERB
ejpam-4520	131	45	set	set	VERB
ejpam-4520	131	46	e(pn⊙sm	e(pn⊙sm	NOUN
ejpam-4520	131	47	)	)	PUNCT
ejpam-4520	131	48	=	=	PRON
ejpam-4520	131	49	{	{	PUNCT
ejpam-4520	131	50	x0ix0i+1	x0ix0i+1	PROPN
ejpam-4520	131	51	,	,	PUNCT
ejpam-4520	131	52	1	1	NUM
ejpam-4520	131	53	≤	≤	NUM
ejpam-4520	131	54	i	i	PRON
ejpam-4520	131	55	≤	≤	ADJ
ejpam-4520	131	56	n	n	CCONJ
ejpam-4520	131	57	−	−	PROPN
ejpam-4520	131	58	1	1	NUM
ejpam-4520	131	59	}	}	PUNCT
ejpam-4520	131	60	∪	∪	X
ejpam-4520	131	61	{	{	PUNCT
ejpam-4520	131	62	x0iyi	x0iyi	PROPN
ejpam-4520	131	63	,	,	PUNCT
ejpam-4520	131	64	1	1	NUM
ejpam-4520	131	65	≤	≤	NUM
ejpam-4520	131	66	i	i	PRON
ejpam-4520	131	67	≤	≤	NOUN
ejpam-4520	131	68	n	n	CCONJ
ejpam-4520	131	69	}	}	PUNCT
ejpam-4520	131	70	∪	∪	ADJ
ejpam-4520	131	71	{	{	PUNCT
ejpam-4520	131	72	x0iyij	x0iyij	PROPN
ejpam-4520	131	73	,	,	PUNCT
ejpam-4520	131	74	yiyij	yiyij	NOUN
ejpam-4520	131	75	,	,	PUNCT
ejpam-4520	131	76	1	1	NUM
ejpam-4520	131	77	≤	≤	NUM
ejpam-4520	131	78	i	i	PRON
ejpam-4520	131	79	≤	≤	PROPN
ejpam-4520	131	80	n	n	CCONJ
ejpam-4520	131	81	,	,	PUNCT
ejpam-4520	131	82	1	1	NUM
ejpam-4520	131	83	≤	≤	NUM
ejpam-4520	131	84	j	j	PROPN
ejpam-4520	131	85	≤	≤	PROPN
ejpam-4520	131	86	m	m	PROPN
ejpam-4520	131	87	}	}	PUNCT
ejpam-4520	131	88	.	.	PUNCT
ejpam-4520	132	1	the	the	DET
ejpam-4520	132	2	cardinality	cardinality	NOUN
ejpam-4520	132	3	of	of	ADP
ejpam-4520	132	4	|v	|v	PROPN
ejpam-4520	132	5	(	(	PUNCT
ejpam-4520	132	6	pn	pn	PROPN
ejpam-4520	132	7	⊙	⊙	PROPN
ejpam-4520	133	1	sm)|	sm)|	PROPN
ejpam-4520	133	2	=	=	SYM
ejpam-4520	133	3	2n+	2n+	NUM
ejpam-4520	133	4	nm	nm	NOUN
ejpam-4520	133	5	and	and	CCONJ
ejpam-4520	133	6	the	the	DET
ejpam-4520	133	7	cardinality	cardinality	NOUN
ejpam-4520	133	8	of	of	ADP
ejpam-4520	133	9	|e(pn	|e(pn	PROPN
ejpam-4520	133	10	⊙	⊙	NOUN
ejpam-4520	134	1	sm)|	sm)|	PROPN
ejpam-4520	134	2	=	=	SYM
ejpam-4520	134	3	2n+	2n+	NUM
ejpam-4520	134	4	2nm−	2nm−	NUM
ejpam-4520	134	5	1	1	NUM
ejpam-4520	134	6	.	.	PUNCT
ejpam-4520	134	7	to	to	PART
ejpam-4520	134	8	prove	prove	VERB
ejpam-4520	134	9	the	the	DET
ejpam-4520	134	10	rainbow	rainbow	NOUN
ejpam-4520	134	11	antimagic	antimagic	ADJ
ejpam-4520	134	12	connection	connection	NOUN
ejpam-4520	134	13	number	number	NOUN
ejpam-4520	134	14	of	of	ADP
ejpam-4520	134	15	rac(pn	rac(pn	NOUN
ejpam-4520	134	16	⊙	⊙	X
ejpam-4520	134	17	sm	sm	PROPN
ejpam-4520	134	18	)	)	PUNCT
ejpam-4520	134	19	,	,	PUNCT
ejpam-4520	134	20	first	first	ADV
ejpam-4520	134	21	we	we	PRON
ejpam-4520	134	22	have	have	VERB
ejpam-4520	134	23	to	to	PART
ejpam-4520	134	24	show	show	VERB
ejpam-4520	134	25	that	that	SCONJ
ejpam-4520	134	26	the	the	DET
ejpam-4520	134	27	lower	low	ADJ
ejpam-4520	134	28	bound	bind	VERB
ejpam-4520	134	29	of	of	ADP
ejpam-4520	134	30	rac(pn⊙sm	rac(pn⊙sm	NOUN
ejpam-4520	134	31	)	)	PUNCT
ejpam-4520	134	32	.	.	PUNCT
ejpam-4520	135	1	based	base	VERB
ejpam-4520	135	2	on	on	ADP
ejpam-4520	135	3	lemma	lemma	PROPN
ejpam-4520	135	4	1	1	NUM
ejpam-4520	135	5	,	,	PUNCT
ejpam-4520	135	6	we	we	PRON
ejpam-4520	135	7	have	have	AUX
ejpam-4520	135	8	rac(pn⊙sm	rac(pn⊙sm	NOUN
ejpam-4520	135	9	)	)	PUNCT
ejpam-4520	135	10	≥	≥	NOUN
ejpam-4520	135	11	rac(pn	rac(pn	NOUN
ejpam-4520	135	12	)	)	PUNCT
ejpam-4520	136	1	+	+	NOUN
ejpam-4520	136	2	m+	m+	NUM
ejpam-4520	136	3	2	2	NUM
ejpam-4520	136	4	.	.	PUNCT
ejpam-4520	136	5	since	since	SCONJ
ejpam-4520	136	6	rac(pn	rac(pn	NOUN
ejpam-4520	136	7	)	)	PUNCT
ejpam-4520	136	8	=	=	PUNCT
ejpam-4520	136	9	n−	n−	NOUN
ejpam-4520	136	10	1	1	NUM
ejpam-4520	136	11	,	,	PUNCT
ejpam-4520	136	12	thus	thus	ADV
ejpam-4520	136	13	,	,	PUNCT
ejpam-4520	136	14	rac(pn	rac(pn	NOUN
ejpam-4520	136	15	⊙	⊙	X
ejpam-4520	136	16	sm	sm	PROPN
ejpam-4520	136	17	)	)	PUNCT
ejpam-4520	136	18	≥	≥	PROPN
ejpam-4520	136	19	n+m+	n+m+	X
ejpam-4520	136	20	1	1	NUM
ejpam-4520	136	21	.	.	PUNCT
ejpam-4520	137	1	secondly	secondly	ADV
ejpam-4520	137	2	,	,	PUNCT
ejpam-4520	137	3	we	we	PRON
ejpam-4520	137	4	have	have	VERB
ejpam-4520	137	5	to	to	PART
ejpam-4520	137	6	show	show	VERB
ejpam-4520	137	7	the	the	DET
ejpam-4520	137	8	upper	upper	ADJ
ejpam-4520	137	9	bound	bind	VERB
ejpam-4520	137	10	of	of	ADP
ejpam-4520	137	11	rac(pn	rac(pn	NOUN
ejpam-4520	137	12	⊙	⊙	PROPN
ejpam-4520	137	13	sm	sm	PROPN
ejpam-4520	137	14	)	)	PUNCT
ejpam-4520	137	15	.	.	PUNCT
ejpam-4520	138	1	define	define	VERB
ejpam-4520	138	2	the	the	DET
ejpam-4520	138	3	vertex	vertex	NOUN
ejpam-4520	138	4	labeling	labeling	NOUN
ejpam-4520	139	1	f	f	NOUN
ejpam-4520	139	2	:	:	PUNCT
ejpam-4520	139	3	v	v	X
ejpam-4520	139	4	(	(	PUNCT
ejpam-4520	139	5	pn	pn	PROPN
ejpam-4520	139	6	⊙	⊙	PROPN
ejpam-4520	139	7	sm	sm	PROPN
ejpam-4520	139	8	)	)	PUNCT
ejpam-4520	139	9	→	→	PUNCT
ejpam-4520	139	10	{	{	PUNCT
ejpam-4520	139	11	1	1	NUM
ejpam-4520	139	12	,	,	PUNCT
ejpam-4520	139	13	2	2	NUM
ejpam-4520	139	14	,	,	PUNCT
ejpam-4520	139	15	...	...	PUNCT
ejpam-4520	139	16	,	,	PUNCT
ejpam-4520	139	17	2n+	2n+	NUM
ejpam-4520	139	18	nm	nm	NOUN
ejpam-4520	139	19	}	}	PUNCT
ejpam-4520	139	20	as	as	SCONJ
ejpam-4520	139	21	follows	follow	VERB
ejpam-4520	139	22	.	.	PUNCT
ejpam-4520	140	1	f(x0i	f(x0i	NOUN
ejpam-4520	140	2	)	)	PUNCT
ejpam-4520	140	3	=	=	SYM
ejpam-4520	140	4	⌊n	⌊n	NUM
ejpam-4520	140	5	2	2	NUM
ejpam-4520	140	6	⌋	⌋	NOUN
ejpam-4520	140	7	+	+	CCONJ
ejpam-4520	140	8	i	i	PROPN
ejpam-4520	140	9	,	,	PUNCT
ejpam-4520	140	10	for	for	ADP
ejpam-4520	140	11	1	1	NUM
ejpam-4520	140	12	≤	≤	NUM
ejpam-4520	140	13	i	i	PRON
ejpam-4520	140	14	≤	≤	NOUN
ejpam-4520	140	15	n	n	PRON
ejpam-4520	140	16	f(yi	f(yi	NUM
ejpam-4520	140	17	)	)	PUNCT
ejpam-4520	141	1	=	=	PRON
ejpam-4520	141	2	{	{	PUNCT
ejpam-4520	141	3	⌊	⌊	VERB
ejpam-4520	141	4	n	n	PRON
ejpam-4520	141	5	2	2	NUM
ejpam-4520	141	6	⌋	⌋	NOUN
ejpam-4520	141	7	+	+	CCONJ
ejpam-4520	141	8	i+	i+	NUM
ejpam-4520	141	9	n	n	CCONJ
ejpam-4520	141	10	,	,	PUNCT
ejpam-4520	141	11	for	for	ADP
ejpam-4520	141	12	1	1	NUM
ejpam-4520	141	13	≤	≤	NUM
ejpam-4520	141	14	i	i	PRON
ejpam-4520	141	15	≤	≤	NUM
ejpam-4520	141	16	⌈n2	⌈n2	NOUN
ejpam-4520	141	17	⌉	⌉	X
ejpam-4520	141	18	i−	i−	PROPN
ejpam-4520	141	19	⌈n2	⌈n2	NOUN
ejpam-4520	141	20	⌉	⌉	X
ejpam-4520	141	21	,	,	PUNCT
ejpam-4520	141	22	for	for	ADP
ejpam-4520	141	23	⌈n2	⌈n2	NOUN
ejpam-4520	141	24	⌉	⌉	X
ejpam-4520	141	25	+	+	CCONJ
ejpam-4520	141	26	1	1	NUM
ejpam-4520	141	27	≤	≤	NUM
ejpam-4520	141	28	i	i	PRON
ejpam-4520	141	29	≤	≤	ADJ
ejpam-4520	141	30	n	n	CCONJ
ejpam-4520	141	31	,	,	PUNCT
ejpam-4520	141	32	f(yij	f(yij	NOUN
ejpam-4520	141	33	)	)	PUNCT
ejpam-4520	141	34	=	=	PRON
ejpam-4520	141	35	{	{	PUNCT
ejpam-4520	141	36	2n+	2n+	NUM
ejpam-4520	141	37	jn−	jn−	PROPN
ejpam-4520	141	38	i−	i−	PROPN
ejpam-4520	141	39	1	1	NUM
ejpam-4520	141	40	,	,	PUNCT
ejpam-4520	141	41	for	for	ADP
ejpam-4520	141	42	1	1	NUM
ejpam-4520	141	43	≤	≤	NUM
ejpam-4520	141	44	i	i	PRON
ejpam-4520	141	45	≤	≤	NUM
ejpam-4520	141	46	⌈n2	⌈n2	NOUN
ejpam-4520	141	47	⌉	⌉	NOUN
ejpam-4520	141	48	,	,	PUNCT
ejpam-4520	141	49	1	1	NUM
ejpam-4520	141	50	≤	≤	NUM
ejpam-4520	141	51	j	j	PROPN
ejpam-4520	141	52	≤	≤	NUM
ejpam-4520	141	53	m	m	VERB
ejpam-4520	141	54	2n+	2n+	NUM
ejpam-4520	141	55	jn−	jn−	NOUN
ejpam-4520	141	56	i+	i+	X
ejpam-4520	141	57	4	4	NUM
ejpam-4520	141	58	,	,	PUNCT
ejpam-4520	141	59	for	for	ADP
ejpam-4520	141	60	⌈n2	⌈n2	NOUN
ejpam-4520	141	61	⌉+	⌉+	NOUN
ejpam-4520	141	62	1	1	NUM
ejpam-4520	141	63	≤	≤	NUM
ejpam-4520	141	64	i	i	PRON
ejpam-4520	141	65	≤	≤	PROPN
ejpam-4520	141	66	n	n	CCONJ
ejpam-4520	141	67	,	,	PUNCT
ejpam-4520	141	68	1	1	NUM
ejpam-4520	141	69	≤	≤	NUM
ejpam-4520	141	70	j	j	PROPN
ejpam-4520	141	71	≤	≤	PROPN
ejpam-4520	141	72	m	m	PROPN
ejpam-4520	141	73	,	,	PUNCT
ejpam-4520	141	74	susilowati	susilowati	PROPN
ejpam-4520	141	75	et	et	PROPN
ejpam-4520	141	76	.	.	PUNCT
ejpam-4520	142	1	al	al	PROPN
ejpam-4520	142	2	/	/	PUNCT
ejpam-4520	142	3	eur	eur	PROPN
ejpam-4520	142	4	.	.	PUNCT
ejpam-4520	143	1	j.	j.	PROPN
ejpam-4520	143	2	pure	pure	PROPN
ejpam-4520	143	3	appl	appl	PROPN
ejpam-4520	143	4	.	.	PROPN
ejpam-4520	143	5	math	math	PROPN
ejpam-4520	143	6	,	,	PUNCT
ejpam-4520	143	7	16	16	NUM
ejpam-4520	143	8	(	(	PUNCT
ejpam-4520	143	9	1	1	NUM
ejpam-4520	143	10	)	)	PUNCT
ejpam-4520	143	11	(	(	PUNCT
ejpam-4520	143	12	2023	2023	NUM
ejpam-4520	143	13	)	)	PUNCT
ejpam-4520	143	14	,	,	PUNCT
ejpam-4520	143	15	271	271	NUM
ejpam-4520	143	16	-	-	SYM
ejpam-4520	143	17	285	285	NUM
ejpam-4520	143	18	275	275	NUM
ejpam-4520	143	19	k1	k1	NOUN
ejpam-4520	143	20	+	+	CCONJ
ejpam-4520	143	21	sm	sm	PROPN
ejpam-4520	143	22	t	t	PROPN
ejpam-4520	143	23	figure	figure	NOUN
ejpam-4520	143	24	1	1	NUM
ejpam-4520	143	25	:	:	PUNCT
ejpam-4520	143	26	the	the	DET
ejpam-4520	143	27	illustration	illustration	NOUN
ejpam-4520	143	28	of	of	ADP
ejpam-4520	143	29	graph	graph	NOUN
ejpam-4520	143	30	tn	tn	PROPN
ejpam-4520	143	31	⊙	⊙	PROPN
ejpam-4520	144	1	sm	sm	PROPN
ejpam-4520	144	2	.	.	PUNCT
ejpam-4520	145	1	the	the	DET
ejpam-4520	145	2	edge	edge	NOUN
ejpam-4520	145	3	weights	weight	NOUN
ejpam-4520	145	4	of	of	ADP
ejpam-4520	145	5	the	the	DET
ejpam-4520	145	6	above	above	ADJ
ejpam-4520	145	7	vertex	vertex	NOUN
ejpam-4520	145	8	labeling	labeling	NOUN
ejpam-4520	145	9	f	f	PROPN
ejpam-4520	145	10	can	can	AUX
ejpam-4520	145	11	be	be	AUX
ejpam-4520	145	12	presented	present	VERB
ejpam-4520	145	13	as	as	ADP
ejpam-4520	145	14	:	:	PUNCT
ejpam-4520	145	15	for	for	ADP
ejpam-4520	145	16	1	1	NUM
ejpam-4520	145	17	≤	≤	NUM
ejpam-4520	145	18	i	i	PRON
ejpam-4520	145	19	≤	≤	NOUN
ejpam-4520	145	20	n	n	CCONJ
ejpam-4520	145	21	−	−	PROPN
ejpam-4520	145	22	1	1	NUM
ejpam-4520	145	23	,	,	PUNCT
ejpam-4520	145	24	w(x0ix0i+1	w(x0ix0i+1	NOUN
ejpam-4520	145	25	)	)	PUNCT
ejpam-4520	145	26	=	=	NUM
ejpam-4520	145	27	n+	n+	NUM
ejpam-4520	145	28	2i	2i	NUM
ejpam-4520	145	29	,	,	PUNCT
ejpam-4520	145	30	and	and	CCONJ
ejpam-4520	145	31	for	for	ADP
ejpam-4520	145	32	1	1	NUM
ejpam-4520	145	33	≤	≤	NUM
ejpam-4520	145	34	i	i	PRON
ejpam-4520	145	35	≤	≤	NUM
ejpam-4520	145	36	⌈n2	⌈n2	NOUN
ejpam-4520	145	37	⌉	⌉	NOUN
ejpam-4520	145	38	,	,	PUNCT
ejpam-4520	145	39	1	1	NUM
ejpam-4520	145	40	≤	≤	NUM
ejpam-4520	145	41	j	j	PROPN
ejpam-4520	145	42	≤	≤	NUM
ejpam-4520	145	43	m	m	VERB
ejpam-4520	145	44	w(x0iyi	w(x0iyi	PROPN
ejpam-4520	145	45	)	)	PUNCT
ejpam-4520	145	46	=	=	SYM
ejpam-4520	146	1	2n+	2n+	NUM
ejpam-4520	147	1	2i−	2i−	NUM
ejpam-4520	147	2	1	1	NUM
ejpam-4520	147	3	,	,	PUNCT
ejpam-4520	147	4	w(xiyij	w(xiyij	NOUN
ejpam-4520	147	5	)	)	PUNCT
ejpam-4520	147	6	=	=	SYM
ejpam-4520	147	7	2n+	2n+	NUM
ejpam-4520	147	8	jn+	jn+	ADJ
ejpam-4520	147	9	1	1	NUM
ejpam-4520	147	10	,	,	PUNCT
ejpam-4520	147	11	w(yiyij	w(yiyij	NOUN
ejpam-4520	147	12	)	)	PUNCT
ejpam-4520	147	13	=	=	SYM
ejpam-4520	147	14	3n+	3n+	NUM
ejpam-4520	147	15	jn+	jn+	ADJ
ejpam-4520	147	16	1	1	NUM
ejpam-4520	147	17	.	.	PUNCT
ejpam-4520	147	18	and	and	CCONJ
ejpam-4520	147	19	for	for	ADP
ejpam-4520	147	20	⌈n2	⌈n2	NOUN
ejpam-4520	147	21	⌉+	⌉+	NOUN
ejpam-4520	147	22	1	1	NUM
ejpam-4520	147	23	≤	≤	NUM
ejpam-4520	147	24	i	i	PRON
ejpam-4520	147	25	≤	≤	PROPN
ejpam-4520	147	26	n	n	CCONJ
ejpam-4520	147	27	,	,	PUNCT
ejpam-4520	147	28	1	1	NUM
ejpam-4520	147	29	≤	≤	NUM
ejpam-4520	147	30	j	j	PROPN
ejpam-4520	147	31	≤	≤	PROPN
ejpam-4520	147	32	m	m	PROPN
ejpam-4520	147	33	,	,	PUNCT
ejpam-4520	147	34	w(x0iyi	w(x0iyi	PROPN
ejpam-4520	147	35	)	)	PUNCT
ejpam-4520	147	36	=	=	SYM
ejpam-4520	148	1	2i−	2i−	NUM
ejpam-4520	148	2	1	1	NUM
ejpam-4520	148	3	,	,	PUNCT
ejpam-4520	148	4	w(xiyij	w(xiyij	NOUN
ejpam-4520	148	5	)	)	PUNCT
ejpam-4520	148	6	=	=	SYM
ejpam-4520	148	7	3n+	3n+	NUM
ejpam-4520	148	8	jn+	jn+	ADJ
ejpam-4520	148	9	1	1	NUM
ejpam-4520	148	10	,	,	PUNCT
ejpam-4520	148	11	w(yiyij	w(yiyij	NOUN
ejpam-4520	148	12	)	)	PUNCT
ejpam-4520	148	13	=	=	SYM
ejpam-4520	148	14	2n+	2n+	NUM
ejpam-4520	148	15	jn+	jn+	ADJ
ejpam-4520	148	16	1	1	NUM
ejpam-4520	148	17	.	.	PUNCT
ejpam-4520	148	18	based	base	VERB
ejpam-4520	148	19	on	on	ADP
ejpam-4520	148	20	theorem	theorem	ADJ
ejpam-4520	148	21	3	3	NUM
ejpam-4520	148	22	,	,	PUNCT
ejpam-4520	148	23	rac(pn	rac(pn	NOUN
ejpam-4520	148	24	)	)	PUNCT
ejpam-4520	148	25	=	=	SYM
ejpam-4520	148	26	n	n	CCONJ
ejpam-4520	148	27	−	−	PROPN
ejpam-4520	148	28	1	1	NUM
ejpam-4520	148	29	.	.	PUNCT
ejpam-4520	149	1	since	since	SCONJ
ejpam-4520	149	2	e(pn	e(pn	NUM
ejpam-4520	149	3	)	)	PUNCT
ejpam-4520	149	4	=	=	SYM
ejpam-4520	149	5	n	n	CCONJ
ejpam-4520	149	6	−	−	PROPN
ejpam-4520	149	7	1	1	NUM
ejpam-4520	149	8	,	,	PUNCT
ejpam-4520	149	9	for	for	ADP
ejpam-4520	149	10	u	u	NOUN
ejpam-4520	149	11	,	,	PUNCT
ejpam-4520	149	12	v	v	PROPN
ejpam-4520	149	13	∈	∈	PROPN
ejpam-4520	149	14	e(pn	e(pn	NUM
ejpam-4520	149	15	)	)	PUNCT
ejpam-4520	149	16	has	have	VERB
ejpam-4520	149	17	a	a	DET
ejpam-4520	149	18	different	different	ADJ
ejpam-4520	149	19	colors	color	NOUN
ejpam-4520	149	20	.	.	PUNCT
ejpam-4520	150	1	therefore	therefore	ADV
ejpam-4520	150	2	,	,	PUNCT
ejpam-4520	150	3	the	the	DET
ejpam-4520	150	4	sum	sum	NOUN
ejpam-4520	150	5	of	of	ADP
ejpam-4520	150	6	the	the	DET
ejpam-4520	150	7	weights	weight	NOUN
ejpam-4520	150	8	of	of	ADP
ejpam-4520	150	9	graph	graph	NOUN
ejpam-4520	150	10	pn	pn	PROPN
ejpam-4520	150	11	is	be	AUX
ejpam-4520	150	12	n	n	ADV
ejpam-4520	150	13	−	−	PROPN
ejpam-4520	150	14	1	1	NUM
ejpam-4520	150	15	.	.	PUNCT
ejpam-4520	150	16	based	base	VERB
ejpam-4520	150	17	on	on	ADP
ejpam-4520	150	18	theorem	theorem	NOUN
ejpam-4520	150	19	5	5	NUM
ejpam-4520	150	20	,	,	PUNCT
ejpam-4520	150	21	we	we	PRON
ejpam-4520	150	22	have	have	VERB
ejpam-4520	150	23	rac(k1	rac(k1	PROPN
ejpam-4520	150	24	+	+	CCONJ
ejpam-4520	150	25	sm	sm	NOUN
ejpam-4520	150	26	)	)	PUNCT
ejpam-4520	150	27	=	=	PUNCT
ejpam-4520	151	1	m	m	VERB
ejpam-4520	151	2	+	+	ADJ
ejpam-4520	151	3	2	2	NUM
ejpam-4520	151	4	.	.	PUNCT
ejpam-4520	151	5	based	base	VERB
ejpam-4520	151	6	on	on	ADP
ejpam-4520	151	7	the	the	DET
ejpam-4520	151	8	description	description	NOUN
ejpam-4520	151	9	above	above	ADV
ejpam-4520	151	10	,	,	PUNCT
ejpam-4520	151	11	we	we	PRON
ejpam-4520	151	12	have	have	VERB
ejpam-4520	151	13	that	that	SCONJ
ejpam-4520	151	14	the	the	DET
ejpam-4520	151	15	distinct	distinct	ADJ
ejpam-4520	151	16	weight	weight	NOUN
ejpam-4520	151	17	of	of	ADP
ejpam-4520	151	18	graph	graph	NOUN
ejpam-4520	151	19	(	(	PUNCT
ejpam-4520	151	20	pn	pn	PROPN
ejpam-4520	151	21	⊙	⊙	PROPN
ejpam-4520	151	22	sm	sm	PROPN
ejpam-4520	151	23	)	)	PUNCT
ejpam-4520	151	24	is	be	AUX
ejpam-4520	151	25	n	n	PRON
ejpam-4520	151	26	+	+	NOUN
ejpam-4520	151	27	m	m	VERB
ejpam-4520	151	28	+	+	ADJ
ejpam-4520	151	29	1	1	X
ejpam-4520	151	30	.	.	PUNCT
ejpam-4520	152	1	it	it	PRON
ejpam-4520	152	2	implies	imply	VERB
ejpam-4520	152	3	the	the	DET
ejpam-4520	152	4	edge	edge	NOUN
ejpam-4520	152	5	weights	weight	NOUN
ejpam-4520	152	6	of	of	ADP
ejpam-4520	152	7	f	f	NOUN
ejpam-4520	152	8	:	:	PUNCT
ejpam-4520	152	9	v	v	X
ejpam-4520	152	10	(	(	PUNCT
ejpam-4520	152	11	pn	pn	PROPN
ejpam-4520	152	12	⊙	⊙	PROPN
ejpam-4520	152	13	sm	sm	PROPN
ejpam-4520	152	14	)	)	PUNCT
ejpam-4520	152	15	→	→	PUNCT
ejpam-4520	152	16	{	{	PUNCT
ejpam-4520	152	17	1	1	NUM
ejpam-4520	152	18	,	,	PUNCT
ejpam-4520	152	19	2	2	NUM
ejpam-4520	152	20	,	,	PUNCT
ejpam-4520	152	21	...	...	PUNCT
ejpam-4520	152	22	,	,	PUNCT
ejpam-4520	152	23	2n+	2n+	NUM
ejpam-4520	152	24	nm	nm	NOUN
ejpam-4520	152	25	}	}	PUNCT
ejpam-4520	152	26	induces	induce	VERB
ejpam-4520	152	27	a	a	DET
ejpam-4520	152	28	rainbow	rainbow	NOUN
ejpam-4520	152	29	antimagic	antimagic	ADJ
ejpam-4520	152	30	coloring	coloring	NOUN
ejpam-4520	152	31	of	of	ADP
ejpam-4520	152	32	m+	m+	NUM
ejpam-4520	152	33	n+	n+	ADP
ejpam-4520	152	34	1	1	NUM
ejpam-4520	152	35	colors	color	NOUN
ejpam-4520	152	36	.	.	PUNCT
ejpam-4520	153	1	thus	thus	ADV
ejpam-4520	153	2	rac(pn	rac(pn	NOUN
ejpam-4520	153	3	⊙	⊙	PROPN
ejpam-4520	153	4	sm	sm	PROPN
ejpam-4520	153	5	)	)	PUNCT
ejpam-4520	153	6	≤	≤	NOUN
ejpam-4520	153	7	n	n	PRON
ejpam-4520	153	8	+	+	NOUN
ejpam-4520	153	9	m	m	VERB
ejpam-4520	153	10	+	+	ADJ
ejpam-4520	153	11	1	1	NUM
ejpam-4520	153	12	.	.	PUNCT
ejpam-4520	153	13	comparing	compare	VERB
ejpam-4520	153	14	the	the	DET
ejpam-4520	153	15	two	two	NUM
ejpam-4520	153	16	bounds	bound	NOUN
ejpam-4520	153	17	,	,	PUNCT
ejpam-4520	153	18	we	we	PRON
ejpam-4520	153	19	have	have	VERB
ejpam-4520	153	20	the	the	DET
ejpam-4520	153	21	exact	exact	ADJ
ejpam-4520	153	22	value	value	NOUN
ejpam-4520	153	23	of	of	ADP
ejpam-4520	153	24	rac(pn	rac(pn	NOUN
ejpam-4520	153	25	⊙	⊙	X
ejpam-4520	153	26	sm	sm	PROPN
ejpam-4520	153	27	)	)	PUNCT
ejpam-4520	153	28	=	=	PUNCT
ejpam-4520	153	29	n+m+	n+m+	X
ejpam-4520	153	30	1	1	NUM
ejpam-4520	153	31	.	.	PUNCT
ejpam-4520	154	1	the	the	DET
ejpam-4520	154	2	next	next	ADJ
ejpam-4520	154	3	step	step	NOUN
ejpam-4520	154	4	,	,	PUNCT
ejpam-4520	154	5	evaluate	evaluate	VERB
ejpam-4520	154	6	to	to	PART
ejpam-4520	154	7	prove	prove	VERB
ejpam-4520	154	8	the	the	DET
ejpam-4520	154	9	existence	existence	NOUN
ejpam-4520	154	10	of	of	ADP
ejpam-4520	154	11	a	a	DET
ejpam-4520	154	12	rainbow	rainbow	NOUN
ejpam-4520	154	13	u−v	u−v	PUNCT
ejpam-4520	154	14	path	path	NOUN
ejpam-4520	154	15	pn⊙sm	pn⊙sm	PROPN
ejpam-4520	154	16	.	.	PUNCT
ejpam-4520	155	1	based	base	VERB
ejpam-4520	155	2	on	on	ADP
ejpam-4520	155	3	the	the	DET
ejpam-4520	155	4	definition	definition	NOUN
ejpam-4520	155	5	of	of	ADP
ejpam-4520	155	6	the	the	DET
ejpam-4520	155	7	graph	graph	NOUN
ejpam-4520	155	8	pn⊙sm	pn⊙sm	NOUN
ejpam-4520	155	9	,	,	PUNCT
ejpam-4520	155	10	then	then	ADV
ejpam-4520	155	11	the	the	DET
ejpam-4520	155	12	graph	graph	NOUN
ejpam-4520	155	13	pn⊙sm	pn⊙sm	NOUN
ejpam-4520	155	14	contains	contain	VERB
ejpam-4520	155	15	one	one	NUM
ejpam-4520	155	16	graph	graph	NOUN
ejpam-4520	155	17	pn	pn	NOUN
ejpam-4520	155	18	and	and	CCONJ
ejpam-4520	155	19	|v	|v	PROPN
ejpam-4520	155	20	(	(	PUNCT
ejpam-4520	155	21	pn)|	pn)|	PROPN
ejpam-4520	155	22	copies	copy	NOUN
ejpam-4520	155	23	of	of	ADP
ejpam-4520	155	24	k1	k1	PROPN
ejpam-4520	155	25	+	+	CCONJ
ejpam-4520	155	26	sm	sm	PROPN
ejpam-4520	155	27	,	,	PUNCT
ejpam-4520	155	28	so	so	SCONJ
ejpam-4520	155	29	that	that	SCONJ
ejpam-4520	155	30	we	we	PRON
ejpam-4520	155	31	can	can	AUX
ejpam-4520	155	32	evaluate	evaluate	VERB
ejpam-4520	155	33	the	the	DET
ejpam-4520	155	34	rainbow	rainbow	NOUN
ejpam-4520	155	35	u	u	NOUN
ejpam-4520	155	36	−	−	PROPN
ejpam-4520	155	37	v	v	ADP
ejpam-4520	155	38	path	path	NOUN
ejpam-4520	155	39	of	of	ADP
ejpam-4520	155	40	the	the	DET
ejpam-4520	155	41	graph	graph	NOUN
ejpam-4520	155	42	susilowati	susilowati	PROPN
ejpam-4520	155	43	et	et	NOUN
ejpam-4520	155	44	.	.	PUNCT
ejpam-4520	156	1	al	al	PROPN
ejpam-4520	156	2	/	/	PUNCT
ejpam-4520	156	3	eur	eur	PROPN
ejpam-4520	156	4	.	.	PUNCT
ejpam-4520	157	1	j.	j.	PROPN
ejpam-4520	157	2	pure	pure	PROPN
ejpam-4520	157	3	appl	appl	PROPN
ejpam-4520	157	4	.	.	PROPN
ejpam-4520	157	5	math	math	PROPN
ejpam-4520	157	6	,	,	PUNCT
ejpam-4520	157	7	16	16	NUM
ejpam-4520	157	8	(	(	PUNCT
ejpam-4520	157	9	1	1	NUM
ejpam-4520	157	10	)	)	PUNCT
ejpam-4520	157	11	(	(	PUNCT
ejpam-4520	157	12	2023	2023	NUM
ejpam-4520	157	13	)	)	PUNCT
ejpam-4520	157	14	,	,	PUNCT
ejpam-4520	157	15	271	271	NUM
ejpam-4520	157	16	-	-	SYM
ejpam-4520	157	17	285	285	NUM
ejpam-4520	157	18	276	276	NUM
ejpam-4520	157	19	pn	pn	PROPN
ejpam-4520	157	20	⊙	⊙	PROPN
ejpam-4520	157	21	sm	sm	INTJ
ejpam-4520	157	22	by	by	ADP
ejpam-4520	157	23	evaluating	evaluate	VERB
ejpam-4520	157	24	the	the	DET
ejpam-4520	157	25	rainbow	rainbow	NOUN
ejpam-4520	157	26	u−	u−	PROPN
ejpam-4520	157	27	v	v	ADP
ejpam-4520	157	28	path	path	NOUN
ejpam-4520	157	29	on	on	ADP
ejpam-4520	157	30	the	the	DET
ejpam-4520	157	31	graph	graph	NOUN
ejpam-4520	157	32	pn	pn	NOUN
ejpam-4520	157	33	and	and	CCONJ
ejpam-4520	157	34	the	the	DET
ejpam-4520	157	35	graph	graph	NOUN
ejpam-4520	157	36	k1	k1	NOUN
ejpam-4520	157	37	+	+	CCONJ
ejpam-4520	157	38	sm	sm	PROPN
ejpam-4520	157	39	.	.	PUNCT
ejpam-4520	158	1	since	since	SCONJ
ejpam-4520	158	2	diam(k1	diam(k1	PROPN
ejpam-4520	158	3	+	+	CCONJ
ejpam-4520	158	4	sm	sm	NOUN
ejpam-4520	158	5	)	)	PUNCT
ejpam-4520	158	6	=	=	SYM
ejpam-4520	158	7	2	2	NUM
ejpam-4520	158	8	,	,	PUNCT
ejpam-4520	158	9	based	base	VERB
ejpam-4520	158	10	on	on	ADP
ejpam-4520	158	11	theorem	theorem	NOUN
ejpam-4520	158	12	2	2	NUM
ejpam-4520	158	13	,	,	PUNCT
ejpam-4520	158	14	there	there	PRON
ejpam-4520	158	15	is	be	VERB
ejpam-4520	158	16	a	a	DET
ejpam-4520	158	17	rainbow	rainbow	NOUN
ejpam-4520	158	18	u	u	NOUN
ejpam-4520	158	19	−	−	PROPN
ejpam-4520	158	20	v	v	ADP
ejpam-4520	158	21	path	path	NOUN
ejpam-4520	158	22	for	for	ADP
ejpam-4520	158	23	every	every	DET
ejpam-4520	158	24	u	u	NOUN
ejpam-4520	158	25	,	,	PUNCT
ejpam-4520	158	26	v	v	PROPN
ejpam-4520	158	27	∈	∈	PROPN
ejpam-4520	158	28	v	v	NOUN
ejpam-4520	158	29	(	(	PUNCT
ejpam-4520	158	30	k1+sm	k1+sm	PROPN
ejpam-4520	158	31	)	)	PUNCT
ejpam-4520	158	32	.	.	PUNCT
ejpam-4520	159	1	based	base	VERB
ejpam-4520	159	2	on	on	ADP
ejpam-4520	159	3	theorem	theorem	ADJ
ejpam-4520	159	4	3	3	NUM
ejpam-4520	159	5	,	,	PUNCT
ejpam-4520	159	6	rac(pn	rac(pn	NOUN
ejpam-4520	159	7	)	)	PUNCT
ejpam-4520	159	8	=	=	SYM
ejpam-4520	160	1	n−1	n−1	PROPN
ejpam-4520	160	2	.	.	PUNCT
ejpam-4520	161	1	since	since	SCONJ
ejpam-4520	161	2	pn	pn	PROPN
ejpam-4520	161	3	has	have	VERB
ejpam-4520	161	4	n−1	n−1	PROPN
ejpam-4520	161	5	edges	edge	NOUN
ejpam-4520	161	6	,	,	PUNCT
ejpam-4520	161	7	there	there	PRON
ejpam-4520	161	8	is	be	VERB
ejpam-4520	161	9	a	a	DET
ejpam-4520	161	10	rainbow	rainbow	NOUN
ejpam-4520	161	11	u	u	NOUN
ejpam-4520	161	12	−	−	PROPN
ejpam-4520	161	13	v	v	ADP
ejpam-4520	161	14	path	path	NOUN
ejpam-4520	161	15	for	for	ADP
ejpam-4520	161	16	every	every	DET
ejpam-4520	161	17	u	u	NOUN
ejpam-4520	161	18	,	,	PUNCT
ejpam-4520	161	19	v	v	PROPN
ejpam-4520	161	20	∈	∈	PROPN
ejpam-4520	161	21	v	v	NOUN
ejpam-4520	161	22	(	(	PUNCT
ejpam-4520	161	23	pn	pn	NOUN
ejpam-4520	161	24	)	)	PUNCT
ejpam-4520	161	25	.	.	PUNCT
ejpam-4520	162	1	therefore	therefore	ADV
ejpam-4520	162	2	,	,	PUNCT
ejpam-4520	162	3	according	accord	VERB
ejpam-4520	162	4	to	to	ADP
ejpam-4520	162	5	the	the	DET
ejpam-4520	162	6	explanation	explanation	NOUN
ejpam-4520	162	7	,	,	PUNCT
ejpam-4520	162	8	it	it	PRON
ejpam-4520	162	9	can	can	AUX
ejpam-4520	162	10	be	be	AUX
ejpam-4520	162	11	seen	see	VERB
ejpam-4520	162	12	that	that	SCONJ
ejpam-4520	162	13	there	there	PRON
ejpam-4520	162	14	is	be	VERB
ejpam-4520	162	15	a	a	DET
ejpam-4520	162	16	rainbow	rainbow	NOUN
ejpam-4520	162	17	u−	u−	NOUN
ejpam-4520	162	18	v	v	NUM
ejpam-4520	162	19	path	path	NOUN
ejpam-4520	162	20	for	for	ADP
ejpam-4520	162	21	every	every	DET
ejpam-4520	162	22	u	u	NOUN
ejpam-4520	162	23	,	,	PUNCT
ejpam-4520	162	24	v	v	PROPN
ejpam-4520	162	25	∈	∈	NOUN
ejpam-4520	162	26	v	v	NOUN
ejpam-4520	162	27	(	(	PUNCT
ejpam-4520	162	28	pn	pn	PROPN
ejpam-4520	162	29	⊙	⊙	PROPN
ejpam-4520	162	30	sm	sm	PROPN
ejpam-4520	162	31	)	)	PUNCT
ejpam-4520	162	32	.	.	PUNCT
ejpam-4520	163	1	rainbow	rainbow	VERB
ejpam-4520	163	2	antimagic	antimagic	ADJ
ejpam-4520	163	3	coloring	coloring	NOUN
ejpam-4520	163	4	of	of	ADP
ejpam-4520	163	5	graph	graph	NOUN
ejpam-4520	163	6	pn	pn	PROPN
ejpam-4520	163	7	⊙	⊙	PROPN
ejpam-4520	163	8	sm	sm	PROPN
ejpam-4520	163	9	can	can	AUX
ejpam-4520	163	10	be	be	AUX
ejpam-4520	163	11	seen	see	VERB
ejpam-4520	163	12	in	in	ADP
ejpam-4520	163	13	figure	figure	NOUN
ejpam-4520	163	14	2	2	NUM
ejpam-4520	163	15	.	.	PUNCT
ejpam-4520	164	1	y1	y1	PROPN
ejpam-4520	164	2	y3	y3	PROPN
ejpam-4520	164	3	x03	x03	PROPN
ejpam-4520	164	4	x02	x02	PROPN
ejpam-4520	164	5	x01	x01	PROPN
ejpam-4520	164	6	y24y23y22y21	y24y23y22y21	PROPN
ejpam-4520	164	7	y34y33y32y31y14y13y12y11	y34y33y32y31y14y13y12y11	NOUN
ejpam-4520	164	8	y2	y2	PROPN
ejpam-4520	164	9	4	4	NUM
ejpam-4520	164	10	10	10	NUM
ejpam-4520	164	11	13	13	NUM
ejpam-4520	164	12	16	16	NUM
ejpam-4520	164	13	22	22	NUM
ejpam-4520	164	14	10	10	NUM
ejpam-4520	164	15	16	16	NUM
ejpam-4520	164	16	19	19	NUM
ejpam-4520	164	17	13	13	NUM
ejpam-4520	164	18	16	16	NUM
ejpam-4520	164	19	22	22	NUM
ejpam-4520	164	20	13	13	NUM
ejpam-4520	164	21	10	10	NUM
ejpam-4520	164	22	7	7	NUM
ejpam-4520	164	23	5	5	NUM
ejpam-4520	164	24	9	9	NUM
ejpam-4520	164	25	14	14	NUM
ejpam-4520	164	26	5	5	NUM
ejpam-4520	164	27	7	7	NUM
ejpam-4520	164	28	10	10	NUM
ejpam-4520	164	29	32	32	NUM
ejpam-4520	164	30	1	1	NUM
ejpam-4520	164	31	16	16	NUM
ejpam-4520	164	32	19	19	NUM
ejpam-4520	164	33	13	13	NUM
ejpam-4520	164	34	16	16	NUM
ejpam-4520	164	35	13	13	NUM
ejpam-4520	164	36	19	19	NUM
ejpam-4520	164	37	1916	1916	NUM
ejpam-4520	164	38	1913	1913	NUM
ejpam-4520	164	39	75	75	NUM
ejpam-4520	164	40	1815129	1815129	NUM
ejpam-4520	164	41	1613	1613	NUM
ejpam-4520	164	42	6	6	NUM
ejpam-4520	164	43	17	17	NUM
ejpam-4520	164	44	22	22	NUM
ejpam-4520	164	45	118	118	NUM
ejpam-4520	164	46	19	19	NUM
ejpam-4520	164	47	figure	figure	NOUN
ejpam-4520	164	48	2	2	NUM
ejpam-4520	164	49	:	:	PUNCT
ejpam-4520	164	50	rainbow	rainbow	VERB
ejpam-4520	164	51	antimagic	antimagic	ADJ
ejpam-4520	164	52	coloring	coloring	NOUN
ejpam-4520	164	53	of	of	ADP
ejpam-4520	164	54	graph	graph	NOUN
ejpam-4520	164	55	p3	p3	PROPN
ejpam-4520	164	56	⊙	⊙	PROPN
ejpam-4520	164	57	s4	s4	PROPN
ejpam-4520	164	58	.	.	PUNCT
ejpam-4520	165	1	theorem	theorem	VERB
ejpam-4520	165	2	7	7	NUM
ejpam-4520	165	3	.	.	X
ejpam-4520	165	4	for	for	ADP
ejpam-4520	165	5	odd	odd	ADJ
ejpam-4520	165	6	integers	integer	NOUN
ejpam-4520	165	7	n	n	PRON
ejpam-4520	165	8	≥	≥	NOUN
ejpam-4520	165	9	3	3	NUM
ejpam-4520	165	10	and	and	CCONJ
ejpam-4520	165	11	m	m	PROPN
ejpam-4520	165	12	≥	≥	NOUN
ejpam-4520	165	13	3	3	NUM
ejpam-4520	165	14	,	,	PUNCT
ejpam-4520	165	15	rac(sn	rac(sn	VERB
ejpam-4520	165	16	⊙	⊙	PROPN
ejpam-4520	165	17	sm	sm	PROPN
ejpam-4520	165	18	)	)	PUNCT
ejpam-4520	165	19	=	=	PUNCT
ejpam-4520	165	20	n+m+	n+m+	X
ejpam-4520	165	21	2	2	NUM
ejpam-4520	165	22	.	.	PUNCT
ejpam-4520	165	23	proof	proof	NOUN
ejpam-4520	165	24	.	.	PUNCT
ejpam-4520	166	1	the	the	DET
ejpam-4520	166	2	graph	graph	NOUN
ejpam-4520	166	3	sn	sn	PROPN
ejpam-4520	166	4	⊙	⊙	PROPN
ejpam-4520	166	5	sm	sm	PROPN
ejpam-4520	166	6	is	be	AUX
ejpam-4520	166	7	a	a	DET
ejpam-4520	166	8	connected	connected	ADJ
ejpam-4520	166	9	graph	graph	NOUN
ejpam-4520	166	10	with	with	ADP
ejpam-4520	166	11	vertex	vertex	NOUN
ejpam-4520	166	12	set	set	VERB
ejpam-4520	166	13	v	v	NOUN
ejpam-4520	166	14	(	(	PUNCT
ejpam-4520	166	15	sn	sn	PROPN
ejpam-4520	166	16	⊙	⊙	PROPN
ejpam-4520	166	17	sm	sm	PROPN
ejpam-4520	166	18	)	)	PUNCT
ejpam-4520	166	19	=	=	PRON
ejpam-4520	166	20	{	{	PUNCT
ejpam-4520	166	21	x0	x0	PROPN
ejpam-4520	166	22	}	}	PUNCT
ejpam-4520	166	23	∪	∪	X
ejpam-4520	166	24	{	{	PUNCT
ejpam-4520	166	25	x0i	x0i	PROPN
ejpam-4520	166	26	,	,	PUNCT
ejpam-4520	166	27	1	1	NUM
ejpam-4520	166	28	≤	≤	NUM
ejpam-4520	166	29	i	i	PRON
ejpam-4520	166	30	≤	≤	NOUN
ejpam-4520	166	31	n	n	CCONJ
ejpam-4520	166	32	}	}	PUNCT
ejpam-4520	166	33	∪	∪	X
ejpam-4520	166	34	{	{	PUNCT
ejpam-4520	166	35	yi	yi	NOUN
ejpam-4520	166	36	,	,	PUNCT
ejpam-4520	166	37	1	1	NUM
ejpam-4520	166	38	≤	≤	NUM
ejpam-4520	167	1	i	i	X
ejpam-4520	167	2	≤	≤	NOUN
ejpam-4520	167	3	n+1	n+1	VERB
ejpam-4520	167	4	}	}	PUNCT
ejpam-4520	167	5	∪	∪	ADJ
ejpam-4520	167	6	{	{	PUNCT
ejpam-4520	167	7	yij	yij	NOUN
ejpam-4520	167	8	,	,	PUNCT
ejpam-4520	167	9	1	1	NUM
ejpam-4520	167	10	≤	≤	NUM
ejpam-4520	167	11	i	i	X
ejpam-4520	167	12	≤	≤	PROPN
ejpam-4520	167	13	n+1	n+1	PROPN
ejpam-4520	167	14	,	,	PUNCT
ejpam-4520	167	15	1	1	NUM
ejpam-4520	167	16	≤	≤	NUM
ejpam-4520	167	17	j	j	PROPN
ejpam-4520	167	18	≤	≤	PROPN
ejpam-4520	167	19	m	m	PROPN
ejpam-4520	167	20	}	}	PUNCT
ejpam-4520	167	21	and	and	CCONJ
ejpam-4520	167	22	edge	edge	VERB
ejpam-4520	167	23	set	set	NOUN
ejpam-4520	167	24	e(sn⊙sm	e(sn⊙sm	NOUN
ejpam-4520	167	25	)	)	PUNCT
ejpam-4520	167	26	=	=	SYM
ejpam-4520	167	27	{	{	PUNCT
ejpam-4520	167	28	x0xi	x0xi	NOUN
ejpam-4520	167	29	,	,	PUNCT
ejpam-4520	167	30	1	1	NUM
ejpam-4520	167	31	≤	≤	NUM
ejpam-4520	167	32	i	i	PRON
ejpam-4520	167	33	≤	≤	PROPN
ejpam-4520	167	34	n}∪{x0yn+1}∪{x0iyi	n}∪{x0yn+1}∪{x0iyi	NOUN
ejpam-4520	167	35	,	,	PUNCT
ejpam-4520	167	36	1	1	NUM
ejpam-4520	167	37	≤	≤	NUM
ejpam-4520	167	38	i	i	NOUN
ejpam-4520	167	39	≤	≤	ADJ
ejpam-4520	167	40	n}∪{x0yn+1j	n}∪{x0yn+1j	NOUN
ejpam-4520	167	41	,	,	PUNCT
ejpam-4520	167	42	yn+1yn+1j	yn+1yn+1j	NOUN
ejpam-4520	167	43	,	,	PUNCT
ejpam-4520	167	44	1	1	NUM
ejpam-4520	167	45	≤	≤	NUM
ejpam-4520	167	46	j	j	PROPN
ejpam-4520	167	47	≤	≤	PROPN
ejpam-4520	167	48	m}∪{x0iyi	m}∪{x0iyi	PROPN
ejpam-4520	167	49	,	,	PUNCT
ejpam-4520	167	50	yiyij	yiyij	NOUN
ejpam-4520	167	51	,	,	PUNCT
ejpam-4520	167	52	1	1	NUM
ejpam-4520	167	53	≤	≤	NUM
ejpam-4520	167	54	i	i	PRON
ejpam-4520	167	55	≤	≤	PROPN
ejpam-4520	167	56	n	n	CCONJ
ejpam-4520	167	57	,	,	PUNCT
ejpam-4520	167	58	1	1	NUM
ejpam-4520	167	59	≤	≤	NUM
ejpam-4520	167	60	j	j	PROPN
ejpam-4520	167	61	≤	≤	PROPN
ejpam-4520	167	62	m	m	PROPN
ejpam-4520	167	63	}	}	PUNCT
ejpam-4520	167	64	.	.	PUNCT
ejpam-4520	168	1	the	the	DET
ejpam-4520	168	2	cardinality	cardinality	NOUN
ejpam-4520	168	3	of	of	ADP
ejpam-4520	168	4	|v	|v	PROPN
ejpam-4520	168	5	(	(	PUNCT
ejpam-4520	168	6	sn⊙sm)|	sn⊙sm)|	PROPN
ejpam-4520	168	7	=	=	SYM
ejpam-4520	168	8	2n+nm+2	2n+nm+2	NUM
ejpam-4520	168	9	and	and	CCONJ
ejpam-4520	168	10	the	the	DET
ejpam-4520	168	11	cardinality	cardinality	NOUN
ejpam-4520	168	12	of	of	ADP
ejpam-4520	168	13	|e(sn	|e(sn	PROPN
ejpam-4520	168	14	⊙	⊙	NOUN
ejpam-4520	168	15	sm)|	sm)|	PROPN
ejpam-4520	168	16	=	=	SYM
ejpam-4520	168	17	2nm+	2nm+	NUM
ejpam-4520	168	18	2n+	2n+	NUM
ejpam-4520	168	19	2m+	2m+	NUM
ejpam-4520	168	20	1	1	NUM
ejpam-4520	168	21	.	.	PUNCT
ejpam-4520	168	22	to	to	PART
ejpam-4520	168	23	prove	prove	VERB
ejpam-4520	168	24	the	the	DET
ejpam-4520	168	25	rainbow	rainbow	NOUN
ejpam-4520	168	26	antimagic	antimagic	ADJ
ejpam-4520	168	27	connection	connection	NOUN
ejpam-4520	168	28	number	number	NOUN
ejpam-4520	168	29	of	of	ADP
ejpam-4520	168	30	rac(sn	rac(sn	PROPN
ejpam-4520	168	31	⊙	⊙	PROPN
ejpam-4520	168	32	sm	sm	PROPN
ejpam-4520	168	33	)	)	PUNCT
ejpam-4520	168	34	,	,	PUNCT
ejpam-4520	168	35	first	first	ADV
ejpam-4520	168	36	we	we	PRON
ejpam-4520	168	37	have	have	VERB
ejpam-4520	168	38	to	to	PART
ejpam-4520	168	39	show	show	VERB
ejpam-4520	168	40	that	that	SCONJ
ejpam-4520	168	41	the	the	DET
ejpam-4520	168	42	lower	low	ADJ
ejpam-4520	168	43	bound	bind	VERB
ejpam-4520	168	44	of	of	ADP
ejpam-4520	168	45	rac(sn⊙sm	rac(sn⊙sm	NOUN
ejpam-4520	168	46	)	)	PUNCT
ejpam-4520	168	47	.	.	PUNCT
ejpam-4520	169	1	based	base	VERB
ejpam-4520	169	2	on	on	ADP
ejpam-4520	169	3	lemma	lemma	PROPN
ejpam-4520	169	4	1	1	NUM
ejpam-4520	169	5	,	,	PUNCT
ejpam-4520	169	6	we	we	PRON
ejpam-4520	169	7	have	have	VERB
ejpam-4520	169	8	rac(sn⊙sm	rac(sn⊙sm	NOUN
ejpam-4520	169	9	)	)	PUNCT
ejpam-4520	169	10	≥	≥	NOUN
ejpam-4520	169	11	rac(sn	rac(sn	PUNCT
ejpam-4520	169	12	)	)	PUNCT
ejpam-4520	170	1	+	+	NOUN
ejpam-4520	170	2	m+	m+	NUM
ejpam-4520	170	3	2	2	NUM
ejpam-4520	170	4	.	.	PUNCT
ejpam-4520	170	5	since	since	SCONJ
ejpam-4520	170	6	rac(sn	rac(sn	ADJ
ejpam-4520	170	7	)	)	PUNCT
ejpam-4520	170	8	=	=	SYM
ejpam-4520	170	9	n	n	CCONJ
ejpam-4520	170	10	,	,	PUNCT
ejpam-4520	170	11	thus	thus	ADV
ejpam-4520	170	12	,	,	PUNCT
ejpam-4520	170	13	rac(sn	rac(sn	VERB
ejpam-4520	170	14	⊙	⊙	PROPN
ejpam-4520	170	15	sm	sm	PROPN
ejpam-4520	170	16	)	)	PUNCT
ejpam-4520	170	17	≥	≥	PROPN
ejpam-4520	170	18	n+m+	n+m+	X
ejpam-4520	170	19	2	2	NUM
ejpam-4520	170	20	.	.	PUNCT
ejpam-4520	171	1	secondly	secondly	ADV
ejpam-4520	171	2	,	,	PUNCT
ejpam-4520	171	3	we	we	PRON
ejpam-4520	171	4	have	have	VERB
ejpam-4520	171	5	to	to	PART
ejpam-4520	171	6	show	show	VERB
ejpam-4520	171	7	the	the	DET
ejpam-4520	171	8	upper	upper	ADJ
ejpam-4520	171	9	bound	bound	NOUN
ejpam-4520	171	10	of	of	ADP
ejpam-4520	171	11	rac(sn⊙sm	rac(sn⊙sm	NOUN
ejpam-4520	171	12	)	)	PUNCT
ejpam-4520	171	13	.	.	PUNCT
ejpam-4520	172	1	define	define	VERB
ejpam-4520	172	2	the	the	DET
ejpam-4520	172	3	vertex	vertex	NOUN
ejpam-4520	172	4	labeling	labeling	NOUN
ejpam-4520	173	1	f	f	NOUN
ejpam-4520	173	2	:	:	PUNCT
ejpam-4520	173	3	v	v	X
ejpam-4520	173	4	(	(	PUNCT
ejpam-4520	173	5	sn	sn	PROPN
ejpam-4520	173	6	⊙	⊙	PROPN
ejpam-4520	173	7	sm	sm	PROPN
ejpam-4520	173	8	)	)	PUNCT
ejpam-4520	173	9	→	→	PUNCT
ejpam-4520	173	10	{	{	PUNCT
ejpam-4520	173	11	1	1	NUM
ejpam-4520	173	12	,	,	PUNCT
ejpam-4520	173	13	2	2	NUM
ejpam-4520	173	14	,	,	PUNCT
ejpam-4520	173	15	.	.	PUNCT
ejpam-4520	173	16	.	.	PUNCT
ejpam-4520	173	17	.	.	PUNCT
ejpam-4520	174	1	2n+	2n+	NUM
ejpam-4520	174	2	nm+	nm+	NOUN
ejpam-4520	174	3	2	2	NUM
ejpam-4520	174	4	}	}	PUNCT
ejpam-4520	174	5	as	as	SCONJ
ejpam-4520	174	6	follows	follow	VERB
ejpam-4520	174	7	.	.	PUNCT
ejpam-4520	175	1	f(x0	f(x0	NOUN
ejpam-4520	175	2	)	)	PUNCT
ejpam-4520	176	1	=	=	PRON
ejpam-4520	176	2	n+	n+	ADP
ejpam-4520	176	3	1	1	NUM
ejpam-4520	176	4	f(xi	f(xi	PROPN
ejpam-4520	176	5	)	)	PUNCT
ejpam-4520	176	6	=	=	PUNCT
ejpam-4520	176	7			PUNCT
ejpam-4520	176	8	n+	n+	NOUN
ejpam-4520	176	9	i+	i+	ADV
ejpam-4520	176	10	1	1	NUM
ejpam-4520	176	11	for	for	ADP
ejpam-4520	176	12	1	1	NUM
ejpam-4520	176	13	≤	≤	NUM
ejpam-4520	176	14	i	i	PRON
ejpam-4520	176	15	≤	≤	ADJ
ejpam-4520	177	1	n	n	CCONJ
ejpam-4520	178	1	and	and	CCONJ
ejpam-4520	178	2	i	i	PRON
ejpam-4520	178	3	is	be	AUX
ejpam-4520	178	4	odd	odd	ADJ
ejpam-4520	178	5	i	i	PRON
ejpam-4520	178	6	for	for	ADP
ejpam-4520	178	7	1	1	NUM
ejpam-4520	178	8	≤	≤	NUM
ejpam-4520	178	9	i	i	PRON
ejpam-4520	179	1	≤	≤	ADJ
ejpam-4520	180	1	n	n	CCONJ
ejpam-4520	181	1	and	and	CCONJ
ejpam-4520	181	2	i	i	PRON
ejpam-4520	181	3	is	be	AUX
ejpam-4520	181	4	even	even	ADV
ejpam-4520	181	5	i	i	PRON
ejpam-4520	181	6	for	for	ADP
ejpam-4520	181	7	i	i	PRON
ejpam-4520	181	8	=	=	PUNCT
ejpam-4520	181	9	n+	n+	ADP
ejpam-4520	181	10	1	1	NUM
ejpam-4520	181	11	f(yi	f(yi	NUM
ejpam-4520	181	12	)	)	PUNCT
ejpam-4520	181	13	=	=	PUNCT
ejpam-4520	182	1			PUNCT
ejpam-4520	182	2	i	i	PRON
ejpam-4520	182	3	for	for	ADP
ejpam-4520	182	4	1	1	NUM
ejpam-4520	182	5	≤	≤	NUM
ejpam-4520	182	6	i	i	PRON
ejpam-4520	182	7	≤	≤	ADJ
ejpam-4520	182	8	n	n	CCONJ
ejpam-4520	183	1	and	and	CCONJ
ejpam-4520	183	2	i	i	PRON
ejpam-4520	183	3	is	be	AUX
ejpam-4520	183	4	odd	odd	ADJ
ejpam-4520	183	5	n+	n+	ADP
ejpam-4520	183	6	i+	i+	ADV
ejpam-4520	183	7	1	1	NUM
ejpam-4520	183	8	for	for	ADP
ejpam-4520	183	9	1	1	NUM
ejpam-4520	183	10	≤	≤	NUM
ejpam-4520	184	1	i	i	PRON
ejpam-4520	185	1	≤	≤	ADJ
ejpam-4520	186	1	n	n	CCONJ
ejpam-4520	187	1	and	and	CCONJ
ejpam-4520	187	2	i	i	PRON
ejpam-4520	187	3	is	be	AUX
ejpam-4520	187	4	even	even	ADV
ejpam-4520	187	5	2n+	2n+	NUM
ejpam-4520	187	6	2	2	NUM
ejpam-4520	187	7	for	for	ADP
ejpam-4520	187	8	i	i	PRON
ejpam-4520	187	9	=	=	SYM
ejpam-4520	187	10	n+	n+	NUM
ejpam-4520	187	11	1	1	NUM
ejpam-4520	187	12	,	,	PUNCT
ejpam-4520	187	13	susilowati	susilowati	PROPN
ejpam-4520	187	14	et	et	NOUN
ejpam-4520	187	15	.	.	PUNCT
ejpam-4520	188	1	al	al	PROPN
ejpam-4520	188	2	/	/	PUNCT
ejpam-4520	188	3	eur	eur	PROPN
ejpam-4520	188	4	.	.	PUNCT
ejpam-4520	189	1	j.	j.	PROPN
ejpam-4520	189	2	pure	pure	PROPN
ejpam-4520	189	3	appl	appl	PROPN
ejpam-4520	189	4	.	.	PROPN
ejpam-4520	189	5	math	math	PROPN
ejpam-4520	189	6	,	,	PUNCT
ejpam-4520	189	7	16	16	NUM
ejpam-4520	189	8	(	(	PUNCT
ejpam-4520	189	9	1	1	NUM
ejpam-4520	189	10	)	)	PUNCT
ejpam-4520	189	11	(	(	PUNCT
ejpam-4520	189	12	2023	2023	NUM
ejpam-4520	189	13	)	)	PUNCT
ejpam-4520	189	14	,	,	PUNCT
ejpam-4520	189	15	271	271	NUM
ejpam-4520	189	16	-	-	SYM
ejpam-4520	189	17	285	285	NUM
ejpam-4520	189	18	277	277	NUM
ejpam-4520	189	19	f(yij	f(yij	NOUN
ejpam-4520	189	20	)	)	PUNCT
ejpam-4520	189	21	=	=	SYM
ejpam-4520	190	1	2n+	2n+	NUM
ejpam-4520	191	1	jn−	jn−	NOUN
ejpam-4520	191	2	i+	i+	NUM
ejpam-4520	191	3	j	j	NOUN
ejpam-4520	191	4	+	+	NOUN
ejpam-4520	191	5	3	3	NUM
ejpam-4520	191	6	,	,	PUNCT
ejpam-4520	191	7	for	for	ADP
ejpam-4520	191	8	1	1	NUM
ejpam-4520	191	9	≤	≤	NUM
ejpam-4520	191	10	i	i	PRON
ejpam-4520	191	11	≤	≤	NOUN
ejpam-4520	191	12	n+	n+	PUNCT
ejpam-4520	191	13	1	1	NUM
ejpam-4520	191	14	,	,	PUNCT
ejpam-4520	191	15	1	1	NUM
ejpam-4520	191	16	≤	≤	NUM
ejpam-4520	191	17	j	j	PROPN
ejpam-4520	191	18	≤	≤	PROPN
ejpam-4520	191	19	m	m	PROPN
ejpam-4520	191	20	,	,	PUNCT
ejpam-4520	191	21	the	the	DET
ejpam-4520	191	22	edge	edge	NOUN
ejpam-4520	191	23	weights	weight	NOUN
ejpam-4520	191	24	of	of	ADP
ejpam-4520	191	25	the	the	DET
ejpam-4520	191	26	above	above	ADJ
ejpam-4520	191	27	vertex	vertex	NOUN
ejpam-4520	191	28	labeling	labeling	NOUN
ejpam-4520	191	29	f	f	PROPN
ejpam-4520	191	30	can	can	AUX
ejpam-4520	191	31	be	be	AUX
ejpam-4520	191	32	presented	present	VERB
ejpam-4520	191	33	as	as	ADP
ejpam-4520	191	34	w(x0x0i	w(x0x0i	NOUN
ejpam-4520	191	35	)	)	PUNCT
ejpam-4520	192	1	=	=	PRON
ejpam-4520	192	2	{	{	PUNCT
ejpam-4520	192	3	2n+	2n+	NUM
ejpam-4520	192	4	i+	i+	PRON
ejpam-4520	192	5	2	2	NUM
ejpam-4520	192	6	for	for	ADP
ejpam-4520	192	7	1	1	NUM
ejpam-4520	192	8	≤	≤	NUM
ejpam-4520	192	9	i	i	PRON
ejpam-4520	192	10	≤	≤	ADJ
ejpam-4520	192	11	n	n	CCONJ
ejpam-4520	193	1	and	and	CCONJ
ejpam-4520	193	2	i	i	PRON
ejpam-4520	193	3	is	be	AUX
ejpam-4520	193	4	odd	odd	ADJ
ejpam-4520	193	5	n+	n+	ADP
ejpam-4520	193	6	i+	i+	ADV
ejpam-4520	193	7	1	1	NUM
ejpam-4520	193	8	for	for	ADP
ejpam-4520	193	9	1	1	NUM
ejpam-4520	193	10	≤	≤	NUM
ejpam-4520	194	1	i	i	PRON
ejpam-4520	195	1	≤	≤	ADJ
ejpam-4520	196	1	n	n	CCONJ
ejpam-4520	197	1	and	and	CCONJ
ejpam-4520	197	2	i	i	PRON
ejpam-4520	197	3	is	be	AUX
ejpam-4520	197	4	even	even	ADV
ejpam-4520	197	5	w(x0yn+1	w(x0yn+1	ADJ
ejpam-4520	197	6	)	)	PUNCT
ejpam-4520	198	1	=	=	SYM
ejpam-4520	198	2	3n+	3n+	NUM
ejpam-4520	198	3	3	3	NUM
ejpam-4520	198	4	w(xiyi	w(xiyi	NOUN
ejpam-4520	198	5	)	)	PUNCT
ejpam-4520	198	6	=	=	SYM
ejpam-4520	198	7	n+	n+	ADP
ejpam-4520	198	8	2i+	2i+	NUM
ejpam-4520	198	9	1	1	NUM
ejpam-4520	198	10	,	,	PUNCT
ejpam-4520	198	11	for	for	ADP
ejpam-4520	198	12	1	1	NUM
ejpam-4520	198	13	≤	≤	NUM
ejpam-4520	198	14	i	i	PRON
ejpam-4520	198	15	≤	≤	ADJ
ejpam-4520	198	16	n.	n.	NOUN
ejpam-4520	198	17	w(x0yn+1j	w(x0yn+1j	PROPN
ejpam-4520	198	18	)	)	PUNCT
ejpam-4520	199	1	=	=	SYM
ejpam-4520	199	2	2n+	2n+	NUM
ejpam-4520	199	3	jn+	jn+	PROPN
ejpam-4520	199	4	j	j	PROPN
ejpam-4520	199	5	+	+	CCONJ
ejpam-4520	199	6	3	3	NUM
ejpam-4520	199	7	,	,	PUNCT
ejpam-4520	199	8	for	for	ADP
ejpam-4520	199	9	1	1	NUM
ejpam-4520	199	10	≤	≤	NUM
ejpam-4520	199	11	j	j	PROPN
ejpam-4520	199	12	≤	≤	PROPN
ejpam-4520	199	13	m	m	VERB
ejpam-4520	199	14	w(x0iyij	w(x0iyij	PROPN
ejpam-4520	199	15	)	)	PUNCT
ejpam-4520	199	16	=	=	PRON
ejpam-4520	199	17	{	{	PUNCT
ejpam-4520	199	18	3n+	3n+	NUM
ejpam-4520	199	19	jn+	jn+	PROPN
ejpam-4520	199	20	j	j	PROPN
ejpam-4520	199	21	+	+	CCONJ
ejpam-4520	199	22	4	4	NUM
ejpam-4520	199	23	for	for	ADP
ejpam-4520	199	24	1	1	NUM
ejpam-4520	199	25	≤	≤	NUM
ejpam-4520	199	26	i	i	PRON
ejpam-4520	199	27	≤	≤	PROPN
ejpam-4520	199	28	n	n	CCONJ
ejpam-4520	199	29	,	,	PUNCT
ejpam-4520	199	30	1	1	NUM
ejpam-4520	199	31	≤	≤	NUM
ejpam-4520	199	32	j	j	PROPN
ejpam-4520	199	33	≤	≤	NUM
ejpam-4520	199	34	m	m	PROPN
ejpam-4520	200	1	and	and	CCONJ
ejpam-4520	200	2	i	i	PRON
ejpam-4520	200	3	is	be	AUX
ejpam-4520	200	4	odd	odd	ADJ
ejpam-4520	200	5	2n+	2n+	NUM
ejpam-4520	200	6	jn+	jn+	PROPN
ejpam-4520	200	7	j	j	PROPN
ejpam-4520	201	1	+	+	CCONJ
ejpam-4520	201	2	3	3	NUM
ejpam-4520	201	3	for	for	ADP
ejpam-4520	201	4	1	1	NUM
ejpam-4520	201	5	≤	≤	NUM
ejpam-4520	201	6	i	i	PRON
ejpam-4520	201	7	≤	≤	PROPN
ejpam-4520	201	8	n	n	CCONJ
ejpam-4520	201	9	,	,	PUNCT
ejpam-4520	201	10	1	1	NUM
ejpam-4520	201	11	≤	≤	NUM
ejpam-4520	201	12	j	j	PROPN
ejpam-4520	201	13	≤	≤	NUM
ejpam-4520	201	14	m	m	PROPN
ejpam-4520	202	1	and	and	CCONJ
ejpam-4520	202	2	i	i	PRON
ejpam-4520	202	3	is	be	AUX
ejpam-4520	202	4	even	even	ADV
ejpam-4520	202	5	w(yiyij	w(yiyij	NOUN
ejpam-4520	202	6	)	)	PUNCT
ejpam-4520	203	1	=	=	PUNCT
ejpam-4520	203	2			PUNCT
ejpam-4520	203	3	2n+	2n+	NUM
ejpam-4520	203	4	jn+	jn+	PROPN
ejpam-4520	203	5	j	j	PROPN
ejpam-4520	204	1	+	+	CCONJ
ejpam-4520	204	2	3	3	NUM
ejpam-4520	204	3	for	for	ADP
ejpam-4520	204	4	1	1	NUM
ejpam-4520	204	5	≤	≤	NUM
ejpam-4520	204	6	i	i	PRON
ejpam-4520	204	7	≤	≤	NOUN
ejpam-4520	204	8	n+	n+	PUNCT
ejpam-4520	204	9	1	1	NUM
ejpam-4520	204	10	,	,	PUNCT
ejpam-4520	204	11	1	1	NUM
ejpam-4520	204	12	≤	≤	NUM
ejpam-4520	204	13	j	j	PROPN
ejpam-4520	204	14	≤	≤	NUM
ejpam-4520	204	15	m	m	PROPN
ejpam-4520	205	1	and	and	CCONJ
ejpam-4520	205	2	i	i	PRON
ejpam-4520	205	3	is	be	AUX
ejpam-4520	205	4	odd	odd	ADJ
ejpam-4520	205	5	3n+	3n+	NUM
ejpam-4520	205	6	jn+	jn+	PROPN
ejpam-4520	205	7	j	j	PROPN
ejpam-4520	206	1	+	+	CCONJ
ejpam-4520	206	2	4	4	NUM
ejpam-4520	206	3	for	for	ADP
ejpam-4520	206	4	1	1	NUM
ejpam-4520	206	5	≤	≤	NUM
ejpam-4520	206	6	i	i	PRON
ejpam-4520	206	7	≤	≤	NOUN
ejpam-4520	206	8	n+	n+	PUNCT
ejpam-4520	206	9	1	1	NUM
ejpam-4520	206	10	,	,	PUNCT
ejpam-4520	206	11	1	1	NUM
ejpam-4520	206	12	≤	≤	NUM
ejpam-4520	206	13	j	j	PROPN
ejpam-4520	206	14	≤	≤	NUM
ejpam-4520	206	15	m	m	PROPN
ejpam-4520	207	1	and	and	CCONJ
ejpam-4520	207	2	i	i	PRON
ejpam-4520	207	3	is	be	AUX
ejpam-4520	207	4	even	even	ADV
ejpam-4520	207	5	3n+	3n+	NUM
ejpam-4520	207	6	jn+	jn+	PROPN
ejpam-4520	207	7	j	j	PROPN
ejpam-4520	208	1	+	+	CCONJ
ejpam-4520	208	2	4	4	NUM
ejpam-4520	208	3	for	for	ADP
ejpam-4520	208	4	i	i	PRON
ejpam-4520	208	5	=	=	SYM
ejpam-4520	208	6	n+	n+	NUM
ejpam-4520	208	7	1	1	NUM
ejpam-4520	208	8	,	,	PUNCT
ejpam-4520	208	9	based	base	VERB
ejpam-4520	208	10	on	on	ADP
ejpam-4520	208	11	theorem	theorem	NOUN
ejpam-4520	208	12	3	3	NUM
ejpam-4520	208	13	,	,	PUNCT
ejpam-4520	208	14	rac(sn	rac(sn	ADJ
ejpam-4520	208	15	)	)	PUNCT
ejpam-4520	208	16	=	=	VERB
ejpam-4520	208	17	n.	n.	NOUN
ejpam-4520	208	18	since	since	SCONJ
ejpam-4520	208	19	e(sn	e(sn	NOUN
ejpam-4520	208	20	)	)	PUNCT
ejpam-4520	208	21	=	=	SYM
ejpam-4520	208	22	n	n	CCONJ
ejpam-4520	208	23	,	,	PUNCT
ejpam-4520	208	24	for	for	ADP
ejpam-4520	208	25	u	u	NOUN
ejpam-4520	208	26	,	,	PUNCT
ejpam-4520	208	27	v	v	PROPN
ejpam-4520	208	28	∈	∈	PROPN
ejpam-4520	208	29	e(sn	e(sn	PROPN
ejpam-4520	208	30	)	)	PUNCT
ejpam-4520	208	31	has	have	VERB
ejpam-4520	208	32	a	a	DET
ejpam-4520	208	33	different	different	ADJ
ejpam-4520	208	34	colors	color	NOUN
ejpam-4520	208	35	.	.	PUNCT
ejpam-4520	209	1	therefore	therefore	ADV
ejpam-4520	209	2	,	,	PUNCT
ejpam-4520	209	3	the	the	DET
ejpam-4520	209	4	sum	sum	NOUN
ejpam-4520	209	5	of	of	ADP
ejpam-4520	209	6	the	the	DET
ejpam-4520	209	7	weights	weight	NOUN
ejpam-4520	209	8	of	of	ADP
ejpam-4520	209	9	graph	graph	NOUN
ejpam-4520	209	10	sn	sn	PROPN
ejpam-4520	209	11	is	be	AUX
ejpam-4520	209	12	n.	n.	NOUN
ejpam-4520	209	13	based	base	VERB
ejpam-4520	209	14	on	on	ADP
ejpam-4520	209	15	theorem	theorem	NOUN
ejpam-4520	209	16	5	5	NUM
ejpam-4520	209	17	,	,	PUNCT
ejpam-4520	209	18	we	we	PRON
ejpam-4520	209	19	have	have	VERB
ejpam-4520	209	20	rac(k1	rac(k1	PROPN
ejpam-4520	209	21	+	+	CCONJ
ejpam-4520	209	22	sm	sm	NOUN
ejpam-4520	209	23	)	)	PUNCT
ejpam-4520	209	24	=	=	PUNCT
ejpam-4520	210	1	m	m	VERB
ejpam-4520	210	2	+	+	ADJ
ejpam-4520	210	3	2	2	NUM
ejpam-4520	210	4	.	.	PUNCT
ejpam-4520	210	5	based	base	VERB
ejpam-4520	210	6	on	on	ADP
ejpam-4520	210	7	the	the	DET
ejpam-4520	210	8	description	description	NOUN
ejpam-4520	210	9	above	above	ADV
ejpam-4520	210	10	,	,	PUNCT
ejpam-4520	210	11	we	we	PRON
ejpam-4520	210	12	have	have	VERB
ejpam-4520	210	13	that	that	SCONJ
ejpam-4520	210	14	the	the	DET
ejpam-4520	210	15	distinct	distinct	ADJ
ejpam-4520	210	16	weight	weight	NOUN
ejpam-4520	210	17	of	of	ADP
ejpam-4520	210	18	graph	graph	NOUN
ejpam-4520	210	19	(	(	PUNCT
ejpam-4520	210	20	sn	sn	PROPN
ejpam-4520	210	21	⊙	⊙	PROPN
ejpam-4520	210	22	sm	sm	PROPN
ejpam-4520	210	23	)	)	PUNCT
ejpam-4520	210	24	is	be	AUX
ejpam-4520	210	25	n+m+	n+m+	X
ejpam-4520	210	26	2	2	NUM
ejpam-4520	210	27	.	.	PUNCT
ejpam-4520	211	1	it	it	PRON
ejpam-4520	211	2	implies	imply	VERB
ejpam-4520	211	3	the	the	DET
ejpam-4520	211	4	edge	edge	NOUN
ejpam-4520	211	5	weights	weight	NOUN
ejpam-4520	211	6	of	of	ADP
ejpam-4520	211	7	f	f	NOUN
ejpam-4520	211	8	:	:	PUNCT
ejpam-4520	211	9	v	v	X
ejpam-4520	211	10	(	(	PUNCT
ejpam-4520	211	11	sn	sn	PROPN
ejpam-4520	211	12	⊙	⊙	PROPN
ejpam-4520	211	13	sm	sm	PROPN
ejpam-4520	211	14	)	)	PUNCT
ejpam-4520	211	15	→	→	PUNCT
ejpam-4520	211	16	{	{	PUNCT
ejpam-4520	211	17	1	1	NUM
ejpam-4520	211	18	,	,	PUNCT
ejpam-4520	211	19	2	2	NUM
ejpam-4520	211	20	,	,	PUNCT
ejpam-4520	211	21	...	...	PUNCT
ejpam-4520	211	22	,	,	PUNCT
ejpam-4520	211	23	2n	2n	NUM
ejpam-4520	211	24	+	+	CCONJ
ejpam-4520	211	25	nm	nm	ADJ
ejpam-4520	211	26	+	+	NOUN
ejpam-4520	211	27	2	2	NUM
ejpam-4520	211	28	}	}	PUNCT
ejpam-4520	211	29	induces	induce	VERB
ejpam-4520	211	30	a	a	DET
ejpam-4520	211	31	rainbow	rainbow	NOUN
ejpam-4520	211	32	antimagic	antimagic	ADJ
ejpam-4520	211	33	coloring	coloring	NOUN
ejpam-4520	211	34	of	of	ADP
ejpam-4520	211	35	m	m	PROPN
ejpam-4520	211	36	+	+	NOUN
ejpam-4520	211	37	n	n	CCONJ
ejpam-4520	211	38	+	+	CCONJ
ejpam-4520	211	39	2	2	NUM
ejpam-4520	211	40	colors	color	NOUN
ejpam-4520	211	41	.	.	PUNCT
ejpam-4520	212	1	thus	thus	ADV
ejpam-4520	212	2	rac(sn	rac(sn	VERB
ejpam-4520	212	3	⊙	⊙	PROPN
ejpam-4520	212	4	sm	sm	PROPN
ejpam-4520	212	5	)	)	PUNCT
ejpam-4520	212	6	≤	≤	NOUN
ejpam-4520	212	7	n	n	PROPN
ejpam-4520	212	8	+	+	NOUN
ejpam-4520	212	9	m	m	VERB
ejpam-4520	212	10	+	+	ADJ
ejpam-4520	212	11	2	2	NUM
ejpam-4520	212	12	.	.	PUNCT
ejpam-4520	212	13	comparing	compare	VERB
ejpam-4520	212	14	the	the	DET
ejpam-4520	212	15	two	two	NUM
ejpam-4520	212	16	bounds	bound	NOUN
ejpam-4520	212	17	,	,	PUNCT
ejpam-4520	212	18	we	we	PRON
ejpam-4520	212	19	have	have	VERB
ejpam-4520	212	20	the	the	DET
ejpam-4520	212	21	exact	exact	ADJ
ejpam-4520	212	22	value	value	NOUN
ejpam-4520	212	23	of	of	ADP
ejpam-4520	212	24	rac(sn	rac(sn	PROPN
ejpam-4520	212	25	⊙	⊙	PROPN
ejpam-4520	212	26	sm	sm	PROPN
ejpam-4520	212	27	)	)	PUNCT
ejpam-4520	212	28	=	=	PUNCT
ejpam-4520	212	29	n+m+	n+m+	X
ejpam-4520	212	30	2	2	NUM
ejpam-4520	212	31	.	.	PUNCT
ejpam-4520	213	1	the	the	DET
ejpam-4520	213	2	next	next	ADJ
ejpam-4520	213	3	step	step	NOUN
ejpam-4520	213	4	,	,	PUNCT
ejpam-4520	213	5	evaluate	evaluate	VERB
ejpam-4520	213	6	to	to	PART
ejpam-4520	213	7	prove	prove	VERB
ejpam-4520	213	8	the	the	DET
ejpam-4520	213	9	existence	existence	NOUN
ejpam-4520	213	10	of	of	ADP
ejpam-4520	213	11	a	a	DET
ejpam-4520	213	12	rainbow	rainbow	NOUN
ejpam-4520	213	13	u−v	u−v	PUNCT
ejpam-4520	213	14	path	path	PROPN
ejpam-4520	213	15	sn⊙sm	sn⊙sm	PROPN
ejpam-4520	213	16	.	.	PUNCT
ejpam-4520	214	1	based	base	VERB
ejpam-4520	214	2	on	on	ADP
ejpam-4520	214	3	the	the	DET
ejpam-4520	214	4	definition	definition	NOUN
ejpam-4520	214	5	of	of	ADP
ejpam-4520	214	6	the	the	DET
ejpam-4520	214	7	graph	graph	NOUN
ejpam-4520	214	8	sn⊙sm	sn⊙sm	NOUN
ejpam-4520	214	9	,	,	PUNCT
ejpam-4520	214	10	then	then	ADV
ejpam-4520	214	11	the	the	DET
ejpam-4520	214	12	graph	graph	NOUN
ejpam-4520	214	13	sn⊙sm	sn⊙sm	NOUN
ejpam-4520	214	14	contains	contain	VERB
ejpam-4520	214	15	one	one	NUM
ejpam-4520	214	16	graph	graph	NOUN
ejpam-4520	214	17	sn	sn	PROPN
ejpam-4520	214	18	and	and	CCONJ
ejpam-4520	214	19	|v	|v	PROPN
ejpam-4520	214	20	(	(	PUNCT
ejpam-4520	214	21	sn)|	sn)|	NOUN
ejpam-4520	214	22	copies	copy	NOUN
ejpam-4520	214	23	of	of	ADP
ejpam-4520	214	24	k1	k1	PROPN
ejpam-4520	214	25	+	+	CCONJ
ejpam-4520	214	26	sm	sm	PROPN
ejpam-4520	214	27	,	,	PUNCT
ejpam-4520	214	28	so	so	SCONJ
ejpam-4520	214	29	that	that	SCONJ
ejpam-4520	214	30	we	we	PRON
ejpam-4520	214	31	can	can	AUX
ejpam-4520	214	32	evaluate	evaluate	VERB
ejpam-4520	214	33	the	the	DET
ejpam-4520	214	34	rainbow	rainbow	NOUN
ejpam-4520	214	35	u	u	NOUN
ejpam-4520	214	36	−	−	PROPN
ejpam-4520	214	37	v	v	ADP
ejpam-4520	214	38	path	path	NOUN
ejpam-4520	214	39	of	of	ADP
ejpam-4520	214	40	the	the	DET
ejpam-4520	214	41	graph	graph	NOUN
ejpam-4520	214	42	sn	sn	PROPN
ejpam-4520	214	43	⊙	⊙	PROPN
ejpam-4520	214	44	sm	sm	INTJ
ejpam-4520	214	45	by	by	ADP
ejpam-4520	214	46	evaluating	evaluate	VERB
ejpam-4520	214	47	the	the	DET
ejpam-4520	214	48	rainbow	rainbow	NOUN
ejpam-4520	214	49	u−	u−	PROPN
ejpam-4520	214	50	v	v	ADP
ejpam-4520	214	51	path	path	NOUN
ejpam-4520	214	52	on	on	ADP
ejpam-4520	214	53	the	the	DET
ejpam-4520	214	54	graph	graph	NOUN
ejpam-4520	214	55	sn	sn	PROPN
ejpam-4520	214	56	and	and	CCONJ
ejpam-4520	214	57	the	the	DET
ejpam-4520	214	58	graph	graph	NOUN
ejpam-4520	214	59	k1	k1	NOUN
ejpam-4520	214	60	+	+	CCONJ
ejpam-4520	214	61	sm	sm	PROPN
ejpam-4520	214	62	.	.	PUNCT
ejpam-4520	215	1	since	since	SCONJ
ejpam-4520	215	2	diam(k1	diam(k1	PROPN
ejpam-4520	215	3	+	+	CCONJ
ejpam-4520	215	4	sm	sm	NOUN
ejpam-4520	215	5	)	)	PUNCT
ejpam-4520	215	6	=	=	SYM
ejpam-4520	215	7	2	2	NUM
ejpam-4520	215	8	,	,	PUNCT
ejpam-4520	215	9	based	base	VERB
ejpam-4520	215	10	on	on	ADP
ejpam-4520	215	11	theorem	theorem	NOUN
ejpam-4520	215	12	2	2	NUM
ejpam-4520	215	13	,	,	PUNCT
ejpam-4520	215	14	there	there	PRON
ejpam-4520	215	15	is	be	VERB
ejpam-4520	215	16	a	a	DET
ejpam-4520	215	17	rainbow	rainbow	NOUN
ejpam-4520	215	18	u	u	NOUN
ejpam-4520	215	19	−	−	PROPN
ejpam-4520	215	20	v	v	ADP
ejpam-4520	215	21	path	path	NOUN
ejpam-4520	215	22	for	for	ADP
ejpam-4520	215	23	every	every	DET
ejpam-4520	215	24	u	u	NOUN
ejpam-4520	215	25	,	,	PUNCT
ejpam-4520	215	26	v	v	PROPN
ejpam-4520	215	27	∈	∈	PROPN
ejpam-4520	215	28	v	v	NOUN
ejpam-4520	215	29	(	(	PUNCT
ejpam-4520	215	30	k1	k1	NOUN
ejpam-4520	215	31	+	+	CCONJ
ejpam-4520	215	32	sm	sm	NOUN
ejpam-4520	215	33	)	)	PUNCT
ejpam-4520	215	34	.	.	PUNCT
ejpam-4520	216	1	based	base	VERB
ejpam-4520	216	2	on	on	ADP
ejpam-4520	216	3	theorem	theorem	ADJ
ejpam-4520	216	4	3	3	NUM
ejpam-4520	216	5	,	,	PUNCT
ejpam-4520	216	6	rac(sn	rac(sn	ADJ
ejpam-4520	216	7	)	)	PUNCT
ejpam-4520	216	8	=	=	VERB
ejpam-4520	216	9	n.	n.	NOUN
ejpam-4520	216	10	since	since	SCONJ
ejpam-4520	216	11	sn	sn	PROPN
ejpam-4520	216	12	has	have	VERB
ejpam-4520	216	13	n	n	NUM
ejpam-4520	216	14	edges	edge	NOUN
ejpam-4520	216	15	,	,	PUNCT
ejpam-4520	216	16	there	there	PRON
ejpam-4520	216	17	is	be	VERB
ejpam-4520	216	18	a	a	DET
ejpam-4520	216	19	rainbow	rainbow	NOUN
ejpam-4520	216	20	u	u	NOUN
ejpam-4520	216	21	−	−	PROPN
ejpam-4520	216	22	v	v	ADP
ejpam-4520	216	23	path	path	NOUN
ejpam-4520	216	24	for	for	ADP
ejpam-4520	216	25	every	every	DET
ejpam-4520	216	26	u	u	NOUN
ejpam-4520	216	27	,	,	PUNCT
ejpam-4520	216	28	v	v	PROPN
ejpam-4520	216	29	∈	∈	PROPN
ejpam-4520	216	30	v	v	NOUN
ejpam-4520	216	31	(	(	PUNCT
ejpam-4520	216	32	sn	sn	PROPN
ejpam-4520	216	33	)	)	PUNCT
ejpam-4520	216	34	.	.	PUNCT
ejpam-4520	217	1	therefore	therefore	ADV
ejpam-4520	217	2	,	,	PUNCT
ejpam-4520	217	3	according	accord	VERB
ejpam-4520	217	4	to	to	ADP
ejpam-4520	217	5	the	the	DET
ejpam-4520	217	6	explanation	explanation	NOUN
ejpam-4520	217	7	,	,	PUNCT
ejpam-4520	217	8	it	it	PRON
ejpam-4520	217	9	can	can	AUX
ejpam-4520	217	10	be	be	AUX
ejpam-4520	217	11	seen	see	VERB
ejpam-4520	217	12	that	that	SCONJ
ejpam-4520	217	13	there	there	PRON
ejpam-4520	217	14	is	be	VERB
ejpam-4520	217	15	a	a	DET
ejpam-4520	217	16	rainbow	rainbow	NOUN
ejpam-4520	217	17	u−	u−	NOUN
ejpam-4520	217	18	v	v	NUM
ejpam-4520	217	19	path	path	NOUN
ejpam-4520	217	20	for	for	ADP
ejpam-4520	217	21	every	every	DET
ejpam-4520	217	22	u	u	NOUN
ejpam-4520	217	23	,	,	PUNCT
ejpam-4520	217	24	v	v	PROPN
ejpam-4520	217	25	∈	∈	PROPN
ejpam-4520	217	26	v	v	NOUN
ejpam-4520	217	27	(	(	PUNCT
ejpam-4520	217	28	sn	sn	PROPN
ejpam-4520	217	29	⊙	⊙	PROPN
ejpam-4520	217	30	sm	sm	PROPN
ejpam-4520	217	31	)	)	PUNCT
ejpam-4520	217	32	.	.	PUNCT
ejpam-4520	218	1	rainbow	rainbow	VERB
ejpam-4520	218	2	antimagic	antimagic	ADJ
ejpam-4520	218	3	coloring	coloring	NOUN
ejpam-4520	218	4	of	of	ADP
ejpam-4520	218	5	graph	graph	NOUN
ejpam-4520	218	6	sn	sn	PROPN
ejpam-4520	218	7	⊙	⊙	PROPN
ejpam-4520	218	8	sm	sm	PROPN
ejpam-4520	218	9	can	can	AUX
ejpam-4520	218	10	be	be	AUX
ejpam-4520	218	11	seen	see	VERB
ejpam-4520	218	12	in	in	ADP
ejpam-4520	218	13	figure	figure	NOUN
ejpam-4520	218	14	3	3	NUM
ejpam-4520	218	15	.	.	PUNCT
ejpam-4520	218	16	theorem	theorem	VERB
ejpam-4520	218	17	8	8	NUM
ejpam-4520	218	18	.	.	PUNCT
ejpam-4520	219	1	for	for	ADP
ejpam-4520	219	2	n	n	NOUN
ejpam-4520	219	3	=	=	SYM
ejpam-4520	219	4	2	2	NUM
ejpam-4520	219	5	,	,	PUNCT
ejpam-4520	219	6	m	m	VERB
ejpam-4520	219	7	≥	≥	NOUN
ejpam-4520	219	8	3	3	NUM
ejpam-4520	219	9	and	and	CCONJ
ejpam-4520	219	10	odd	odd	ADJ
ejpam-4520	219	11	integers	integer	NOUN
ejpam-4520	219	12	p	p	X
ejpam-4520	219	13	≥	≥	NUM
ejpam-4520	219	14	3	3	NUM
ejpam-4520	219	15	,	,	PUNCT
ejpam-4520	219	16	rac(sn	rac(sn	ADJ
ejpam-4520	219	17	,	,	PUNCT
ejpam-4520	219	18	p	p	NOUN
ejpam-4520	219	19	⊙	⊙	PROPN
ejpam-4520	219	20	sm	sm	PROPN
ejpam-4520	219	21	)	)	PUNCT
ejpam-4520	219	22	=	=	SYM
ejpam-4520	219	23	m+	m+	NUM
ejpam-4520	219	24	p+	p+	NOUN
ejpam-4520	219	25	5	5	NUM
ejpam-4520	219	26	.	.	PUNCT
ejpam-4520	219	27	proof	proof	NOUN
ejpam-4520	219	28	.	.	PUNCT
ejpam-4520	220	1	the	the	DET
ejpam-4520	220	2	graph	graph	NOUN
ejpam-4520	220	3	sn	sn	PROPN
ejpam-4520	220	4	,	,	PUNCT
ejpam-4520	220	5	p	p	PROPN
ejpam-4520	220	6	⊙	⊙	PROPN
ejpam-4520	220	7	sm	sm	PROPN
ejpam-4520	220	8	is	be	AUX
ejpam-4520	220	9	a	a	DET
ejpam-4520	220	10	connected	connected	ADJ
ejpam-4520	220	11	graph	graph	NOUN
ejpam-4520	220	12	with	with	ADP
ejpam-4520	220	13	vertex	vertex	NOUN
ejpam-4520	220	14	set	set	VERB
ejpam-4520	220	15	v	v	NOUN
ejpam-4520	220	16	(	(	PUNCT
ejpam-4520	220	17	sn	sn	PROPN
ejpam-4520	220	18	,	,	PUNCT
ejpam-4520	220	19	p	p	PROPN
ejpam-4520	220	20	⊙	⊙	PROPN
ejpam-4520	220	21	sm	sm	PROPN
ejpam-4520	220	22	)	)	PUNCT
ejpam-4520	220	23	=	=	PRON
ejpam-4520	220	24	{	{	PUNCT
ejpam-4520	220	25	x	x	NOUN
ejpam-4520	220	26	,	,	PUNCT
ejpam-4520	220	27	y	y	PROPN
ejpam-4520	220	28	,	,	PUNCT
ejpam-4520	220	29	b	b	PROPN
ejpam-4520	220	30	,	,	PUNCT
ejpam-4520	220	31	z	z	NOUN
ejpam-4520	220	32	}	}	PUNCT
ejpam-4520	220	33	∪	∪	X
ejpam-4520	220	34	{	{	PUNCT
ejpam-4520	220	35	xi	xi	PROPN
ejpam-4520	220	36	,	,	PUNCT
ejpam-4520	220	37	x0i	x0i	PROPN
ejpam-4520	220	38	,	,	PUNCT
ejpam-4520	220	39	1	1	NUM
ejpam-4520	220	40	≤	≤	NUM
ejpam-4520	220	41	i	i	X
ejpam-4520	220	42	≤	≤	ADV
ejpam-4520	220	43	2	2	NUM
ejpam-4520	220	44	}	}	PUNCT
ejpam-4520	220	45	∪	∪	NOUN
ejpam-4520	220	46	{	{	PUNCT
ejpam-4520	220	47	yj	yj	PROPN
ejpam-4520	220	48	,	,	PUNCT
ejpam-4520	220	49	y0j	y0j	PROPN
ejpam-4520	220	50	,	,	PUNCT
ejpam-4520	220	51	1	1	NUM
ejpam-4520	220	52	≤	≤	NUM
ejpam-4520	220	53	j	j	PROPN
ejpam-4520	220	54	≤	≤	ADV
ejpam-4520	220	55	p	p	X
ejpam-4520	220	56	}	}	PUNCT
ejpam-4520	220	57	∪	∪	X
ejpam-4520	220	58	{	{	PUNCT
ejpam-4520	220	59	bk	bk	PROPN
ejpam-4520	220	60	,	,	PUNCT
ejpam-4520	220	61	zk	zk	PROPN
ejpam-4520	220	62	,	,	PUNCT
ejpam-4520	220	63	1	1	NUM
ejpam-4520	220	64	≤	≤	NUM
ejpam-4520	220	65	k	k	X
ejpam-4520	220	66	≤	≤	NUM
ejpam-4520	220	67	m	m	VERB
ejpam-4520	220	68	}	}	PUNCT
ejpam-4520	220	69	∪	∪	ADJ
ejpam-4520	220	70	{	{	PUNCT
ejpam-4520	220	71	xik	xik	PROPN
ejpam-4520	220	72	,	,	PUNCT
ejpam-4520	220	73	1	1	NUM
ejpam-4520	220	74	≤	≤	NUM
ejpam-4520	220	75	i	i	X
ejpam-4520	220	76	≤	≤	ADV
ejpam-4520	220	77	2	2	NUM
ejpam-4520	220	78	,	,	PUNCT
ejpam-4520	220	79	1	1	NUM
ejpam-4520	220	80	≤	≤	NUM
ejpam-4520	220	81	k	k	X
ejpam-4520	220	82	≤	≤	NUM
ejpam-4520	220	83	m	m	VERB
ejpam-4520	220	84	}	}	PUNCT
ejpam-4520	220	85	∪	∪	ADJ
ejpam-4520	220	86	{	{	PUNCT
ejpam-4520	220	87	yjk	yjk	NOUN
ejpam-4520	220	88	,	,	PUNCT
ejpam-4520	220	89	1	1	NUM
ejpam-4520	220	90	≤	≤	NUM
ejpam-4520	220	91	j	j	PROPN
ejpam-4520	220	92	≤	≤	PROPN
ejpam-4520	220	93	p	p	X
ejpam-4520	220	94	,	,	PUNCT
ejpam-4520	220	95	1	1	NUM
ejpam-4520	220	96	≤	≤	NUM
ejpam-4520	220	97	k	k	X
ejpam-4520	220	98	≤	≤	NUM
ejpam-4520	220	99	m	m	VERB
ejpam-4520	220	100	}	}	PUNCT
ejpam-4520	220	101	and	and	CCONJ
ejpam-4520	220	102	edge	edge	VERB
ejpam-4520	220	103	set	set	VERB
ejpam-4520	220	104	e(sn	e(sn	PROPN
ejpam-4520	220	105	,	,	PUNCT
ejpam-4520	220	106	p	p	NOUN
ejpam-4520	220	107	⊙	⊙	PROPN
ejpam-4520	220	108	sm	sm	PROPN
ejpam-4520	220	109	)	)	PUNCT
ejpam-4520	220	110	=	=	PRON
ejpam-4520	220	111	{	{	PUNCT
ejpam-4520	220	112	xy	xy	PROPN
ejpam-4520	220	113	,	,	PUNCT
ejpam-4520	220	114	xb	xb	PROPN
ejpam-4520	220	115	,	,	PUNCT
ejpam-4520	220	116	yz	yz	PROPN
ejpam-4520	220	117	}	}	PUNCT
ejpam-4520	220	118	∪	∪	ADJ
ejpam-4520	220	119	{	{	PUNCT
ejpam-4520	220	120	xxi	xxi	PROPN
ejpam-4520	220	121	,	,	PUNCT
ejpam-4520	220	122	xix0i	xix0i	PROPN
ejpam-4520	220	123	,	,	PUNCT
ejpam-4520	220	124	1	1	NUM
ejpam-4520	220	125	≤	≤	NUM
ejpam-4520	220	126	i	i	X
ejpam-4520	220	127	≤	≤	ADV
ejpam-4520	220	128	2	2	NUM
ejpam-4520	220	129	}	}	PUNCT
ejpam-4520	220	130	∪	∪	NOUN
ejpam-4520	220	131	{	{	PUNCT
ejpam-4520	220	132	yyj	yyj	PROPN
ejpam-4520	220	133	,	,	PUNCT
ejpam-4520	220	134	yjy0j	yjy0j	PROPN
ejpam-4520	220	135	,	,	PUNCT
ejpam-4520	220	136	1	1	NUM
ejpam-4520	220	137	≤	≤	NUM
ejpam-4520	220	138	j	j	PROPN
ejpam-4520	220	139	≤	≤	ADV
ejpam-4520	220	140	p	p	X
ejpam-4520	220	141	}	}	PUNCT
ejpam-4520	220	142	∪	∪	X
ejpam-4520	220	143	{	{	PUNCT
ejpam-4520	220	144	xbk	xbk	PROPN
ejpam-4520	220	145	,	,	PUNCT
ejpam-4520	220	146	bbk	bbk	INTJ
ejpam-4520	220	147	,	,	PUNCT
ejpam-4520	220	148	yzk	yzk	PROPN
ejpam-4520	220	149	,	,	PUNCT
ejpam-4520	220	150	zzk	zzk	NOUN
ejpam-4520	220	151	,	,	PUNCT
ejpam-4520	220	152	1	1	NUM
ejpam-4520	220	153	≤	≤	NUM
ejpam-4520	220	154	i	i	X
ejpam-4520	220	155	≤	≤	NOUN
ejpam-4520	220	156	m	m	VERB
ejpam-4520	220	157	}	}	PUNCT
ejpam-4520	220	158	∪	∪	ADJ
ejpam-4520	220	159	{	{	PUNCT
ejpam-4520	220	160	xixik	xixik	PROPN
ejpam-4520	220	161	,	,	PUNCT
ejpam-4520	220	162	x0ixik	x0ixik	PROPN
ejpam-4520	220	163	,	,	PUNCT
ejpam-4520	220	164	1	1	NUM
ejpam-4520	220	165	≤	≤	NUM
ejpam-4520	220	166	i	i	X
ejpam-4520	220	167	≤	≤	ADV
ejpam-4520	220	168	2	2	NUM
ejpam-4520	220	169	,	,	PUNCT
ejpam-4520	220	170	1	1	NUM
ejpam-4520	220	171	≤	≤	NUM
ejpam-4520	220	172	k	k	X
ejpam-4520	220	173	≤	≤	NUM
ejpam-4520	220	174	m	m	VERB
ejpam-4520	220	175	}	}	PUNCT
ejpam-4520	220	176	∪	∪	ADJ
ejpam-4520	220	177	{	{	PUNCT
ejpam-4520	220	178	yjyjk	yjyjk	NOUN
ejpam-4520	220	179	,	,	PUNCT
ejpam-4520	220	180	y0jyjk	y0jyjk	PROPN
ejpam-4520	220	181	,	,	PUNCT
ejpam-4520	220	182	1	1	NUM
ejpam-4520	220	183	≤	≤	NUM
ejpam-4520	220	184	j	j	PROPN
ejpam-4520	220	185	≤	≤	PROPN
ejpam-4520	220	186	p	p	X
ejpam-4520	220	187	,	,	PUNCT
ejpam-4520	220	188	1	1	NUM
ejpam-4520	220	189	≤	≤	NUM
ejpam-4520	220	190	k	k	X
ejpam-4520	220	191	≤	≤	NUM
ejpam-4520	220	192	m	m	PROPN
ejpam-4520	220	193	}	}	PUNCT
ejpam-4520	220	194	.	.	PUNCT
ejpam-4520	221	1	the	the	DET
ejpam-4520	221	2	cardinality	cardinality	NOUN
ejpam-4520	221	3	of	of	ADP
ejpam-4520	221	4	|v	|v	PROPN
ejpam-4520	221	5	(	(	PUNCT
ejpam-4520	221	6	sn	sn	PROPN
ejpam-4520	221	7	,	,	PUNCT
ejpam-4520	221	8	p	p	NOUN
ejpam-4520	221	9	⊙	⊙	X
ejpam-4520	221	10	sm)|	sm)|	X
ejpam-4520	221	11	=	=	SYM
ejpam-4520	221	12	2p+4m+	2p+4m+	NUM
ejpam-4520	221	13	pm+8	pm+8	NOUN
ejpam-4520	221	14	and	and	CCONJ
ejpam-4520	221	15	the	the	DET
ejpam-4520	221	16	cardinality	cardinality	NOUN
ejpam-4520	221	17	of	of	ADP
ejpam-4520	221	18	|e(sn	|e(sn	PROPN
ejpam-4520	221	19	,	,	PUNCT
ejpam-4520	221	20	p	p	NOUN
ejpam-4520	221	21	⊙	⊙	X
ejpam-4520	221	22	sm)|	sm)|	PROPN
ejpam-4520	221	23	=	=	NOUN
ejpam-4520	221	24	2p+	2p+	NUM
ejpam-4520	221	25	8m+	8m+	NUM
ejpam-4520	221	26	2pm+	2pm+	NUM
ejpam-4520	221	27	7	7	NUM
ejpam-4520	221	28	.	.	PUNCT
ejpam-4520	221	29	to	to	PART
ejpam-4520	221	30	prove	prove	VERB
ejpam-4520	221	31	the	the	DET
ejpam-4520	221	32	rainbow	rainbow	NOUN
ejpam-4520	221	33	antimagic	antimagic	ADJ
ejpam-4520	221	34	connection	connection	NOUN
ejpam-4520	221	35	number	number	NOUN
ejpam-4520	221	36	of	of	ADP
ejpam-4520	221	37	rac(sn	rac(sn	ADJ
ejpam-4520	221	38	,	,	PUNCT
ejpam-4520	221	39	p⊙sm	p⊙sm	NOUN
ejpam-4520	221	40	)	)	PUNCT
ejpam-4520	221	41	,	,	PUNCT
ejpam-4520	221	42	first	first	ADV
ejpam-4520	221	43	we	we	PRON
ejpam-4520	221	44	have	have	VERB
ejpam-4520	221	45	to	to	PART
ejpam-4520	221	46	show	show	VERB
ejpam-4520	221	47	that	that	SCONJ
ejpam-4520	221	48	the	the	DET
ejpam-4520	221	49	lower	low	ADJ
ejpam-4520	221	50	bound	bind	VERB
ejpam-4520	221	51	of	of	ADP
ejpam-4520	221	52	rac(sn	rac(sn	ADJ
ejpam-4520	221	53	,	,	PUNCT
ejpam-4520	221	54	p⊙sm	p⊙sm	NOUN
ejpam-4520	221	55	)	)	PUNCT
ejpam-4520	221	56	.	.	PUNCT
ejpam-4520	222	1	based	base	VERB
ejpam-4520	222	2	on	on	ADP
ejpam-4520	222	3	lemma	lemma	PROPN
ejpam-4520	222	4	1	1	NUM
ejpam-4520	222	5	,	,	PUNCT
ejpam-4520	222	6	we	we	PRON
ejpam-4520	222	7	have	have	AUX
ejpam-4520	222	8	rac(sn	rac(sn	VERB
ejpam-4520	222	9	,	,	PUNCT
ejpam-4520	222	10	p⊙sm	p⊙sm	NOUN
ejpam-4520	222	11	)	)	PUNCT
ejpam-4520	222	12	≥	≥	PROPN
ejpam-4520	222	13	susilowati	susilowati	PROPN
ejpam-4520	222	14	et	et	PROPN
ejpam-4520	222	15	.	.	PUNCT
ejpam-4520	223	1	al	al	PROPN
ejpam-4520	223	2	/	/	PUNCT
ejpam-4520	223	3	eur	eur	PROPN
ejpam-4520	223	4	.	.	PUNCT
ejpam-4520	224	1	j.	j.	PROPN
ejpam-4520	224	2	pure	pure	PROPN
ejpam-4520	224	3	appl	appl	PROPN
ejpam-4520	224	4	.	.	PROPN
ejpam-4520	224	5	math	math	PROPN
ejpam-4520	224	6	,	,	PUNCT
ejpam-4520	224	7	16	16	NUM
ejpam-4520	224	8	(	(	PUNCT
ejpam-4520	224	9	1	1	NUM
ejpam-4520	224	10	)	)	PUNCT
ejpam-4520	224	11	(	(	PUNCT
ejpam-4520	224	12	2023	2023	NUM
ejpam-4520	224	13	)	)	PUNCT
ejpam-4520	224	14	,	,	PUNCT
ejpam-4520	224	15	271	271	NUM
ejpam-4520	224	16	-	-	SYM
ejpam-4520	224	17	285	285	NUM
ejpam-4520	224	18	278	278	NUM
ejpam-4520	224	19	y4	y4	ADJ
ejpam-4520	224	20	y2	y2	NOUN
ejpam-4520	224	21	y3	y3	PROPN
ejpam-4520	224	22	y43	y43	PROPN
ejpam-4520	224	23	y42	y42	NOUN
ejpam-4520	224	24	y41	y41	NOUN
ejpam-4520	224	25	y51	y51	NOUN
ejpam-4520	224	26	y52	y52	PROPN
ejpam-4520	224	27	y5	y5	PROPN
ejpam-4520	224	28	y53	y53	PROPN
ejpam-4520	224	29	y31	y31	PROPN
ejpam-4520	225	1	y32	y32	PROPN
ejpam-4520	225	2	y33	y33	PROPN
ejpam-4520	225	3	y21	y21	PROPN
ejpam-4520	225	4	y22	y22	PROPN
ejpam-4520	225	5	y23	y23	NOUN
ejpam-4520	225	6	y11	y11	NOUN
ejpam-4520	225	7	y12	y12	PROPN
ejpam-4520	225	8	y13	y13	PROPN
ejpam-4520	225	9	x04	x04	PROPN
ejpam-4520	225	10	x01	x01	PROPN
ejpam-4520	225	11	x02	x02	PROPN
ejpam-4520	225	12	x03	x03	PROPN
ejpam-4520	225	13	x0	x0	PROPN
ejpam-4520	225	14	y1	y1	PROPN
ejpam-4520	225	15	6	6	NUM
ejpam-4520	225	16	12	12	NUM
ejpam-4520	225	17	17	17	NUM
ejpam-4520	225	18	22	22	NUM
ejpam-4520	225	19	15	15	NUM
ejpam-4520	225	20	21	21	NUM
ejpam-4520	225	21	26	26	NUM
ejpam-4520	225	22	31	31	NUM
ejpam-4520	225	23	16	16	NUM
ejpam-4520	225	24	21	21	NUM
ejpam-4520	225	25	26	26	NUM
ejpam-4520	225	26	21	21	NUM
ejpam-4520	225	27	26	26	NUM
ejpam-4520	225	28	31	31	NUM
ejpam-4520	225	29	16	16	NUM
ejpam-4520	225	30	21	21	NUM
ejpam-4520	225	31	26	26	NUM
ejpam-4520	225	32	139	139	NUM
ejpam-4520	225	33	1613	1613	NUM
ejpam-4520	225	34	21	21	NUM
ejpam-4520	225	35	26	26	NUM
ejpam-4520	225	36	21	21	NUM
ejpam-4520	225	37	26	26	NUM
ejpam-4520	225	38	31	31	NUM
ejpam-4520	225	39	1116	1116	NUM
ejpam-4520	225	40	21	21	NUM
ejpam-4520	225	41	26	26	NUM
ejpam-4520	225	42	21	21	NUM
ejpam-4520	225	43	26	26	NUM
ejpam-4520	225	44	31	31	NUM
ejpam-4520	225	45	16	16	NUM
ejpam-4520	225	46	21	21	NUM
ejpam-4520	225	47	26	26	NUM
ejpam-4520	225	48	31	31	NUM
ejpam-4520	225	49	7	7	NUM
ejpam-4520	225	50	26	26	NUM
ejpam-4520	225	51	21	21	NUM
ejpam-4520	225	52	7	7	NUM
ejpam-4520	225	53	9	9	NUM
ejpam-4520	225	54	11	11	NUM
ejpam-4520	225	55	4	4	NUM
ejpam-4520	225	56	211611	211611	NUM
ejpam-4520	225	57	10	10	NUM
ejpam-4520	225	58	5	5	NUM
ejpam-4520	225	59	23	23	NUM
ejpam-4520	225	60	18	18	NUM
ejpam-4520	225	61	13	13	NUM
ejpam-4520	225	62	3	3	NUM
ejpam-4520	225	63	8	8	NUM
ejpam-4520	225	64	24	24	NUM
ejpam-4520	225	65	19	19	NUM
ejpam-4520	225	66	14	14	NUM
ejpam-4520	225	67	7	7	NUM
ejpam-4520	225	68	2	2	NUM
ejpam-4520	225	69	25	25	NUM
ejpam-4520	225	70	20	20	NUM
ejpam-4520	225	71	15	15	NUM
ejpam-4520	225	72	1	1	NUM
ejpam-4520	225	73	9	9	NUM
ejpam-4520	225	74	figure	figure	NOUN
ejpam-4520	225	75	3	3	NUM
ejpam-4520	225	76	:	:	PUNCT
ejpam-4520	225	77	rainbow	rainbow	VERB
ejpam-4520	225	78	antimagic	antimagic	ADJ
ejpam-4520	225	79	coloring	coloring	NOUN
ejpam-4520	225	80	of	of	ADP
ejpam-4520	225	81	graph	graph	NOUN
ejpam-4520	225	82	s4	s4	PROPN
ejpam-4520	225	83	⊙	⊙	PROPN
ejpam-4520	225	84	s3	s3	PROPN
ejpam-4520	225	85	.	.	PROPN
ejpam-4520	225	86	rac(sn	rac(sn	PROPN
ejpam-4520	225	87	,	,	PUNCT
ejpam-4520	225	88	p	p	NOUN
ejpam-4520	225	89	)	)	PUNCT
ejpam-4520	226	1	+	+	NOUN
ejpam-4520	226	2	m+	m+	NUM
ejpam-4520	226	3	2	2	NUM
ejpam-4520	226	4	.	.	PUNCT
ejpam-4520	226	5	since	since	SCONJ
ejpam-4520	226	6	rac(sn	rac(sn	VERB
ejpam-4520	226	7	,	,	PUNCT
ejpam-4520	226	8	p	p	NOUN
ejpam-4520	226	9	)	)	PUNCT
ejpam-4520	226	10	=	=	SYM
ejpam-4520	226	11	p+	p+	X
ejpam-4520	226	12	3	3	NUM
ejpam-4520	226	13	,	,	PUNCT
ejpam-4520	226	14	thus	thus	ADV
ejpam-4520	226	15	,	,	PUNCT
ejpam-4520	226	16	rac(sn	rac(sn	ADJ
ejpam-4520	226	17	,	,	PUNCT
ejpam-4520	226	18	p	p	PROPN
ejpam-4520	226	19	⊙	⊙	PROPN
ejpam-4520	226	20	sm	sm	PROPN
ejpam-4520	226	21	)	)	PUNCT
ejpam-4520	226	22	≥	≥	PROPN
ejpam-4520	226	23	m+	m+	NUM
ejpam-4520	226	24	p+	p+	PROPN
ejpam-4520	226	25	5	5	NUM
ejpam-4520	226	26	.	.	PUNCT
ejpam-4520	227	1	secondly	secondly	ADV
ejpam-4520	227	2	,	,	PUNCT
ejpam-4520	227	3	we	we	PRON
ejpam-4520	227	4	have	have	VERB
ejpam-4520	227	5	to	to	PART
ejpam-4520	227	6	show	show	VERB
ejpam-4520	227	7	the	the	DET
ejpam-4520	227	8	upper	upper	ADJ
ejpam-4520	227	9	bound	bind	VERB
ejpam-4520	227	10	of	of	ADP
ejpam-4520	227	11	rac(sn	rac(sn	NOUN
ejpam-4520	227	12	,	,	PUNCT
ejpam-4520	227	13	p	p	NOUN
ejpam-4520	227	14	⊙	⊙	PROPN
ejpam-4520	227	15	sm	sm	PROPN
ejpam-4520	227	16	)	)	PUNCT
ejpam-4520	227	17	.	.	PUNCT
ejpam-4520	228	1	define	define	VERB
ejpam-4520	228	2	the	the	DET
ejpam-4520	228	3	vertex	vertex	NOUN
ejpam-4520	228	4	labeling	labeling	NOUN
ejpam-4520	228	5	f	f	NOUN
ejpam-4520	228	6	:	:	PUNCT
ejpam-4520	228	7	v	v	X
ejpam-4520	228	8	(	(	PUNCT
ejpam-4520	228	9	sn	sn	PROPN
ejpam-4520	228	10	,	,	PUNCT
ejpam-4520	228	11	p	p	PROPN
ejpam-4520	228	12	⊙	⊙	PROPN
ejpam-4520	228	13	sm	sm	PROPN
ejpam-4520	228	14	)	)	PUNCT
ejpam-4520	228	15	→	→	PUNCT
ejpam-4520	228	16	{	{	PUNCT
ejpam-4520	228	17	1	1	NUM
ejpam-4520	228	18	,	,	PUNCT
ejpam-4520	228	19	2	2	NUM
ejpam-4520	228	20	,	,	PUNCT
ejpam-4520	228	21	.	.	PUNCT
ejpam-4520	228	22	.	.	PUNCT
ejpam-4520	228	23	.	.	PUNCT
ejpam-4520	229	1	2p+	2p+	NUM
ejpam-4520	229	2	4m+	4m+	NUM
ejpam-4520	229	3	pm+	pm+	VERB
ejpam-4520	229	4	8	8	NUM
ejpam-4520	229	5	}	}	PUNCT
ejpam-4520	229	6	as	as	SCONJ
ejpam-4520	229	7	follows	follow	VERB
ejpam-4520	229	8	.	.	PUNCT
ejpam-4520	230	1	f(x	f(x	NOUN
ejpam-4520	230	2	)	)	PUNCT
ejpam-4520	231	1	=	=	PRON
ejpam-4520	231	2	p+	p+	VERB
ejpam-4520	231	3	2	2	NUM
ejpam-4520	231	4	f(y	f(y	NOUN
ejpam-4520	231	5	)	)	PUNCT
ejpam-4520	231	6	=	=	PRON
ejpam-4520	231	7	p+	p+	VERB
ejpam-4520	231	8	3	3	NUM
ejpam-4520	231	9	f(xi	f(xi	NUM
ejpam-4520	231	10	)	)	PUNCT
ejpam-4520	231	11	=	=	PRON
ejpam-4520	231	12	{	{	PUNCT
ejpam-4520	231	13	p+	p+	NOUN
ejpam-4520	231	14	5	5	NUM
ejpam-4520	231	15	for	for	ADP
ejpam-4520	231	16	i	i	PRON
ejpam-4520	231	17	=	=	NOUN
ejpam-4520	231	18	1	1	NUM
ejpam-4520	231	19	2p+	2p+	NUM
ejpam-4520	231	20	8	8	NUM
ejpam-4520	231	21	for	for	ADP
ejpam-4520	231	22	i	i	PRON
ejpam-4520	231	23	=	=	SYM
ejpam-4520	231	24	2	2	NUM
ejpam-4520	231	25	f(yj	f(yj	NOUN
ejpam-4520	231	26	)	)	PUNCT
ejpam-4520	232	1	=	=	PRON
ejpam-4520	232	2	{	{	PUNCT
ejpam-4520	232	3	2j	2j	NUM
ejpam-4520	232	4	+	+	CCONJ
ejpam-4520	232	5	1	1	NUM
ejpam-4520	232	6	for	for	ADP
ejpam-4520	232	7	1	1	NUM
ejpam-4520	232	8	≤	≤	NUM
ejpam-4520	232	9	j	j	PROPN
ejpam-4520	232	10	≤	≤	PROPN
ejpam-4520	232	11	⌊p	⌊p	VERB
ejpam-4520	232	12	2	2	NUM
ejpam-4520	232	13	⌋	⌋	NOUN
ejpam-4520	232	14	2j	2j	NOUN
ejpam-4520	232	15	+	+	CCONJ
ejpam-4520	232	16	5	5	NUM
ejpam-4520	232	17	for	for	ADP
ejpam-4520	232	18	⌈p2⌉+	⌈p2⌉+	PROPN
ejpam-4520	232	19	1	1	NUM
ejpam-4520	232	20	≤	≤	NUM
ejpam-4520	232	21	j	j	PROPN
ejpam-4520	232	22	≤	≤	PROPN
ejpam-4520	232	23	p	p	DET
ejpam-4520	232	24	f(x0i	f(x0i	NOUN
ejpam-4520	232	25	)	)	PUNCT
ejpam-4520	232	26	=	=	PRON
ejpam-4520	232	27	{	{	PUNCT
ejpam-4520	232	28	1	1	NUM
ejpam-4520	232	29	for	for	ADP
ejpam-4520	232	30	i	i	PRON
ejpam-4520	232	31	=	=	SYM
ejpam-4520	232	32	1	1	NUM
ejpam-4520	232	33	,	,	PUNCT
ejpam-4520	232	34	p+	p+	VERB
ejpam-4520	232	35	4	4	NUM
ejpam-4520	232	36	for	for	ADP
ejpam-4520	232	37	i	i	PRON
ejpam-4520	232	38	=	=	SYM
ejpam-4520	232	39	2	2	NUM
ejpam-4520	232	40	f(y0j	f(y0j	NOUN
ejpam-4520	232	41	)	)	PUNCT
ejpam-4520	232	42	=	=	PRON
ejpam-4520	232	43	{	{	PUNCT
ejpam-4520	233	1	p+	p+	VERB
ejpam-4520	233	2	2j	2j	NUM
ejpam-4520	233	3	+	+	CCONJ
ejpam-4520	233	4	5	5	NUM
ejpam-4520	233	5	for	for	ADP
ejpam-4520	233	6	1	1	NUM
ejpam-4520	233	7	≤	≤	NUM
ejpam-4520	233	8	j	j	PROPN
ejpam-4520	233	9	≤	≤	PROPN
ejpam-4520	233	10	⌊p	⌊p	VERB
ejpam-4520	233	11	2	2	NUM
ejpam-4520	233	12	⌋	⌋	NOUN
ejpam-4520	234	1	2j	2j	NOUN
ejpam-4520	235	1	+	+	CCONJ
ejpam-4520	235	2	1−	1−	NUM
ejpam-4520	235	3	p	p	NOUN
ejpam-4520	235	4	for	for	ADP
ejpam-4520	235	5	⌈p2⌉	⌈p2⌉	PROPN
ejpam-4520	235	6	≤	≤	NUM
ejpam-4520	235	7	j	j	PROPN
ejpam-4520	235	8	≤	≤	PROPN
ejpam-4520	235	9	p	p	ADJ
ejpam-4520	235	10	f(b	f(b	PROPN
ejpam-4520	235	11	)	)	PUNCT
ejpam-4520	235	12	=	=	PUNCT
ejpam-4520	236	1	2p+	2p+	NUM
ejpam-4520	236	2	6	6	NUM
ejpam-4520	236	3	f(z	f(z	NOUN
ejpam-4520	236	4	)	)	PUNCT
ejpam-4520	236	5	=	=	PUNCT
ejpam-4520	237	1	2p+	2p+	NUM
ejpam-4520	237	2	7	7	NUM
ejpam-4520	237	3	f(xik	f(xik	X
ejpam-4520	237	4	)	)	PUNCT
ejpam-4520	238	1	=	=	PRON
ejpam-4520	238	2	{	{	PUNCT
ejpam-4520	238	3	k(p+	k(p+	PROPN
ejpam-4520	238	4	4	4	NUM
ejpam-4520	238	5	)	)	PUNCT
ejpam-4520	238	6	+	+	CCONJ
ejpam-4520	238	7	2p+	2p+	NUM
ejpam-4520	238	8	8	8	NUM
ejpam-4520	238	9	for	for	ADP
ejpam-4520	238	10	,	,	PUNCT
ejpam-4520	238	11	i	i	PRON
ejpam-4520	238	12	=	=	NOUN
ejpam-4520	238	13	1	1	NUM
ejpam-4520	238	14	,	,	PUNCT
ejpam-4520	238	15	1	1	NUM
ejpam-4520	238	16	≤	≤	NUM
ejpam-4520	238	17	k	k	X
ejpam-4520	238	18	≤	≤	NUM
ejpam-4520	238	19	m	m	PROPN
ejpam-4520	238	20	,	,	PUNCT
ejpam-4520	238	21	k(p+	k(p+	PROPN
ejpam-4520	238	22	4	4	NUM
ejpam-4520	238	23	)	)	PUNCT
ejpam-4520	238	24	+	+	NOUN
ejpam-4520	238	25	p+	p+	VERB
ejpam-4520	238	26	5	5	NUM
ejpam-4520	238	27	for	for	ADP
ejpam-4520	238	28	,	,	PUNCT
ejpam-4520	238	29	i	i	PRON
ejpam-4520	238	30	=	=	NOUN
ejpam-4520	238	31	2	2	NUM
ejpam-4520	238	32	,	,	PUNCT
ejpam-4520	238	33	1	1	NUM
ejpam-4520	238	34	≤	≤	NUM
ejpam-4520	238	35	k	k	X
ejpam-4520	238	36	≤	≤	NUM
ejpam-4520	238	37	m	m	PROPN
ejpam-4520	238	38	,	,	PUNCT
ejpam-4520	238	39	f(zk	f(zk	NOUN
ejpam-4520	238	40	)	)	PUNCT
ejpam-4520	238	41	=	=	SYM
ejpam-4520	239	1	k(p+	k(p+	PROPN
ejpam-4520	239	2	4	4	NUM
ejpam-4520	239	3	)	)	PUNCT
ejpam-4520	240	1	+	+	NOUN
ejpam-4520	240	2	p+	p+	VERB
ejpam-4520	240	3	6	6	NUM
ejpam-4520	240	4	for	for	ADP
ejpam-4520	240	5	1	1	NUM
ejpam-4520	240	6	≤	≤	NOUN
ejpam-4520	240	7	k	k	PROPN
ejpam-4520	240	8	≤	≤	NUM
ejpam-4520	240	9	m	m	PROPN
ejpam-4520	240	10	,	,	PUNCT
ejpam-4520	240	11	f(bk	f(bk	PROPN
ejpam-4520	240	12	)	)	PUNCT
ejpam-4520	240	13	=	=	SYM
ejpam-4520	241	1	k(p+	k(p+	PROPN
ejpam-4520	241	2	4	4	NUM
ejpam-4520	241	3	)	)	PUNCT
ejpam-4520	242	1	+	+	NOUN
ejpam-4520	242	2	p+	p+	VERB
ejpam-4520	242	3	7	7	NUM
ejpam-4520	242	4	for	for	ADP
ejpam-4520	242	5	1	1	NUM
ejpam-4520	242	6	≤	≤	NOUN
ejpam-4520	242	7	k	k	X
ejpam-4520	242	8	≤	≤	NUM
ejpam-4520	242	9	m	m	PROPN
ejpam-4520	242	10	,	,	PUNCT
ejpam-4520	242	11	susilowati	susilowati	PROPN
ejpam-4520	242	12	et	et	PROPN
ejpam-4520	242	13	.	.	PUNCT
ejpam-4520	243	1	al	al	PROPN
ejpam-4520	243	2	/	/	PUNCT
ejpam-4520	243	3	eur	eur	PROPN
ejpam-4520	243	4	.	.	PUNCT
ejpam-4520	244	1	j.	j.	PROPN
ejpam-4520	244	2	pure	pure	PROPN
ejpam-4520	244	3	appl	appl	PROPN
ejpam-4520	244	4	.	.	PROPN
ejpam-4520	244	5	math	math	PROPN
ejpam-4520	244	6	,	,	PUNCT
ejpam-4520	244	7	16	16	NUM
ejpam-4520	244	8	(	(	PUNCT
ejpam-4520	244	9	1	1	NUM
ejpam-4520	244	10	)	)	PUNCT
ejpam-4520	244	11	(	(	PUNCT
ejpam-4520	244	12	2023	2023	NUM
ejpam-4520	244	13	)	)	PUNCT
ejpam-4520	244	14	,	,	PUNCT
ejpam-4520	244	15	271	271	NUM
ejpam-4520	244	16	-	-	SYM
ejpam-4520	244	17	285	285	NUM
ejpam-4520	244	18	279	279	NUM
ejpam-4520	244	19	f(yjk	f(yjk	NOUN
ejpam-4520	244	20	)	)	PUNCT
ejpam-4520	244	21	=	=	PRON
ejpam-4520	244	22	{	{	PUNCT
ejpam-4520	245	1	k(p+	k(p+	INTJ
ejpam-4520	246	1	4)−	4)−	INTJ
ejpam-4520	246	2	2j	2j	NOUN
ejpam-4520	246	3	+	+	CCONJ
ejpam-4520	247	1	2p+	2p+	NUM
ejpam-4520	247	2	8	8	NUM
ejpam-4520	247	3	for	for	ADP
ejpam-4520	247	4	1	1	NUM
ejpam-4520	247	5	≤	≤	NUM
ejpam-4520	247	6	j	j	PROPN
ejpam-4520	247	7	≤	≤	PROPN
ejpam-4520	247	8	⌊p	⌊p	VERB
ejpam-4520	247	9	2	2	NUM
ejpam-4520	247	10	⌋	⌋	NOUN
ejpam-4520	247	11	,	,	PUNCT
ejpam-4520	247	12	1	1	NUM
ejpam-4520	247	13	≤	≤	NUM
ejpam-4520	247	14	k	k	X
ejpam-4520	247	15	≤	≤	NUM
ejpam-4520	247	16	m	m	PROPN
ejpam-4520	247	17	,	,	PUNCT
ejpam-4520	247	18	k(p+	k(p+	PROPN
ejpam-4520	248	1	4)−	4)−	INTJ
ejpam-4520	248	2	2j	2j	X
ejpam-4520	248	3	+	+	CCONJ
ejpam-4520	248	4	3p+	3p+	NUM
ejpam-4520	248	5	8	8	NUM
ejpam-4520	248	6	for	for	ADP
ejpam-4520	248	7	⌈p2⌉	⌈p2⌉	NOUN
ejpam-4520	248	8	,	,	PUNCT
ejpam-4520	248	9	1	1	NUM
ejpam-4520	248	10	≤	≤	NUM
ejpam-4520	248	11	k	k	X
ejpam-4520	248	12	≤	≤	PROPN
ejpam-4520	248	13	m.	m.	NOUN
ejpam-4520	248	14	the	the	DET
ejpam-4520	248	15	edge	edge	NOUN
ejpam-4520	248	16	weight	weight	NOUN
ejpam-4520	248	17	of	of	ADP
ejpam-4520	248	18	the	the	DET
ejpam-4520	248	19	above	above	ADJ
ejpam-4520	248	20	vertex	vertex	NOUN
ejpam-4520	248	21	labeling	labeling	NOUN
ejpam-4520	248	22	f	f	PROPN
ejpam-4520	248	23	can	can	AUX
ejpam-4520	248	24	be	be	AUX
ejpam-4520	248	25	presented	present	VERB
ejpam-4520	248	26	as	as	ADP
ejpam-4520	248	27	w(xy	w(xy	PROPN
ejpam-4520	248	28	)	)	PUNCT
ejpam-4520	248	29	=	=	PUNCT
ejpam-4520	249	1	2p+	2p+	NUM
ejpam-4520	249	2	5	5	NUM
ejpam-4520	249	3	w(xxi	w(xxi	NOUN
ejpam-4520	249	4	)	)	PUNCT
ejpam-4520	249	5	=	=	NOUN
ejpam-4520	249	6	{	{	PUNCT
ejpam-4520	249	7	2p+	2p+	NUM
ejpam-4520	249	8	7	7	NUM
ejpam-4520	249	9	for	for	ADP
ejpam-4520	249	10	i	i	PRON
ejpam-4520	249	11	=	=	NOUN
ejpam-4520	249	12	1	1	NUM
ejpam-4520	249	13	3p+	3p+	NUM
ejpam-4520	249	14	10	10	NUM
ejpam-4520	249	15	for	for	ADP
ejpam-4520	249	16	i	i	PRON
ejpam-4520	249	17	=	=	SYM
ejpam-4520	249	18	2	2	NUM
ejpam-4520	249	19	w(yyj	w(yyj	PROPN
ejpam-4520	249	20	)	)	PUNCT
ejpam-4520	249	21	=	=	PRON
ejpam-4520	249	22	{	{	PUNCT
ejpam-4520	249	23	p+	p+	VERB
ejpam-4520	249	24	2j	2j	NOUN
ejpam-4520	249	25	+	+	CCONJ
ejpam-4520	249	26	4	4	NUM
ejpam-4520	249	27	for	for	ADP
ejpam-4520	249	28	1	1	NUM
ejpam-4520	249	29	≤	≤	NUM
ejpam-4520	249	30	j	j	PROPN
ejpam-4520	249	31	≤	≤	PROPN
ejpam-4520	249	32	⌊p	⌊p	VERB
ejpam-4520	249	33	2	2	NUM
ejpam-4520	249	34	⌋	⌋	NOUN
ejpam-4520	249	35	p+	p+	VERB
ejpam-4520	249	36	2j	2j	NUM
ejpam-4520	249	37	+	+	CCONJ
ejpam-4520	249	38	8	8	NUM
ejpam-4520	249	39	for	for	ADP
ejpam-4520	249	40	⌈p2⌉	⌈p2⌉	NOUN
ejpam-4520	249	41	,	,	PUNCT
ejpam-4520	249	42	1	1	NUM
ejpam-4520	249	43	≤	≤	NUM
ejpam-4520	249	44	k	k	X
ejpam-4520	249	45	≤	≤	NUM
ejpam-4520	249	46	m	m	VERB
ejpam-4520	249	47	w(xix0i	w(xix0i	NOUN
ejpam-4520	249	48	)	)	PUNCT
ejpam-4520	250	1	=	=	PRON
ejpam-4520	250	2	{	{	PUNCT
ejpam-4520	250	3	p+	p+	NOUN
ejpam-4520	250	4	6	6	NUM
ejpam-4520	250	5	for	for	ADP
ejpam-4520	250	6	i	i	PRON
ejpam-4520	250	7	=	=	NOUN
ejpam-4520	250	8	1	1	NUM
ejpam-4520	250	9	3p+	3p+	NUM
ejpam-4520	250	10	12	12	NUM
ejpam-4520	250	11	for	for	ADP
ejpam-4520	250	12	i	i	PRON
ejpam-4520	250	13	=	=	SYM
ejpam-4520	250	14	2	2	NUM
ejpam-4520	250	15	w(xb	w(xb	NOUN
ejpam-4520	250	16	)	)	PUNCT
ejpam-4520	250	17	=	=	PUNCT
ejpam-4520	250	18	3p+	3p+	NUM
ejpam-4520	250	19	8	8	NUM
ejpam-4520	250	20	w(yz	w(yz	PROPN
ejpam-4520	250	21	)	)	PUNCT
ejpam-4520	250	22	=	=	PUNCT
ejpam-4520	251	1	3p+	3p+	NUM
ejpam-4520	251	2	10	10	NUM
ejpam-4520	251	3	w(yjy0j	w(yjy0j	ADV
ejpam-4520	251	4	)	)	PUNCT
ejpam-4520	251	5	=	=	PRON
ejpam-4520	251	6	{	{	PUNCT
ejpam-4520	251	7	p+	p+	VERB
ejpam-4520	251	8	4j	4j	NOUN
ejpam-4520	251	9	+	+	CCONJ
ejpam-4520	251	10	6	6	NUM
ejpam-4520	251	11	for	for	ADP
ejpam-4520	251	12	1	1	NUM
ejpam-4520	251	13	≤	≤	NUM
ejpam-4520	251	14	j	j	PROPN
ejpam-4520	251	15	≤	≤	PROPN
ejpam-4520	251	16	⌊p	⌊p	VERB
ejpam-4520	251	17	2	2	NUM
ejpam-4520	251	18	⌋	⌋	NOUN
ejpam-4520	251	19	4j	4j	NOUN
ejpam-4520	251	20	+	+	CCONJ
ejpam-4520	251	21	6−	6−	NUM
ejpam-4520	251	22	p	p	NOUN
ejpam-4520	251	23	for	for	ADP
ejpam-4520	251	24	⌈p2⌉	⌈p2⌉	NOUN
ejpam-4520	251	25	,	,	PUNCT
ejpam-4520	251	26	1	1	NUM
ejpam-4520	251	27	≤	≤	NUM
ejpam-4520	251	28	k	k	X
ejpam-4520	251	29	≤	≤	NUM
ejpam-4520	251	30	m	m	PROPN
ejpam-4520	251	31	w(xixik	w(xixik	NOUN
ejpam-4520	251	32	)	)	PUNCT
ejpam-4520	252	1	=	=	PUNCT
ejpam-4520	252	2	k(p+	k(p+	PROPN
ejpam-4520	252	3	4	4	NUM
ejpam-4520	252	4	)	)	PUNCT
ejpam-4520	252	5	+	+	CCONJ
ejpam-4520	252	6	3p+	3p+	NUM
ejpam-4520	252	7	13	13	NUM
ejpam-4520	252	8	,	,	PUNCT
ejpam-4520	252	9	for	for	ADP
ejpam-4520	252	10	1	1	NUM
ejpam-4520	252	11	≤	≤	NOUN
ejpam-4520	252	12	≤	≤	NUM
ejpam-4520	252	13	2	2	NUM
ejpam-4520	252	14	,	,	PUNCT
ejpam-4520	252	15	1	1	NUM
ejpam-4520	252	16	≤	≤	NUM
ejpam-4520	252	17	k	k	X
ejpam-4520	253	1	≤	≤	NUM
ejpam-4520	253	2	m	m	VERB
ejpam-4520	253	3	w(x0ixik	w(x0ixik	PRON
ejpam-4520	253	4	)	)	PUNCT
ejpam-4520	253	5	=	=	PUNCT
ejpam-4520	254	1	k(p+	k(p+	PROPN
ejpam-4520	254	2	4	4	NUM
ejpam-4520	254	3	)	)	PUNCT
ejpam-4520	254	4	+	+	CCONJ
ejpam-4520	254	5	2p+	2p+	NUM
ejpam-4520	254	6	9	9	NUM
ejpam-4520	254	7	,	,	PUNCT
ejpam-4520	254	8	for	for	ADP
ejpam-4520	254	9	1	1	NUM
ejpam-4520	254	10	≤	≤	NOUN
ejpam-4520	254	11	≤	≤	NUM
ejpam-4520	254	12	2	2	NUM
ejpam-4520	254	13	,	,	PUNCT
ejpam-4520	254	14	1	1	NUM
ejpam-4520	254	15	≤	≤	NUM
ejpam-4520	254	16	k	k	X
ejpam-4520	254	17	≤	≤	PROPN
ejpam-4520	254	18	m	m	VERB
ejpam-4520	254	19	w(xbk	w(xbk	NOUN
ejpam-4520	254	20	)	)	PUNCT
ejpam-4520	254	21	=	=	SYM
ejpam-4520	255	1	k(p+	k(p+	PROPN
ejpam-4520	255	2	4	4	NUM
ejpam-4520	255	3	)	)	PUNCT
ejpam-4520	255	4	+	+	CCONJ
ejpam-4520	255	5	2p+	2p+	NUM
ejpam-4520	255	6	9	9	NUM
ejpam-4520	255	7	,	,	PUNCT
ejpam-4520	255	8	for	for	ADP
ejpam-4520	255	9	1	1	NUM
ejpam-4520	255	10	≤	≤	NUM
ejpam-4520	255	11	k	k	PROPN
ejpam-4520	256	1	≤	≤	NUM
ejpam-4520	256	2	m	m	VERB
ejpam-4520	256	3	w(bbk	w(bbk	NOUN
ejpam-4520	256	4	)	)	PUNCT
ejpam-4520	256	5	=	=	SYM
ejpam-4520	257	1	k(p+	k(p+	PROPN
ejpam-4520	257	2	4	4	NUM
ejpam-4520	257	3	)	)	PUNCT
ejpam-4520	257	4	+	+	CCONJ
ejpam-4520	257	5	3p+	3p+	NUM
ejpam-4520	257	6	13	13	NUM
ejpam-4520	257	7	,	,	PUNCT
ejpam-4520	257	8	for	for	ADP
ejpam-4520	257	9	1	1	NUM
ejpam-4520	257	10	≤	≤	NUM
ejpam-4520	257	11	k	k	PROPN
ejpam-4520	257	12	≤	≤	NUM
ejpam-4520	257	13	m	m	VERB
ejpam-4520	257	14	w(yzk	w(yzk	NOUN
ejpam-4520	257	15	)	)	PUNCT
ejpam-4520	257	16	=	=	SYM
ejpam-4520	258	1	k(p+	k(p+	PROPN
ejpam-4520	258	2	4	4	NUM
ejpam-4520	258	3	)	)	PUNCT
ejpam-4520	258	4	+	+	CCONJ
ejpam-4520	258	5	2p+	2p+	NUM
ejpam-4520	258	6	9	9	NUM
ejpam-4520	258	7	,	,	PUNCT
ejpam-4520	258	8	for	for	ADP
ejpam-4520	258	9	1	1	NUM
ejpam-4520	258	10	≤	≤	NUM
ejpam-4520	258	11	k	k	PROPN
ejpam-4520	258	12	≤	≤	PROPN
ejpam-4520	258	13	m	m	PROPN
ejpam-4520	258	14	w(zzk	w(zzk	PROPN
ejpam-4520	258	15	)	)	PUNCT
ejpam-4520	259	1	=	=	PUNCT
ejpam-4520	259	2	k(p+	k(p+	PROPN
ejpam-4520	259	3	4	4	NUM
ejpam-4520	259	4	)	)	PUNCT
ejpam-4520	259	5	+	+	CCONJ
ejpam-4520	259	6	3p+	3p+	NUM
ejpam-4520	259	7	13	13	NUM
ejpam-4520	259	8	,	,	PUNCT
ejpam-4520	259	9	for	for	ADP
ejpam-4520	259	10	1	1	NUM
ejpam-4520	259	11	≤	≤	NUM
ejpam-4520	259	12	k	k	PROPN
ejpam-4520	259	13	≤	≤	NUM
ejpam-4520	259	14	m	m	VERB
ejpam-4520	259	15	w(yjyjk	w(yjyjk	PROPN
ejpam-4520	259	16	)	)	PUNCT
ejpam-4520	259	17	=	=	PRON
ejpam-4520	259	18	{	{	PUNCT
ejpam-4520	259	19	k(p+	k(p+	PROPN
ejpam-4520	259	20	4	4	NUM
ejpam-4520	259	21	)	)	PUNCT
ejpam-4520	259	22	+	+	CCONJ
ejpam-4520	259	23	2p+	2p+	NUM
ejpam-4520	259	24	9	9	NUM
ejpam-4520	259	25	for	for	ADP
ejpam-4520	259	26	1	1	NUM
ejpam-4520	259	27	≤	≤	NUM
ejpam-4520	259	28	j	j	PROPN
ejpam-4520	259	29	≤	≤	PROPN
ejpam-4520	259	30	⌊p	⌊p	VERB
ejpam-4520	259	31	2	2	NUM
ejpam-4520	259	32	⌋	⌋	NOUN
ejpam-4520	259	33	,	,	PUNCT
ejpam-4520	259	34	1	1	NUM
ejpam-4520	259	35	≤	≤	NUM
ejpam-4520	259	36	k	k	X
ejpam-4520	259	37	≤	≤	NUM
ejpam-4520	259	38	m	m	PROPN
ejpam-4520	259	39	,	,	PUNCT
ejpam-4520	259	40	k(p+	k(p+	PROPN
ejpam-4520	259	41	4	4	NUM
ejpam-4520	259	42	)	)	PUNCT
ejpam-4520	259	43	+	+	CCONJ
ejpam-4520	259	44	3p+	3p+	NUM
ejpam-4520	259	45	13	13	NUM
ejpam-4520	259	46	for	for	ADP
ejpam-4520	259	47	⌈p2⌉	⌈p2⌉	NOUN
ejpam-4520	259	48	,	,	PUNCT
ejpam-4520	259	49	1	1	NUM
ejpam-4520	259	50	≤	≤	NUM
ejpam-4520	259	51	k	k	PROPN
ejpam-4520	259	52	≤	≤	PROPN
ejpam-4520	259	53	m.	m.	NOUN
ejpam-4520	259	54	w(y0jyjk	w(y0jyjk	PROPN
ejpam-4520	259	55	)	)	PUNCT
ejpam-4520	259	56	=	=	PRON
ejpam-4520	259	57	{	{	PUNCT
ejpam-4520	259	58	k(p+	k(p+	PROPN
ejpam-4520	259	59	4	4	NUM
ejpam-4520	259	60	)	)	PUNCT
ejpam-4520	259	61	+	+	CCONJ
ejpam-4520	259	62	3p+	3p+	NUM
ejpam-4520	259	63	13	13	NUM
ejpam-4520	259	64	for	for	ADP
ejpam-4520	259	65	1	1	NUM
ejpam-4520	259	66	≤	≤	NUM
ejpam-4520	259	67	j	j	PROPN
ejpam-4520	259	68	≤	≤	PROPN
ejpam-4520	259	69	⌊p	⌊p	VERB
ejpam-4520	259	70	2	2	NUM
ejpam-4520	259	71	⌋	⌋	NOUN
ejpam-4520	259	72	,	,	PUNCT
ejpam-4520	259	73	1	1	NUM
ejpam-4520	259	74	≤	≤	NUM
ejpam-4520	259	75	k	k	X
ejpam-4520	259	76	≤	≤	NUM
ejpam-4520	259	77	m	m	PROPN
ejpam-4520	259	78	,	,	PUNCT
ejpam-4520	259	79	k(p+	k(p+	PROPN
ejpam-4520	259	80	4	4	NUM
ejpam-4520	259	81	)	)	PUNCT
ejpam-4520	259	82	+	+	CCONJ
ejpam-4520	259	83	2p+	2p+	NUM
ejpam-4520	259	84	9	9	NUM
ejpam-4520	259	85	for	for	ADP
ejpam-4520	259	86	⌈p2⌉	⌈p2⌉	NOUN
ejpam-4520	259	87	,	,	PUNCT
ejpam-4520	259	88	1	1	NUM
ejpam-4520	259	89	≤	≤	NUM
ejpam-4520	259	90	k	k	PROPN
ejpam-4520	259	91	≤	≤	PROPN
ejpam-4520	259	92	m.	m.	NOUN
ejpam-4520	259	93	based	base	VERB
ejpam-4520	259	94	on	on	ADP
ejpam-4520	259	95	theorem	theorem	NOUN
ejpam-4520	259	96	3	3	NUM
ejpam-4520	259	97	,	,	PUNCT
ejpam-4520	259	98	rac(sn	rac(sn	ADJ
ejpam-4520	259	99	,	,	PUNCT
ejpam-4520	259	100	p	p	NOUN
ejpam-4520	259	101	)	)	PUNCT
ejpam-4520	259	102	=	=	SYM
ejpam-4520	260	1	p	p	NOUN
ejpam-4520	260	2	+	+	NOUN
ejpam-4520	260	3	3	3	X
ejpam-4520	260	4	.	.	PUNCT
ejpam-4520	260	5	since	since	SCONJ
ejpam-4520	260	6	e(sn	e(sn	PROPN
ejpam-4520	260	7	,	,	PUNCT
ejpam-4520	260	8	p	p	NOUN
ejpam-4520	260	9	)	)	PUNCT
ejpam-4520	261	1	=	=	SYM
ejpam-4520	262	1	p	p	NOUN
ejpam-4520	262	2	+	+	NOUN
ejpam-4520	262	3	3	3	NUM
ejpam-4520	262	4	,	,	PUNCT
ejpam-4520	262	5	for	for	ADP
ejpam-4520	262	6	u	u	NOUN
ejpam-4520	262	7	,	,	PUNCT
ejpam-4520	262	8	v	v	PROPN
ejpam-4520	262	9	∈	∈	PROPN
ejpam-4520	262	10	e(sn	e(sn	PROPN
ejpam-4520	262	11	,	,	PUNCT
ejpam-4520	262	12	p	p	NOUN
ejpam-4520	262	13	)	)	PUNCT
ejpam-4520	262	14	has	have	VERB
ejpam-4520	262	15	a	a	DET
ejpam-4520	262	16	different	different	ADJ
ejpam-4520	262	17	colors	color	NOUN
ejpam-4520	262	18	.	.	PUNCT
ejpam-4520	263	1	therefore	therefore	ADV
ejpam-4520	263	2	,	,	PUNCT
ejpam-4520	263	3	the	the	DET
ejpam-4520	263	4	sum	sum	NOUN
ejpam-4520	263	5	of	of	ADP
ejpam-4520	263	6	the	the	DET
ejpam-4520	263	7	weights	weight	NOUN
ejpam-4520	263	8	of	of	ADP
ejpam-4520	263	9	graph	graph	NOUN
ejpam-4520	263	10	sn	sn	PROPN
ejpam-4520	263	11	,	,	PUNCT
ejpam-4520	263	12	p	p	PROPN
ejpam-4520	263	13	is	be	AUX
ejpam-4520	263	14	p+	p+	PROPN
ejpam-4520	263	15	3	3	NUM
ejpam-4520	263	16	.	.	PUNCT
ejpam-4520	264	1	based	base	VERB
ejpam-4520	264	2	on	on	ADP
ejpam-4520	264	3	theorem	theorem	NOUN
ejpam-4520	264	4	5	5	NUM
ejpam-4520	264	5	,	,	PUNCT
ejpam-4520	264	6	we	we	PRON
ejpam-4520	264	7	have	have	VERB
ejpam-4520	264	8	rac(k1	rac(k1	PROPN
ejpam-4520	264	9	+	+	CCONJ
ejpam-4520	264	10	sm	sm	NOUN
ejpam-4520	264	11	)	)	PUNCT
ejpam-4520	264	12	=	=	PUNCT
ejpam-4520	265	1	m	m	VERB
ejpam-4520	265	2	+	+	ADJ
ejpam-4520	265	3	2	2	NUM
ejpam-4520	265	4	.	.	PUNCT
ejpam-4520	265	5	based	base	VERB
ejpam-4520	265	6	on	on	ADP
ejpam-4520	265	7	the	the	DET
ejpam-4520	265	8	description	description	NOUN
ejpam-4520	265	9	above	above	ADV
ejpam-4520	265	10	,	,	PUNCT
ejpam-4520	265	11	we	we	PRON
ejpam-4520	265	12	have	have	VERB
ejpam-4520	265	13	that	that	SCONJ
ejpam-4520	265	14	the	the	DET
ejpam-4520	265	15	distinct	distinct	ADJ
ejpam-4520	265	16	weight	weight	NOUN
ejpam-4520	265	17	of	of	ADP
ejpam-4520	265	18	graph	graph	NOUN
ejpam-4520	265	19	(	(	PUNCT
ejpam-4520	265	20	sn	sn	PROPN
ejpam-4520	265	21	,	,	PUNCT
ejpam-4520	265	22	p	p	PROPN
ejpam-4520	265	23	⊙	⊙	PROPN
ejpam-4520	265	24	sm	sm	PROPN
ejpam-4520	265	25	)	)	PUNCT
ejpam-4520	265	26	is	be	AUX
ejpam-4520	265	27	m+	m+	NUM
ejpam-4520	265	28	p+	p+	NOUN
ejpam-4520	265	29	5	5	NUM
ejpam-4520	265	30	.	.	PUNCT
ejpam-4520	266	1	it	it	PRON
ejpam-4520	266	2	implies	imply	VERB
ejpam-4520	266	3	the	the	DET
ejpam-4520	266	4	edge	edge	NOUN
ejpam-4520	266	5	weights	weight	NOUN
ejpam-4520	266	6	of	of	ADP
ejpam-4520	266	7	f	f	NOUN
ejpam-4520	266	8	:	:	PUNCT
ejpam-4520	266	9	v	v	X
ejpam-4520	266	10	(	(	PUNCT
ejpam-4520	266	11	sn	sn	PROPN
ejpam-4520	266	12	,	,	PUNCT
ejpam-4520	266	13	p	p	PROPN
ejpam-4520	266	14	⊙	⊙	PROPN
ejpam-4520	266	15	sm	sm	PROPN
ejpam-4520	266	16	)	)	PUNCT
ejpam-4520	266	17	→	→	PUNCT
ejpam-4520	266	18	{	{	PUNCT
ejpam-4520	266	19	1	1	NUM
ejpam-4520	266	20	,	,	PUNCT
ejpam-4520	266	21	2	2	NUM
ejpam-4520	266	22	,	,	PUNCT
ejpam-4520	266	23	...	...	PUNCT
ejpam-4520	266	24	,	,	PUNCT
ejpam-4520	266	25	2p	2p	NUM
ejpam-4520	266	26	+	+	PUNCT
ejpam-4520	266	27	4	4	NUM
ejpam-4520	266	28	m	m	VERB
ejpam-4520	266	29	+	+	NOUN
ejpam-4520	266	30	pm	pm	NOUN
ejpam-4520	266	31	+	+	CCONJ
ejpam-4520	266	32	8	8	NUM
ejpam-4520	266	33	}	}	PUNCT
ejpam-4520	266	34	induces	induce	VERB
ejpam-4520	266	35	a	a	DET
ejpam-4520	266	36	rainbow	rainbow	NOUN
ejpam-4520	266	37	antimagic	antimagic	ADJ
ejpam-4520	266	38	coloring	coloring	NOUN
ejpam-4520	266	39	of	of	ADP
ejpam-4520	266	40	m+	m+	NUM
ejpam-4520	266	41	n+2	n+2	NUM
ejpam-4520	266	42	colors	color	NOUN
ejpam-4520	266	43	.	.	PUNCT
ejpam-4520	267	1	thus	thus	ADV
ejpam-4520	267	2	rac(sn	rac(sn	VERB
ejpam-4520	267	3	,	,	PUNCT
ejpam-4520	267	4	p	p	PROPN
ejpam-4520	267	5	⊙	⊙	PROPN
ejpam-4520	267	6	sm	sm	PROPN
ejpam-4520	267	7	)	)	PUNCT
ejpam-4520	267	8	≤	≤	NUM
ejpam-4520	267	9	m+	m+	NUM
ejpam-4520	268	1	p+5	p+5	NUM
ejpam-4520	268	2	.	.	NOUN
ejpam-4520	269	1	comparing	compare	VERB
ejpam-4520	269	2	the	the	DET
ejpam-4520	269	3	two	two	NUM
ejpam-4520	269	4	bounds	bound	NOUN
ejpam-4520	269	5	,	,	PUNCT
ejpam-4520	269	6	we	we	PRON
ejpam-4520	269	7	have	have	VERB
ejpam-4520	269	8	the	the	DET
ejpam-4520	269	9	exact	exact	ADJ
ejpam-4520	269	10	value	value	NOUN
ejpam-4520	269	11	of	of	ADP
ejpam-4520	269	12	rac(sn	rac(sn	NOUN
ejpam-4520	269	13	,	,	PUNCT
ejpam-4520	269	14	p	p	NOUN
ejpam-4520	269	15	⊙	⊙	PROPN
ejpam-4520	269	16	sm	sm	PROPN
ejpam-4520	269	17	)	)	PUNCT
ejpam-4520	270	1	=	=	SYM
ejpam-4520	270	2	m+	m+	NUM
ejpam-4520	270	3	p+	p+	ADJ
ejpam-4520	270	4	5	5	NUM
ejpam-4520	270	5	.	.	PUNCT
ejpam-4520	271	1	the	the	DET
ejpam-4520	271	2	next	next	ADJ
ejpam-4520	271	3	step	step	NOUN
ejpam-4520	271	4	,	,	PUNCT
ejpam-4520	271	5	evaluate	evaluate	VERB
ejpam-4520	271	6	to	to	PART
ejpam-4520	271	7	prove	prove	VERB
ejpam-4520	271	8	the	the	DET
ejpam-4520	271	9	existence	existence	NOUN
ejpam-4520	271	10	of	of	ADP
ejpam-4520	271	11	a	a	DET
ejpam-4520	271	12	rainbow	rainbow	NOUN
ejpam-4520	271	13	u	u	NOUN
ejpam-4520	271	14	−	−	PROPN
ejpam-4520	271	15	v	v	ADP
ejpam-4520	271	16	path	path	NOUN
ejpam-4520	271	17	sn	sn	PROPN
ejpam-4520	271	18	,	,	PUNCT
ejpam-4520	271	19	p	p	PROPN
ejpam-4520	271	20	⊙	⊙	PROPN
ejpam-4520	272	1	sm	sm	PROPN
ejpam-4520	272	2	.	.	PROPN
ejpam-4520	273	1	based	base	VERB
ejpam-4520	273	2	on	on	ADP
ejpam-4520	273	3	the	the	DET
ejpam-4520	273	4	definition	definition	NOUN
ejpam-4520	273	5	of	of	ADP
ejpam-4520	273	6	the	the	DET
ejpam-4520	273	7	graph	graph	NOUN
ejpam-4520	273	8	sn	sn	PROPN
ejpam-4520	273	9	,	,	PUNCT
ejpam-4520	273	10	p	p	PROPN
ejpam-4520	273	11	⊙	⊙	PROPN
ejpam-4520	273	12	sm	sm	PROPN
ejpam-4520	273	13	,	,	PUNCT
ejpam-4520	273	14	then	then	ADV
ejpam-4520	273	15	the	the	DET
ejpam-4520	273	16	graph	graph	NOUN
ejpam-4520	273	17	sn	sn	PROPN
ejpam-4520	273	18	,	,	PUNCT
ejpam-4520	273	19	p	p	PROPN
ejpam-4520	273	20	⊙	⊙	PROPN
ejpam-4520	273	21	sm	sm	PROPN
ejpam-4520	273	22	contains	contain	VERB
ejpam-4520	273	23	one	one	NUM
ejpam-4520	273	24	graph	graph	NOUN
ejpam-4520	273	25	sn	sn	PROPN
ejpam-4520	273	26	,	,	PUNCT
ejpam-4520	273	27	p	p	NOUN
ejpam-4520	273	28	and	and	CCONJ
ejpam-4520	273	29	|v	|v	PROPN
ejpam-4520	273	30	(	(	PUNCT
ejpam-4520	273	31	sn	sn	PROPN
ejpam-4520	273	32	,	,	PUNCT
ejpam-4520	273	33	p)|	p)|	ADJ
ejpam-4520	273	34	copies	copy	NOUN
ejpam-4520	273	35	of	of	ADP
ejpam-4520	273	36	k1	k1	PROPN
ejpam-4520	273	37	+	+	CCONJ
ejpam-4520	273	38	sm	sm	PROPN
ejpam-4520	273	39	,	,	PUNCT
ejpam-4520	273	40	so	so	SCONJ
ejpam-4520	273	41	that	that	SCONJ
ejpam-4520	273	42	we	we	PRON
ejpam-4520	273	43	can	can	AUX
ejpam-4520	273	44	evaluate	evaluate	VERB
ejpam-4520	273	45	the	the	DET
ejpam-4520	273	46	rainbow	rainbow	NOUN
ejpam-4520	273	47	u	u	NOUN
ejpam-4520	273	48	−	−	PROPN
ejpam-4520	273	49	v	v	ADP
ejpam-4520	273	50	path	path	NOUN
ejpam-4520	273	51	of	of	ADP
ejpam-4520	273	52	the	the	DET
ejpam-4520	273	53	graph	graph	NOUN
ejpam-4520	273	54	sn	sn	PROPN
ejpam-4520	273	55	,	,	PUNCT
ejpam-4520	273	56	p	p	PROPN
ejpam-4520	273	57	⊙	⊙	PROPN
ejpam-4520	273	58	sm	sm	INTJ
ejpam-4520	273	59	by	by	ADP
ejpam-4520	273	60	evaluating	evaluate	VERB
ejpam-4520	273	61	the	the	DET
ejpam-4520	273	62	rainbow	rainbow	NOUN
ejpam-4520	273	63	u−	u−	PROPN
ejpam-4520	273	64	v	v	ADP
ejpam-4520	273	65	path	path	NOUN
ejpam-4520	273	66	on	on	ADP
ejpam-4520	273	67	the	the	DET
ejpam-4520	273	68	graph	graph	NOUN
ejpam-4520	273	69	sn	sn	PROPN
ejpam-4520	273	70	,	,	PUNCT
ejpam-4520	273	71	p	p	NOUN
ejpam-4520	273	72	and	and	CCONJ
ejpam-4520	273	73	the	the	DET
ejpam-4520	273	74	graph	graph	NOUN
ejpam-4520	273	75	k1	k1	NOUN
ejpam-4520	273	76	+	+	CCONJ
ejpam-4520	274	1	sm	sm	PROPN
ejpam-4520	274	2	.	.	PUNCT
ejpam-4520	275	1	since	since	SCONJ
ejpam-4520	275	2	diam(k1	diam(k1	PROPN
ejpam-4520	275	3	+	+	CCONJ
ejpam-4520	275	4	sm	sm	NOUN
ejpam-4520	275	5	)	)	PUNCT
ejpam-4520	275	6	=	=	SYM
ejpam-4520	275	7	2	2	NUM
ejpam-4520	275	8	,	,	PUNCT
ejpam-4520	275	9	based	base	VERB
ejpam-4520	275	10	on	on	ADP
ejpam-4520	275	11	theorem	theorem	NOUN
ejpam-4520	275	12	2	2	NUM
ejpam-4520	275	13	,	,	PUNCT
ejpam-4520	275	14	there	there	PRON
ejpam-4520	275	15	is	be	VERB
ejpam-4520	275	16	a	a	DET
ejpam-4520	275	17	rainbow	rainbow	NOUN
ejpam-4520	275	18	susilowati	susilowati	NOUN
ejpam-4520	275	19	et	et	NOUN
ejpam-4520	275	20	.	.	PUNCT
ejpam-4520	276	1	al	al	PROPN
ejpam-4520	276	2	/	/	PUNCT
ejpam-4520	276	3	eur	eur	PROPN
ejpam-4520	276	4	.	.	PUNCT
ejpam-4520	277	1	j.	j.	PROPN
ejpam-4520	277	2	pure	pure	PROPN
ejpam-4520	277	3	appl	appl	PROPN
ejpam-4520	277	4	.	.	PROPN
ejpam-4520	277	5	math	math	PROPN
ejpam-4520	277	6	,	,	PUNCT
ejpam-4520	277	7	16	16	NUM
ejpam-4520	277	8	(	(	PUNCT
ejpam-4520	277	9	1	1	NUM
ejpam-4520	277	10	)	)	PUNCT
ejpam-4520	277	11	(	(	PUNCT
ejpam-4520	277	12	2023	2023	NUM
ejpam-4520	277	13	)	)	PUNCT
ejpam-4520	277	14	,	,	PUNCT
ejpam-4520	277	15	271	271	NUM
ejpam-4520	277	16	-	-	SYM
ejpam-4520	277	17	285	285	NUM
ejpam-4520	277	18	280	280	NUM
ejpam-4520	277	19	u−v	u−v	X
ejpam-4520	277	20	path	path	NOUN
ejpam-4520	277	21	for	for	ADP
ejpam-4520	277	22	every	every	DET
ejpam-4520	277	23	u	u	NOUN
ejpam-4520	277	24	,	,	PUNCT
ejpam-4520	277	25	v	v	PROPN
ejpam-4520	277	26	∈	∈	PROPN
ejpam-4520	277	27	v	v	NOUN
ejpam-4520	277	28	(	(	PUNCT
ejpam-4520	277	29	k1+sm	k1+sm	PROPN
ejpam-4520	277	30	)	)	PUNCT
ejpam-4520	277	31	.	.	PUNCT
ejpam-4520	278	1	based	base	VERB
ejpam-4520	278	2	on	on	ADP
ejpam-4520	278	3	theorem	theorem	NOUN
ejpam-4520	278	4	3	3	NUM
ejpam-4520	278	5	,	,	PUNCT
ejpam-4520	278	6	rac(sn	rac(sn	ADJ
ejpam-4520	278	7	,	,	PUNCT
ejpam-4520	278	8	p	p	NOUN
ejpam-4520	278	9	)	)	PUNCT
ejpam-4520	278	10	=	=	SYM
ejpam-4520	278	11	n+p+1	n+p+1	PROPN
ejpam-4520	278	12	.	.	PUNCT
ejpam-4520	279	1	since	since	SCONJ
ejpam-4520	279	2	sn	sn	PROPN
ejpam-4520	279	3	,	,	PUNCT
ejpam-4520	279	4	p	p	PROPN
ejpam-4520	279	5	has	have	VERB
ejpam-4520	279	6	n+	n+	PUNCT
ejpam-4520	279	7	p+1	p+1	PRON
ejpam-4520	279	8	edges	edge	VERB
ejpam-4520	279	9	,	,	PUNCT
ejpam-4520	279	10	there	there	PRON
ejpam-4520	279	11	is	be	VERB
ejpam-4520	279	12	a	a	DET
ejpam-4520	279	13	rainbow	rainbow	NOUN
ejpam-4520	279	14	u−	u−	NOUN
ejpam-4520	279	15	v	v	NUM
ejpam-4520	279	16	path	path	NOUN
ejpam-4520	279	17	for	for	ADP
ejpam-4520	279	18	every	every	DET
ejpam-4520	279	19	u	u	NOUN
ejpam-4520	279	20	,	,	PUNCT
ejpam-4520	279	21	v	v	PROPN
ejpam-4520	279	22	∈	∈	PROPN
ejpam-4520	279	23	v	v	NOUN
ejpam-4520	279	24	(	(	PUNCT
ejpam-4520	279	25	sn	sn	PROPN
ejpam-4520	279	26	,	,	PUNCT
ejpam-4520	279	27	p	p	NOUN
ejpam-4520	279	28	)	)	PUNCT
ejpam-4520	279	29	.	.	PUNCT
ejpam-4520	280	1	therefore	therefore	ADV
ejpam-4520	280	2	,	,	PUNCT
ejpam-4520	280	3	according	accord	VERB
ejpam-4520	280	4	to	to	ADP
ejpam-4520	280	5	the	the	DET
ejpam-4520	280	6	explanation	explanation	NOUN
ejpam-4520	280	7	,	,	PUNCT
ejpam-4520	280	8	it	it	PRON
ejpam-4520	280	9	can	can	AUX
ejpam-4520	280	10	be	be	AUX
ejpam-4520	280	11	seen	see	VERB
ejpam-4520	280	12	that	that	SCONJ
ejpam-4520	280	13	there	there	PRON
ejpam-4520	280	14	is	be	VERB
ejpam-4520	280	15	a	a	DET
ejpam-4520	280	16	rainbow	rainbow	NOUN
ejpam-4520	280	17	u	u	NOUN
ejpam-4520	280	18	−	−	PROPN
ejpam-4520	280	19	v	v	ADP
ejpam-4520	280	20	path	path	NOUN
ejpam-4520	280	21	for	for	ADP
ejpam-4520	280	22	every	every	DET
ejpam-4520	280	23	u	u	NOUN
ejpam-4520	280	24	,	,	PUNCT
ejpam-4520	280	25	v	v	PROPN
ejpam-4520	280	26	∈	∈	PROPN
ejpam-4520	280	27	v	v	NOUN
ejpam-4520	280	28	(	(	PUNCT
ejpam-4520	280	29	sn	sn	PROPN
ejpam-4520	280	30	,	,	PUNCT
ejpam-4520	280	31	p	p	PROPN
ejpam-4520	280	32	⊙	⊙	PROPN
ejpam-4520	280	33	sm	sm	PROPN
ejpam-4520	280	34	)	)	PUNCT
ejpam-4520	280	35	.	.	PUNCT
ejpam-4520	281	1	rainbow	rainbow	VERB
ejpam-4520	281	2	antimagic	antimagic	ADJ
ejpam-4520	281	3	coloring	coloring	NOUN
ejpam-4520	281	4	of	of	ADP
ejpam-4520	281	5	graph	graph	NOUN
ejpam-4520	281	6	sn	sn	PROPN
ejpam-4520	281	7	,	,	PUNCT
ejpam-4520	281	8	p	p	PROPN
ejpam-4520	281	9	⊙	⊙	PROPN
ejpam-4520	281	10	sm	sm	PROPN
ejpam-4520	281	11	can	can	AUX
ejpam-4520	281	12	be	be	AUX
ejpam-4520	281	13	seen	see	VERB
ejpam-4520	281	14	in	in	ADP
ejpam-4520	281	15	figure	figure	NOUN
ejpam-4520	281	16	4	4	NUM
ejpam-4520	281	17	.	.	NOUN
ejpam-4520	282	1	50	50	NUM
ejpam-4520	282	2	36	36	NUM
ejpam-4520	282	3	43	43	NUM
ejpam-4520	282	4	50	50	NUM
ejpam-4520	282	5	22	22	NUM
ejpam-4520	282	6	29	29	NUM
ejpam-4520	282	7	36	36	NUM
ejpam-4520	282	8	43	43	NUM
ejpam-4520	282	9	50	50	NUM
ejpam-4520	282	10	43	43	NUM
ejpam-4520	282	11	36	36	NUM
ejpam-4520	282	12	29	29	NUM
ejpam-4520	282	13	22	22	NUM
ejpam-4520	282	14	29	29	NUM
ejpam-4520	282	15	36	36	NUM
ejpam-4520	282	16	43	43	NUM
ejpam-4520	282	17	29	29	NUM
ejpam-4520	282	18	36	36	NUM
ejpam-4520	282	19	43	43	NUM
ejpam-4520	282	20	50	50	NUM
ejpam-4520	282	21	22	22	NUM
ejpam-4520	282	22	29	29	NUM
ejpam-4520	282	23	36	36	NUM
ejpam-4520	282	24	43	43	NUM
ejpam-4520	282	25	29	29	NUM
ejpam-4520	282	26	36	36	NUM
ejpam-4520	282	27	43	43	NUM
ejpam-4520	282	28	50	50	NUM
ejpam-4520	282	29	22	22	NUM
ejpam-4520	282	30	29	29	NUM
ejpam-4520	282	31	36	36	NUM
ejpam-4520	282	32	43	43	NUM
ejpam-4520	282	33	29	29	NUM
ejpam-4520	282	34	36	36	NUM
ejpam-4520	282	35	43	43	NUM
ejpam-4520	282	36	50	50	NUM
ejpam-4520	282	37	2229	2229	NUM
ejpam-4520	282	38	36	36	NUM
ejpam-4520	282	39	43	43	NUM
ejpam-4520	282	40	29	29	NUM
ejpam-4520	282	41	36	36	NUM
ejpam-4520	282	42	43	43	NUM
ejpam-4520	282	43	1	1	NUM
ejpam-4520	282	44	8	8	NUM
ejpam-4520	282	45	21	21	NUM
ejpam-4520	282	46	28	28	NUM
ejpam-4520	282	47	35	35	NUM
ejpam-4520	282	48	42	42	NUM
ejpam-4520	282	49	5	5	NUM
ejpam-4520	282	50	12	12	NUM
ejpam-4520	282	51	7	7	NUM
ejpam-4520	282	52	15	15	NUM
ejpam-4520	282	53	22	22	NUM
ejpam-4520	282	54	29	29	NUM
ejpam-4520	282	55	36	36	NUM
ejpam-4520	282	56	14	14	NUM
ejpam-4520	282	57	17	17	NUM
ejpam-4520	282	58	24	24	NUM
ejpam-4520	282	59	31	31	NUM
ejpam-4520	282	60	38	38	NUM
ejpam-4520	282	61	6	6	NUM
ejpam-4520	282	62	13	13	NUM
ejpam-4520	282	63	16	16	NUM
ejpam-4520	282	64	23	23	NUM
ejpam-4520	282	65	30	30	NUM
ejpam-4520	282	66	37	37	NUM
ejpam-4520	282	67	3	3	NUM
ejpam-4520	282	68	9	9	NUM
ejpam-4520	282	69	11	11	NUM
ejpam-4520	282	70	10	10	NUM
ejpam-4520	282	71	2	2	NUM
ejpam-4520	282	72	4	4	NUM
ejpam-4520	282	73	19	19	NUM
ejpam-4520	282	74	26	26	NUM
ejpam-4520	282	75	33	33	NUM
ejpam-4520	282	76	40	40	NUM
ejpam-4520	282	77	20	20	NUM
ejpam-4520	282	78	27	27	NUM
ejpam-4520	282	79	34	34	NUM
ejpam-4520	282	80	41	41	NUM
ejpam-4520	282	81	18	18	NUM
ejpam-4520	282	82	25	25	NUM
ejpam-4520	282	83	32	32	NUM
ejpam-4520	282	84	39	39	NUM
ejpam-4520	282	85	13	13	NUM
ejpam-4520	282	86	19	19	NUM
ejpam-4520	282	87	11	11	NUM
ejpam-4520	282	88	9	9	NUM
ejpam-4520	282	89	15	15	NUM
ejpam-4520	282	90	17	17	NUM
ejpam-4520	282	91	9	9	NUM
ejpam-4520	282	92	11	11	NUM
ejpam-4520	282	93	13	13	NUM
ejpam-4520	282	94	15	15	NUM
ejpam-4520	282	95	17	17	NUM
ejpam-4520	282	96	19	19	NUM
ejpam-4520	282	97	21	21	NUM
ejpam-4520	282	98	22	22	NUM
ejpam-4520	282	99	29	29	NUM
ejpam-4520	282	100	36	36	NUM
ejpam-4520	282	101	43	43	NUM
ejpam-4520	282	102	29	29	NUM
ejpam-4520	282	103	36	36	NUM
ejpam-4520	282	104	43	43	NUM
ejpam-4520	282	105	50	50	NUM
ejpam-4520	282	106	22	22	NUM
ejpam-4520	282	107	29	29	NUM
ejpam-4520	282	108	36	36	NUM
ejpam-4520	282	109	43	43	NUM
ejpam-4520	282	110	29	29	NUM
ejpam-4520	282	111	x02	x02	PROPN
ejpam-4520	282	112	y	y	PROPN
ejpam-4520	282	113	x1	x1	PROPN
ejpam-4520	282	114	y1	y1	NOUN
ejpam-4520	282	115	y2	y2	NOUN
ejpam-4520	282	116	y3	y3	NOUN
ejpam-4520	282	117	y03	y03	NOUN
ejpam-4520	282	118	y02	y02	NOUN
ejpam-4520	282	119	y01	y01	PROPN
ejpam-4520	282	120	x01	x01	PROPN
ejpam-4520	282	121	b1	b1	PROPN
ejpam-4520	282	122	b2	b2	PROPN
ejpam-4520	282	123	b3	b3	PROPN
ejpam-4520	282	124	b4	b4	PROPN
ejpam-4520	282	125	b	b	PROPN
ejpam-4520	282	126	z	z	PROPN
ejpam-4520	282	127	z2	z2	PROPN
ejpam-4520	282	128	z3	z3	PROPN
ejpam-4520	282	129	x	x	SYM
ejpam-4520	282	130	z1	z1	PROPN
ejpam-4520	282	131	z4	z4	PROPN
ejpam-4520	282	132	x11	x11	PROPN
ejpam-4520	282	133	x12	x12	NUM
ejpam-4520	282	134	x13	x13	PROPN
ejpam-4520	282	135	x14	x14	PROPN
ejpam-4520	282	136	x21	x21	PROPN
ejpam-4520	282	137	x22	x22	NUM
ejpam-4520	282	138	x23	x23	PROPN
ejpam-4520	282	139	x24	x24	PROPN
ejpam-4520	282	140	y11	y11	NOUN
ejpam-4520	282	141	y12	y12	PROPN
ejpam-4520	282	142	y13	y13	PROPN
ejpam-4520	282	143	y14	y14	PROPN
ejpam-4520	282	144	y21	y21	PROPN
ejpam-4520	282	145	y22	y22	PROPN
ejpam-4520	282	146	y23	y23	PROPN
ejpam-4520	282	147	y24	y24	PROPN
ejpam-4520	282	148	y31	y31	PROPN
ejpam-4520	282	149	y32	y32	PROPN
ejpam-4520	282	150	y33	y33	PROPN
ejpam-4520	282	151	y34	y34	NOUN
ejpam-4520	282	152	x2	x2	NOUN
ejpam-4520	282	153	figure	figure	VERB
ejpam-4520	282	154	4	4	NUM
ejpam-4520	282	155	:	:	PUNCT
ejpam-4520	282	156	rainbow	rainbow	VERB
ejpam-4520	282	157	antimagic	antimagic	ADJ
ejpam-4520	282	158	coloring	coloring	NOUN
ejpam-4520	282	159	of	of	ADP
ejpam-4520	282	160	graph	graph	NOUN
ejpam-4520	282	161	s2,3	s2,3	PROPN
ejpam-4520	282	162	⊙	⊙	PROPN
ejpam-4520	282	163	s4	s4	PROPN
ejpam-4520	282	164	.	.	PUNCT
ejpam-4520	283	1	theorem	theorem	VERB
ejpam-4520	283	2	9	9	NUM
ejpam-4520	283	3	.	.	PUNCT
ejpam-4520	284	1	for	for	ADP
ejpam-4520	284	2	odd	odd	ADJ
ejpam-4520	284	3	integers	integer	NOUN
ejpam-4520	284	4	n	n	PRON
ejpam-4520	284	5	≥	≥	NOUN
ejpam-4520	284	6	3	3	NUM
ejpam-4520	284	7	and	and	CCONJ
ejpam-4520	284	8	m	m	PROPN
ejpam-4520	284	9	≤	≤	NOUN
ejpam-4520	284	10	3	3	NUM
ejpam-4520	284	11	,	,	PUNCT
ejpam-4520	284	12	rac(fn,3	rac(fn,3	PROPN
ejpam-4520	284	13	⊙	⊙	NOUN
ejpam-4520	284	14	sm	sm	INTJ
ejpam-4520	284	15	)	)	PUNCT
ejpam-4520	284	16	=	=	PUNCT
ejpam-4520	285	1	3n+m+	3n+m+	NUM
ejpam-4520	285	2	1	1	NUM
ejpam-4520	285	3	.	.	PUNCT
ejpam-4520	286	1	proof	proof	NOUN
ejpam-4520	286	2	.	.	PUNCT
ejpam-4520	287	1	the	the	DET
ejpam-4520	287	2	graph	graph	NOUN
ejpam-4520	287	3	fn,3	fn,3	PROPN
ejpam-4520	287	4	⊙	⊙	PROPN
ejpam-4520	287	5	sm	sm	PROPN
ejpam-4520	287	6	is	be	AUX
ejpam-4520	287	7	a	a	DET
ejpam-4520	287	8	graph	graph	NOUN
ejpam-4520	287	9	with	with	ADP
ejpam-4520	287	10	v	v	NOUN
ejpam-4520	287	11	(	(	PUNCT
ejpam-4520	287	12	fn,3	fn,3	PROPN
ejpam-4520	287	13	⊙	⊙	PROPN
ejpam-4520	287	14	sm	sm	PROPN
ejpam-4520	287	15	)	)	PUNCT
ejpam-4520	287	16	=	=	PRON
ejpam-4520	287	17	{	{	PUNCT
ejpam-4520	287	18	xi	xi	PROPN
ejpam-4520	287	19	,	,	PUNCT
ejpam-4520	287	20	yi	yi	PROPN
ejpam-4520	287	21	,	,	PUNCT
ejpam-4520	287	22	zi	zi	PROPN
ejpam-4520	287	23	,	,	PUNCT
ejpam-4520	287	24	x0i	x0i	PROPN
ejpam-4520	287	25	,	,	PUNCT
ejpam-4520	287	26	y0i	y0i	PROPN
ejpam-4520	287	27	,	,	PUNCT
ejpam-4520	287	28	z0i1	z0i1	PROPN
ejpam-4520	287	29	≤	≤	NUM
ejpam-4520	287	30	i	i	PRON
ejpam-4520	287	31	≤	≤	NOUN
ejpam-4520	287	32	n	n	CCONJ
ejpam-4520	287	33	}	}	PUNCT
ejpam-4520	287	34	∪	∪	X
ejpam-4520	287	35	{	{	PUNCT
ejpam-4520	287	36	xij	xij	PROPN
ejpam-4520	287	37	,	,	PUNCT
ejpam-4520	287	38	yij	yij	PROPN
ejpam-4520	287	39	,	,	PUNCT
ejpam-4520	287	40	zij	zij	PROPN
ejpam-4520	287	41	,	,	PUNCT
ejpam-4520	287	42	1	1	NUM
ejpam-4520	287	43	≤	≤	NUM
ejpam-4520	287	44	i	i	PRON
ejpam-4520	287	45	≤	≤	PROPN
ejpam-4520	287	46	n	n	CCONJ
ejpam-4520	287	47	,	,	PUNCT
ejpam-4520	287	48	1	1	NUM
ejpam-4520	287	49	≤	≤	NUM
ejpam-4520	287	50	j	j	PROPN
ejpam-4520	287	51	≤	≤	PROPN
ejpam-4520	287	52	m	m	PROPN
ejpam-4520	287	53	}	}	PUNCT
ejpam-4520	287	54	and	and	CCONJ
ejpam-4520	287	55	edge	edge	NOUN
ejpam-4520	287	56	set	set	VERB
ejpam-4520	287	57	e(fn,3	e(fn,3	PROPN
ejpam-4520	287	58	⊙	⊙	PROPN
ejpam-4520	287	59	sm	sm	PROPN
ejpam-4520	287	60	)	)	PUNCT
ejpam-4520	287	61	=	=	PRON
ejpam-4520	287	62	{	{	PUNCT
ejpam-4520	287	63	xixi+1	xixi+1	PROPN
ejpam-4520	287	64	,	,	PUNCT
ejpam-4520	287	65	1	1	NUM
ejpam-4520	287	66	≤	≤	NUM
ejpam-4520	287	67	i	i	PROPN
ejpam-4520	287	68	≤	≤	NUM
ejpam-4520	287	69	n−1}∪{xiyi	n−1}∪{xiyi	PROPN
ejpam-4520	287	70	,	,	PUNCT
ejpam-4520	287	71	yizi	yizi	PROPN
ejpam-4520	287	72	,	,	PUNCT
ejpam-4520	287	73	xix0i	xix0i	PROPN
ejpam-4520	287	74	,	,	PUNCT
ejpam-4520	287	75	yiy0i	yiy0i	PROPN
ejpam-4520	287	76	,	,	PUNCT
ejpam-4520	287	77	ziz0i	ziz0i	PROPN
ejpam-4520	287	78	,	,	PUNCT
ejpam-4520	287	79	1	1	NUM
ejpam-4520	287	80	≤	≤	NUM
ejpam-4520	287	81	i	i	PRON
ejpam-4520	287	82	≤	≤	ADV
ejpam-4520	287	83	n}∪{xixij	n}∪{xixij	PROPN
ejpam-4520	287	84	,	,	PUNCT
ejpam-4520	287	85	x0ixij	x0ixij	PROPN
ejpam-4520	287	86	,	,	PUNCT
ejpam-4520	287	87	yiyij	yiyij	NOUN
ejpam-4520	287	88	,	,	PUNCT
ejpam-4520	287	89	y0iyij	y0iyij	PROPN
ejpam-4520	287	90	,	,	PUNCT
ejpam-4520	287	91	zizij	zizij	PROPN
ejpam-4520	287	92	,	,	PUNCT
ejpam-4520	287	93	z0izij	z0izij	PROPN
ejpam-4520	287	94	,	,	PUNCT
ejpam-4520	287	95	1	1	NUM
ejpam-4520	287	96	≤	≤	NUM
ejpam-4520	287	97	i	i	PRON
ejpam-4520	287	98	≤	≤	PROPN
ejpam-4520	287	99	n	n	CCONJ
ejpam-4520	287	100	,	,	PUNCT
ejpam-4520	287	101	1	1	NUM
ejpam-4520	287	102	≤	≤	NUM
ejpam-4520	287	103	j	j	PROPN
ejpam-4520	287	104	≤	≤	PROPN
ejpam-4520	287	105	m	m	PROPN
ejpam-4520	287	106	}	}	PUNCT
ejpam-4520	287	107	.	.	PUNCT
ejpam-4520	288	1	the	the	DET
ejpam-4520	288	2	cardinality	cardinality	NOUN
ejpam-4520	288	3	of	of	ADP
ejpam-4520	288	4	|v	|v	PROPN
ejpam-4520	288	5	(	(	PUNCT
ejpam-4520	288	6	fn,3	fn,3	NOUN
ejpam-4520	288	7	⊙	⊙	X
ejpam-4520	289	1	sm)|	sm)|	PROPN
ejpam-4520	289	2	=	=	SYM
ejpam-4520	289	3	6n+	6n+	NUM
ejpam-4520	289	4	3	3	NUM
ejpam-4520	289	5	nm	nm	NOUN
ejpam-4520	289	6	and	and	CCONJ
ejpam-4520	289	7	the	the	DET
ejpam-4520	289	8	cardinality	cardinality	NOUN
ejpam-4520	289	9	of	of	ADP
ejpam-4520	289	10	|e(fn,3	|e(fn,3	PROPN
ejpam-4520	289	11	⊙	⊙	NOUN
ejpam-4520	289	12	sm)|	sm)|	PROPN
ejpam-4520	289	13	=	=	NOUN
ejpam-4520	289	14	6n+	6n+	NUM
ejpam-4520	289	15	6nm−	6nm−	NUM
ejpam-4520	289	16	1	1	NUM
ejpam-4520	289	17	.	.	PUNCT
ejpam-4520	289	18	to	to	PART
ejpam-4520	289	19	prove	prove	VERB
ejpam-4520	289	20	the	the	DET
ejpam-4520	289	21	rainbow	rainbow	NOUN
ejpam-4520	289	22	antimagic	antimagic	ADJ
ejpam-4520	289	23	connection	connection	NOUN
ejpam-4520	289	24	number	number	NOUN
ejpam-4520	289	25	of	of	ADP
ejpam-4520	289	26	rac(fn,3⊙sm	rac(fn,3⊙sm	NOUN
ejpam-4520	289	27	)	)	PUNCT
ejpam-4520	289	28	,	,	PUNCT
ejpam-4520	289	29	first	first	ADV
ejpam-4520	289	30	we	we	PRON
ejpam-4520	289	31	have	have	VERB
ejpam-4520	289	32	to	to	PART
ejpam-4520	289	33	show	show	VERB
ejpam-4520	289	34	that	that	SCONJ
ejpam-4520	289	35	the	the	DET
ejpam-4520	289	36	lower	low	ADJ
ejpam-4520	289	37	bound	bind	VERB
ejpam-4520	289	38	of	of	ADP
ejpam-4520	289	39	rac(fn,3⊙sm	rac(fn,3⊙sm	NOUN
ejpam-4520	289	40	)	)	PUNCT
ejpam-4520	289	41	.	.	PUNCT
ejpam-4520	290	1	based	base	VERB
ejpam-4520	290	2	on	on	ADP
ejpam-4520	290	3	lemma	lemma	PROPN
ejpam-4520	290	4	1	1	NUM
ejpam-4520	290	5	,	,	PUNCT
ejpam-4520	290	6	we	we	PRON
ejpam-4520	290	7	have	have	VERB
ejpam-4520	290	8	rac(fn,3⊙sm	rac(fn,3⊙sm	NOUN
ejpam-4520	290	9	)	)	PUNCT
ejpam-4520	290	10	≥	≥	NOUN
ejpam-4520	290	11	rac(fn,3	rac(fn,3	NUM
ejpam-4520	290	12	)	)	PUNCT
ejpam-4520	291	1	+	+	NOUN
ejpam-4520	291	2	m+	m+	NUM
ejpam-4520	291	3	2	2	NUM
ejpam-4520	291	4	.	.	PUNCT
ejpam-4520	291	5	since	since	SCONJ
ejpam-4520	291	6	rac(fn,3	rac(fn,3	PROPN
ejpam-4520	291	7	)	)	PUNCT
ejpam-4520	292	1	=	=	SYM
ejpam-4520	293	1	3n−	3n−	NUM
ejpam-4520	293	2	1	1	NUM
ejpam-4520	293	3	,	,	PUNCT
ejpam-4520	293	4	thus	thus	ADV
ejpam-4520	293	5	,	,	PUNCT
ejpam-4520	293	6	rac(fn,3	rac(fn,3	PROPN
ejpam-4520	293	7	⊙	⊙	X
ejpam-4520	293	8	sm	sm	PROPN
ejpam-4520	293	9	)	)	PUNCT
ejpam-4520	293	10	≥	≥	NOUN
ejpam-4520	293	11	3n+m+	3n+m+	NUM
ejpam-4520	293	12	1	1	NUM
ejpam-4520	293	13	.	.	PUNCT
ejpam-4520	294	1	secondly	secondly	ADV
ejpam-4520	294	2	,	,	PUNCT
ejpam-4520	294	3	we	we	PRON
ejpam-4520	294	4	have	have	VERB
ejpam-4520	294	5	to	to	PART
ejpam-4520	294	6	show	show	VERB
ejpam-4520	294	7	the	the	DET
ejpam-4520	294	8	upper	upper	ADJ
ejpam-4520	294	9	bound	bound	NOUN
ejpam-4520	294	10	of	of	ADP
ejpam-4520	294	11	rac(fn,3	rac(fn,3	PROPN
ejpam-4520	294	12	⊙	⊙	NOUN
ejpam-4520	294	13	sm	sm	PROPN
ejpam-4520	294	14	)	)	PUNCT
ejpam-4520	294	15	.	.	PUNCT
ejpam-4520	295	1	define	define	VERB
ejpam-4520	295	2	the	the	DET
ejpam-4520	295	3	vertex	vertex	NOUN
ejpam-4520	295	4	labeling	labeling	NOUN
ejpam-4520	296	1	f	f	NOUN
ejpam-4520	296	2	:	:	PUNCT
ejpam-4520	296	3	v	v	X
ejpam-4520	296	4	(	(	PUNCT
ejpam-4520	296	5	fn,3	fn,3	PROPN
ejpam-4520	296	6	⊙	⊙	PROPN
ejpam-4520	296	7	sm	sm	PROPN
ejpam-4520	296	8	)	)	PUNCT
ejpam-4520	296	9	→	→	PUNCT
ejpam-4520	296	10	{	{	PUNCT
ejpam-4520	296	11	1	1	NUM
ejpam-4520	296	12	,	,	PUNCT
ejpam-4520	296	13	2	2	NUM
ejpam-4520	296	14	,	,	PUNCT
ejpam-4520	296	15	...	...	PUNCT
ejpam-4520	296	16	,	,	PUNCT
ejpam-4520	296	17	6n+	6n+	NUM
ejpam-4520	296	18	3	3	NUM
ejpam-4520	296	19	nm	nm	NOUN
ejpam-4520	296	20	}	}	PUNCT
ejpam-4520	296	21	as	as	SCONJ
ejpam-4520	296	22	follows	follow	VERB
ejpam-4520	296	23	.	.	PUNCT
ejpam-4520	297	1	f(xi	f(xi	X
ejpam-4520	297	2	)	)	PUNCT
ejpam-4520	298	1	=	=	PRON
ejpam-4520	298	2	{	{	PUNCT
ejpam-4520	298	3	3i+	3i+	NUM
ejpam-4520	298	4	⌊	⌊	VERB
ejpam-4520	298	5	n	n	PRON
ejpam-4520	298	6	2	2	NUM
ejpam-4520	298	7	⌋	⌋	NOUN
ejpam-4520	298	8	+	+	CCONJ
ejpam-4520	298	9	n	n	CCONJ
ejpam-4520	298	10	for	for	ADP
ejpam-4520	298	11	1	1	NUM
ejpam-4520	298	12	≤	≤	NUM
ejpam-4520	298	13	i	i	PRON
ejpam-4520	298	14	≤	≤	ADJ
ejpam-4520	299	1	n	n	CCONJ
ejpam-4520	300	1	and	and	CCONJ
ejpam-4520	300	2	i	i	PRON
ejpam-4520	300	3	is	be	AUX
ejpam-4520	300	4	odd	odd	ADJ
ejpam-4520	300	5	3i+	3i+	NUM
ejpam-4520	300	6	n+	n+	PUNCT
ejpam-4520	301	1	⌊	⌊	PROPN
ejpam-4520	301	2	n	n	PRON
ejpam-4520	301	3	2	2	NUM
ejpam-4520	301	4	⌋	⌋	NOUN
ejpam-4520	301	5	−	−	NOUN
ejpam-4520	301	6	2	2	NUM
ejpam-4520	301	7	for	for	ADP
ejpam-4520	301	8	1	1	NUM
ejpam-4520	301	9	≤	≤	NUM
ejpam-4520	301	10	i	i	PRON
ejpam-4520	301	11	≤	≤	ADJ
ejpam-4520	302	1	n	n	CCONJ
ejpam-4520	303	1	and	and	CCONJ
ejpam-4520	303	2	i	i	PRON
ejpam-4520	303	3	is	be	AUX
ejpam-4520	303	4	even	even	ADV
ejpam-4520	303	5	susilowati	susilowati	PROPN
ejpam-4520	303	6	et	et	NOUN
ejpam-4520	303	7	.	.	PUNCT
ejpam-4520	304	1	al	al	PROPN
ejpam-4520	304	2	/	/	PUNCT
ejpam-4520	304	3	eur	eur	PROPN
ejpam-4520	304	4	.	.	PUNCT
ejpam-4520	305	1	j.	j.	PROPN
ejpam-4520	305	2	pure	pure	PROPN
ejpam-4520	305	3	appl	appl	PROPN
ejpam-4520	305	4	.	.	PROPN
ejpam-4520	305	5	math	math	PROPN
ejpam-4520	305	6	,	,	PUNCT
ejpam-4520	305	7	16	16	NUM
ejpam-4520	305	8	(	(	PUNCT
ejpam-4520	305	9	1	1	NUM
ejpam-4520	305	10	)	)	PUNCT
ejpam-4520	305	11	(	(	PUNCT
ejpam-4520	305	12	2023	2023	NUM
ejpam-4520	305	13	)	)	PUNCT
ejpam-4520	305	14	,	,	PUNCT
ejpam-4520	305	15	271	271	NUM
ejpam-4520	305	16	-	-	SYM
ejpam-4520	305	17	285	285	NUM
ejpam-4520	305	18	281	281	NUM
ejpam-4520	305	19	f(yi	f(yi	NUM
ejpam-4520	305	20	)	)	PUNCT
ejpam-4520	306	1	=	=	SYM
ejpam-4520	306	2	3i+	3i+	NUM
ejpam-4520	306	3	n+	n+	NUM
ejpam-4520	306	4	⌊n	⌊n	NOUN
ejpam-4520	306	5	2	2	NUM
ejpam-4520	306	6	⌋	⌋	NOUN
ejpam-4520	306	7	−	−	NOUN
ejpam-4520	306	8	1	1	NUM
ejpam-4520	306	9	,	,	PUNCT
ejpam-4520	306	10	for	for	ADP
ejpam-4520	306	11	1	1	NUM
ejpam-4520	306	12	≤	≤	NUM
ejpam-4520	306	13	i	i	PRON
ejpam-4520	306	14	≤	≤	NOUN
ejpam-4520	306	15	n	n	DET
ejpam-4520	306	16	f(zi	f(zi	PROPN
ejpam-4520	306	17	)	)	PUNCT
ejpam-4520	306	18	=	=	SYM
ejpam-4520	306	19	{	{	PUNCT
ejpam-4520	306	20	3i+	3i+	NUM
ejpam-4520	306	21	n+	n+	NUM
ejpam-4520	306	22	⌊	⌊	PROPN
ejpam-4520	306	23	n	n	PRON
ejpam-4520	306	24	2	2	NUM
ejpam-4520	306	25	⌋	⌋	NOUN
ejpam-4520	306	26	−	−	NOUN
ejpam-4520	306	27	2	2	NUM
ejpam-4520	306	28	for	for	ADP
ejpam-4520	306	29	1	1	NUM
ejpam-4520	306	30	≤	≤	NUM
ejpam-4520	306	31	i	i	PRON
ejpam-4520	306	32	≤	≤	ADJ
ejpam-4520	307	1	n	n	CCONJ
ejpam-4520	308	1	and	and	CCONJ
ejpam-4520	308	2	i	i	PRON
ejpam-4520	308	3	is	be	AUX
ejpam-4520	308	4	odd	odd	ADJ
ejpam-4520	308	5	3i+	3i+	NUM
ejpam-4520	308	6	⌊	⌊	PROPN
ejpam-4520	308	7	n	n	ADV
ejpam-4520	308	8	2	2	NUM
ejpam-4520	308	9	⌋	⌋	NOUN
ejpam-4520	308	10	+	+	CCONJ
ejpam-4520	308	11	n	n	CCONJ
ejpam-4520	308	12	for	for	ADP
ejpam-4520	308	13	1	1	NUM
ejpam-4520	308	14	≤	≤	NUM
ejpam-4520	308	15	i	i	PRON
ejpam-4520	308	16	≤	≤	ADJ
ejpam-4520	309	1	n	n	CCONJ
ejpam-4520	310	1	and	and	CCONJ
ejpam-4520	310	2	i	i	PRON
ejpam-4520	310	3	is	be	AUX
ejpam-4520	310	4	even	even	ADV
ejpam-4520	310	5	f(x0i	f(x0i	NOUN
ejpam-4520	310	6	)	)	PUNCT
ejpam-4520	310	7	=	=	SYM
ejpam-4520	310	8			X
ejpam-4520	310	9	3i+	3i+	NUM
ejpam-4520	311	1	⌊	⌊	VERB
ejpam-4520	311	2	n	n	ADV
ejpam-4520	311	3	2	2	NUM
ejpam-4520	311	4	⌋	⌋	NOUN
ejpam-4520	311	5	+	+	CCONJ
ejpam-4520	311	6	4n	4n	NOUN
ejpam-4520	311	7	for	for	ADP
ejpam-4520	311	8	1	1	NUM
ejpam-4520	311	9	≤	≤	NUM
ejpam-4520	312	1	i	i	PRON
ejpam-4520	312	2	≤	≤	PUNCT
ejpam-4520	312	3	⌊	⌊	VERB
ejpam-4520	312	4	n	n	ADV
ejpam-4520	312	5	2	2	NUM
ejpam-4520	312	6	⌋	⌋	NOUN
ejpam-4520	313	1	and	and	CCONJ
ejpam-4520	313	2	i	i	PRON
ejpam-4520	313	3	is	be	AUX
ejpam-4520	313	4	odd	odd	ADJ
ejpam-4520	313	5	,	,	PUNCT
ejpam-4520	313	6	n	n	CCONJ
ejpam-4520	313	7	≡	≡	PROPN
ejpam-4520	313	8	3	3	NUM
ejpam-4520	313	9	mod	mod	NOUN
ejpam-4520	313	10	4	4	NUM
ejpam-4520	313	11	3i−	3i−	NUM
ejpam-4520	313	12	n−	n−	NOUN
ejpam-4520	313	13	⌈n2	⌈n2	NOUN
ejpam-4520	313	14	⌉	⌉	PUNCT
ejpam-4520	313	15	for	for	ADP
ejpam-4520	313	16	⌈n2	⌈n2	NOUN
ejpam-4520	313	17	⌉	⌉	X
ejpam-4520	313	18	≤	≤	NUM
ejpam-4520	314	1	i	i	PRON
ejpam-4520	315	1	≤	≤	NOUN
ejpam-4520	316	1	n	n	CCONJ
ejpam-4520	317	1	and	and	CCONJ
ejpam-4520	317	2	i	i	PRON
ejpam-4520	317	3	is	be	AUX
ejpam-4520	317	4	odd	odd	ADJ
ejpam-4520	317	5	,	,	PUNCT
ejpam-4520	317	6	n	n	CCONJ
ejpam-4520	317	7	≡	≡	PROPN
ejpam-4520	317	8	3	3	NUM
ejpam-4520	317	9	mod	mod	NOUN
ejpam-4520	317	10	4	4	NUM
ejpam-4520	317	11	3i+	3i+	NUM
ejpam-4520	317	12	⌊	⌊	PROPN
ejpam-4520	317	13	n	n	ADV
ejpam-4520	317	14	2	2	NUM
ejpam-4520	317	15	⌋	⌋	NOUN
ejpam-4520	318	1	+	+	CCONJ
ejpam-4520	319	1	4n−	4n−	NUM
ejpam-4520	319	2	2	2	NUM
ejpam-4520	319	3	for	for	ADP
ejpam-4520	319	4	1	1	NUM
ejpam-4520	319	5	≤	≤	NUM
ejpam-4520	319	6	i	i	PRON
ejpam-4520	319	7	≤	≤	PUNCT
ejpam-4520	319	8	⌊	⌊	VERB
ejpam-4520	319	9	n	n	ADV
ejpam-4520	319	10	2	2	NUM
ejpam-4520	319	11	⌋	⌋	NOUN
ejpam-4520	320	1	and	and	CCONJ
ejpam-4520	320	2	i	i	PRON
ejpam-4520	320	3	is	be	AUX
ejpam-4520	320	4	even	even	ADV
ejpam-4520	320	5	,	,	PUNCT
ejpam-4520	320	6	n	n	CCONJ
ejpam-4520	320	7	≡	≡	PROPN
ejpam-4520	320	8	3	3	NUM
ejpam-4520	320	9	mod	mod	NOUN
ejpam-4520	320	10	4	4	NUM
ejpam-4520	320	11	3i−	3i−	NUM
ejpam-4520	320	12	n−	n−	NOUN
ejpam-4520	320	13	⌈n2	⌈n2	NOUN
ejpam-4520	320	14	⌉	⌉	SCONJ
ejpam-4520	320	15	−	−	PROPN
ejpam-4520	320	16	2	2	NUM
ejpam-4520	320	17	for	for	ADP
ejpam-4520	320	18	⌈n2	⌈n2	NOUN
ejpam-4520	320	19	⌉	⌉	X
ejpam-4520	320	20	≤	≤	NUM
ejpam-4520	320	21	i	i	PRON
ejpam-4520	320	22	≤	≤	NOUN
ejpam-4520	320	23	n	n	CCONJ
ejpam-4520	321	1	and	and	CCONJ
ejpam-4520	321	2	i	i	PRON
ejpam-4520	321	3	is	be	AUX
ejpam-4520	321	4	even	even	ADV
ejpam-4520	321	5	,	,	PUNCT
ejpam-4520	321	6	n	n	CCONJ
ejpam-4520	321	7	≡	≡	PROPN
ejpam-4520	321	8	3	3	NUM
ejpam-4520	321	9	mod	mod	NOUN
ejpam-4520	321	10	4	4	NUM
ejpam-4520	321	11	3i+	3i+	NUM
ejpam-4520	321	12	⌊	⌊	PROPN
ejpam-4520	321	13	n	n	ADV
ejpam-4520	321	14	2	2	NUM
ejpam-4520	321	15	⌋	⌋	NOUN
ejpam-4520	321	16	+	+	CCONJ
ejpam-4520	321	17	4n	4n	NOUN
ejpam-4520	321	18	for	for	ADP
ejpam-4520	321	19	1	1	NUM
ejpam-4520	321	20	≤	≤	NUM
ejpam-4520	321	21	i	i	PRON
ejpam-4520	321	22	≤	≤	NUM
ejpam-4520	321	23	⌈n2	⌈n2	NOUN
ejpam-4520	321	24	⌉	⌉	PUNCT
ejpam-4520	321	25	and	and	CCONJ
ejpam-4520	321	26	i	i	PRON
ejpam-4520	321	27	is	be	AUX
ejpam-4520	321	28	odd	odd	ADJ
ejpam-4520	321	29	,	,	PUNCT
ejpam-4520	321	30	n	n	CCONJ
ejpam-4520	321	31	≡	≡	PROPN
ejpam-4520	321	32	1	1	NUM
ejpam-4520	321	33	mod	mod	NOUN
ejpam-4520	321	34	4	4	NUM
ejpam-4520	321	35	3i−	3i−	NUM
ejpam-4520	321	36	n−	n−	NOUN
ejpam-4520	321	37	⌈n2	⌈n2	NOUN
ejpam-4520	321	38	⌉	⌉	PUNCT
ejpam-4520	321	39	for	for	ADP
ejpam-4520	321	40	⌈n2	⌈n2	NOUN
ejpam-4520	321	41	⌉+	⌉+	NOUN
ejpam-4520	321	42	1	1	NUM
ejpam-4520	321	43	≤	≤	NUM
ejpam-4520	321	44	i	i	PRON
ejpam-4520	321	45	≤	≤	ADJ
ejpam-4520	322	1	n	n	CCONJ
ejpam-4520	323	1	and	and	CCONJ
ejpam-4520	323	2	i	i	PRON
ejpam-4520	323	3	is	be	AUX
ejpam-4520	323	4	odd	odd	ADJ
ejpam-4520	323	5	,	,	PUNCT
ejpam-4520	323	6	n	n	CCONJ
ejpam-4520	323	7	≡	≡	PROPN
ejpam-4520	323	8	1	1	NUM
ejpam-4520	323	9	mod	mod	PROPN
ejpam-4520	323	10	4	4	NUM
ejpam-4520	323	11	3i+	3i+	NUM
ejpam-4520	323	12	⌊	⌊	PROPN
ejpam-4520	323	13	n	n	ADV
ejpam-4520	323	14	2	2	NUM
ejpam-4520	323	15	⌋	⌋	NOUN
ejpam-4520	323	16	+	+	CCONJ
ejpam-4520	324	1	4n−	4n−	NUM
ejpam-4520	324	2	2	2	NUM
ejpam-4520	324	3	for	for	ADP
ejpam-4520	324	4	1	1	NUM
ejpam-4520	324	5	≤	≤	NUM
ejpam-4520	324	6	i	i	PRON
ejpam-4520	324	7	≤	≤	NUM
ejpam-4520	324	8	⌈n2	⌈n2	NOUN
ejpam-4520	324	9	⌉	⌉	PUNCT
ejpam-4520	324	10	and	and	CCONJ
ejpam-4520	324	11	i	i	PRON
ejpam-4520	324	12	is	be	AUX
ejpam-4520	324	13	even	even	ADV
ejpam-4520	324	14	,	,	PUNCT
ejpam-4520	324	15	n	n	CCONJ
ejpam-4520	324	16	≡	≡	PROPN
ejpam-4520	324	17	1	1	NUM
ejpam-4520	324	18	mod	mod	NOUN
ejpam-4520	324	19	4	4	NUM
ejpam-4520	324	20	3i−	3i−	NUM
ejpam-4520	324	21	n−	n−	NOUN
ejpam-4520	324	22	⌈n2	⌈n2	NOUN
ejpam-4520	324	23	⌉	⌉	SCONJ
ejpam-4520	324	24	−	−	PROPN
ejpam-4520	324	25	2	2	NUM
ejpam-4520	324	26	for	for	ADP
ejpam-4520	324	27	⌈n2	⌈n2	NOUN
ejpam-4520	324	28	⌉+	⌉+	NOUN
ejpam-4520	324	29	1	1	NUM
ejpam-4520	324	30	≤	≤	NUM
ejpam-4520	324	31	i	i	PRON
ejpam-4520	324	32	≤	≤	ADJ
ejpam-4520	324	33	n	n	CCONJ
ejpam-4520	325	1	and	and	CCONJ
ejpam-4520	325	2	i	i	PRON
ejpam-4520	325	3	is	be	AUX
ejpam-4520	325	4	even	even	ADV
ejpam-4520	325	5	,	,	PUNCT
ejpam-4520	325	6	n	n	CCONJ
ejpam-4520	325	7	≡	≡	PROPN
ejpam-4520	325	8	1	1	NUM
ejpam-4520	325	9	mod	mod	PROPN
ejpam-4520	325	10	4	4	NUM
ejpam-4520	325	11	f(y0i	f(y0i	NUM
ejpam-4520	325	12	)	)	PUNCT
ejpam-4520	325	13	=	=	PRON
ejpam-4520	326	1	{	{	PUNCT
ejpam-4520	326	2	3i+	3i+	NUM
ejpam-4520	326	3	4n+	4n+	NUM
ejpam-4520	326	4	⌊	⌊	VERB
ejpam-4520	326	5	n	n	ADV
ejpam-4520	326	6	2	2	NUM
ejpam-4520	326	7	⌋	⌋	NOUN
ejpam-4520	326	8	−	−	NOUN
ejpam-4520	326	9	1	1	NUM
ejpam-4520	326	10	for	for	ADP
ejpam-4520	326	11	1	1	NUM
ejpam-4520	326	12	≤	≤	NUM
ejpam-4520	326	13	i	i	PRON
ejpam-4520	326	14	≤	≤	NUM
ejpam-4520	326	15	⌈n2	⌈n2	NOUN
ejpam-4520	326	16	⌉	⌉	PRON
ejpam-4520	326	17	3i−	3i−	NUM
ejpam-4520	326	18	⌈n2	⌈n2	NOUN
ejpam-4520	326	19	⌉	⌉	PRON
ejpam-4520	326	20	−	−	PROPN
ejpam-4520	326	21	n−	n−	NOUN
ejpam-4520	326	22	1	1	NUM
ejpam-4520	326	23	for	for	ADP
ejpam-4520	326	24	⌈n2	⌈n2	NOUN
ejpam-4520	326	25	⌉+	⌉+	NOUN
ejpam-4520	326	26	1	1	NUM
ejpam-4520	326	27	≤	≤	NUM
ejpam-4520	327	1	i	i	PRON
ejpam-4520	327	2	≤	≤	PROPN
ejpam-4520	327	3	n	n	PRON
ejpam-4520	327	4	f(z0i	f(z0i	PROPN
ejpam-4520	327	5	)	)	PUNCT
ejpam-4520	327	6	=	=	PUNCT
ejpam-4520	327	7			NUM
ejpam-4520	327	8	3i+	3i+	NUM
ejpam-4520	327	9	⌊	⌊	VERB
ejpam-4520	327	10	n	n	PRON
ejpam-4520	327	11	2	2	NUM
ejpam-4520	327	12	⌋	⌋	NOUN
ejpam-4520	327	13	+	+	CCONJ
ejpam-4520	328	1	4n−	4n−	NUM
ejpam-4520	328	2	2	2	NUM
ejpam-4520	328	3	for	for	ADP
ejpam-4520	328	4	1	1	NUM
ejpam-4520	328	5	≤	≤	NUM
ejpam-4520	328	6	i	i	PRON
ejpam-4520	328	7	≤	≤	PUNCT
ejpam-4520	328	8	⌊	⌊	VERB
ejpam-4520	328	9	n	n	ADV
ejpam-4520	328	10	2	2	NUM
ejpam-4520	328	11	⌋	⌋	NOUN
ejpam-4520	329	1	and	and	CCONJ
ejpam-4520	329	2	i	i	PRON
ejpam-4520	329	3	is	be	AUX
ejpam-4520	329	4	odd	odd	ADJ
ejpam-4520	329	5	,	,	PUNCT
ejpam-4520	329	6	n	n	CCONJ
ejpam-4520	329	7	≡	≡	PROPN
ejpam-4520	329	8	3	3	NUM
ejpam-4520	329	9	mod	mod	NOUN
ejpam-4520	329	10	4	4	NUM
ejpam-4520	329	11	3i−	3i−	NUM
ejpam-4520	329	12	n−	n−	NOUN
ejpam-4520	329	13	⌈n2	⌈n2	NOUN
ejpam-4520	329	14	⌉	⌉	SCONJ
ejpam-4520	329	15	−	−	PROPN
ejpam-4520	329	16	2	2	NUM
ejpam-4520	329	17	for	for	ADP
ejpam-4520	329	18	⌈n2	⌈n2	NOUN
ejpam-4520	329	19	⌉	⌉	X
ejpam-4520	329	20	≤	≤	NUM
ejpam-4520	330	1	i	i	PRON
ejpam-4520	331	1	≤	≤	NOUN
ejpam-4520	332	1	n	n	CCONJ
ejpam-4520	333	1	and	and	CCONJ
ejpam-4520	333	2	i	i	PRON
ejpam-4520	333	3	is	be	AUX
ejpam-4520	333	4	odd	odd	ADJ
ejpam-4520	333	5	,	,	PUNCT
ejpam-4520	333	6	n	n	CCONJ
ejpam-4520	333	7	≡	≡	PROPN
ejpam-4520	333	8	3	3	NUM
ejpam-4520	333	9	mod	mod	NOUN
ejpam-4520	333	10	4	4	NUM
ejpam-4520	333	11	3i+	3i+	NUM
ejpam-4520	333	12	⌊	⌊	PROPN
ejpam-4520	333	13	n	n	ADV
ejpam-4520	333	14	2	2	NUM
ejpam-4520	333	15	⌋	⌋	NOUN
ejpam-4520	334	1	+	+	CCONJ
ejpam-4520	335	1	4n−	4n−	NUM
ejpam-4520	335	2	1	1	NUM
ejpam-4520	335	3	for	for	ADP
ejpam-4520	335	4	1	1	NUM
ejpam-4520	335	5	≤	≤	NUM
ejpam-4520	335	6	i	i	PRON
ejpam-4520	335	7	≤	≤	PUNCT
ejpam-4520	335	8	⌊	⌊	VERB
ejpam-4520	335	9	n	n	ADV
ejpam-4520	335	10	2	2	NUM
ejpam-4520	335	11	⌋	⌋	NOUN
ejpam-4520	336	1	and	and	CCONJ
ejpam-4520	336	2	i	i	PRON
ejpam-4520	336	3	is	be	AUX
ejpam-4520	336	4	even	even	ADV
ejpam-4520	336	5	,	,	PUNCT
ejpam-4520	336	6	n	n	CCONJ
ejpam-4520	336	7	≡	≡	PROPN
ejpam-4520	336	8	3	3	NUM
ejpam-4520	336	9	mod	mod	NOUN
ejpam-4520	336	10	4	4	NUM
ejpam-4520	336	11	3i−	3i−	NUM
ejpam-4520	336	12	n−	n−	NOUN
ejpam-4520	336	13	⌈n2	⌈n2	NOUN
ejpam-4520	336	14	⌉	⌉	PUNCT
ejpam-4520	336	15	for	for	ADP
ejpam-4520	336	16	⌈n2	⌈n2	NOUN
ejpam-4520	336	17	⌉	⌉	X
ejpam-4520	336	18	≤	≤	NUM
ejpam-4520	337	1	i	i	PRON
ejpam-4520	338	1	≤	≤	NOUN
ejpam-4520	339	1	n	n	CCONJ
ejpam-4520	340	1	and	and	CCONJ
ejpam-4520	340	2	i	i	PRON
ejpam-4520	340	3	is	be	AUX
ejpam-4520	340	4	even	even	ADV
ejpam-4520	340	5	,	,	PUNCT
ejpam-4520	340	6	n	n	CCONJ
ejpam-4520	340	7	≡	≡	PROPN
ejpam-4520	340	8	3	3	NUM
ejpam-4520	340	9	mod	mod	NOUN
ejpam-4520	340	10	4	4	NUM
ejpam-4520	340	11	3i+	3i+	NUM
ejpam-4520	340	12	⌊	⌊	PROPN
ejpam-4520	340	13	n	n	ADV
ejpam-4520	340	14	2	2	NUM
ejpam-4520	340	15	⌋	⌋	NOUN
ejpam-4520	340	16	+	+	CCONJ
ejpam-4520	341	1	4n−	4n−	NUM
ejpam-4520	341	2	2	2	NUM
ejpam-4520	341	3	for	for	ADP
ejpam-4520	341	4	1	1	NUM
ejpam-4520	341	5	≤	≤	NUM
ejpam-4520	341	6	i	i	PRON
ejpam-4520	341	7	≤	≤	NUM
ejpam-4520	341	8	⌈n2	⌈n2	NOUN
ejpam-4520	341	9	⌉	⌉	PUNCT
ejpam-4520	341	10	and	and	CCONJ
ejpam-4520	341	11	i	i	PRON
ejpam-4520	341	12	is	be	AUX
ejpam-4520	341	13	odd	odd	ADJ
ejpam-4520	341	14	,	,	PUNCT
ejpam-4520	341	15	n	n	CCONJ
ejpam-4520	341	16	≡	≡	PROPN
ejpam-4520	341	17	1	1	NUM
ejpam-4520	341	18	mod	mod	NOUN
ejpam-4520	341	19	4	4	NUM
ejpam-4520	341	20	3i−	3i−	NUM
ejpam-4520	341	21	n−	n−	NOUN
ejpam-4520	341	22	⌈n2	⌈n2	NOUN
ejpam-4520	341	23	⌉	⌉	SCONJ
ejpam-4520	341	24	−	−	PROPN
ejpam-4520	341	25	2	2	NUM
ejpam-4520	341	26	for	for	ADP
ejpam-4520	341	27	⌈n2	⌈n2	NOUN
ejpam-4520	341	28	⌉+	⌉+	NOUN
ejpam-4520	341	29	1	1	NUM
ejpam-4520	341	30	≤	≤	NUM
ejpam-4520	341	31	i	i	PRON
ejpam-4520	341	32	≤	≤	ADJ
ejpam-4520	341	33	n	n	CCONJ
ejpam-4520	342	1	and	and	CCONJ
ejpam-4520	342	2	i	i	PRON
ejpam-4520	342	3	is	be	AUX
ejpam-4520	342	4	odd	odd	ADJ
ejpam-4520	342	5	,	,	PUNCT
ejpam-4520	342	6	n	n	CCONJ
ejpam-4520	342	7	≡	≡	PROPN
ejpam-4520	342	8	1	1	NUM
ejpam-4520	342	9	mod	mod	PROPN
ejpam-4520	342	10	4	4	NUM
ejpam-4520	342	11	3i+	3i+	NUM
ejpam-4520	342	12	⌊	⌊	PROPN
ejpam-4520	342	13	n	n	ADV
ejpam-4520	342	14	2	2	NUM
ejpam-4520	342	15	⌋	⌋	NOUN
ejpam-4520	343	1	+	+	CCONJ
ejpam-4520	344	1	4n−	4n−	NUM
ejpam-4520	344	2	1	1	NUM
ejpam-4520	344	3	for	for	ADP
ejpam-4520	344	4	1	1	NUM
ejpam-4520	344	5	≤	≤	NUM
ejpam-4520	344	6	i	i	PRON
ejpam-4520	344	7	≤	≤	NUM
ejpam-4520	344	8	⌈n2	⌈n2	NOUN
ejpam-4520	344	9	⌉	⌉	PUNCT
ejpam-4520	344	10	and	and	CCONJ
ejpam-4520	344	11	i	i	PRON
ejpam-4520	344	12	is	be	AUX
ejpam-4520	344	13	even	even	ADV
ejpam-4520	344	14	,	,	PUNCT
ejpam-4520	344	15	n	n	CCONJ
ejpam-4520	344	16	≡	≡	PROPN
ejpam-4520	344	17	1	1	NUM
ejpam-4520	344	18	mod	mod	NOUN
ejpam-4520	344	19	4	4	NUM
ejpam-4520	344	20	3i−	3i−	NUM
ejpam-4520	344	21	n−	n−	NOUN
ejpam-4520	344	22	⌈n2	⌈n2	NOUN
ejpam-4520	344	23	⌉	⌉	PUNCT
ejpam-4520	344	24	for	for	ADP
ejpam-4520	344	25	⌈n2	⌈n2	NOUN
ejpam-4520	344	26	⌉+	⌉+	NOUN
ejpam-4520	344	27	1	1	NUM
ejpam-4520	344	28	≤	≤	NUM
ejpam-4520	344	29	i	i	PRON
ejpam-4520	344	30	≤	≤	ADJ
ejpam-4520	344	31	n	n	CCONJ
ejpam-4520	345	1	and	and	CCONJ
ejpam-4520	345	2	i	i	PRON
ejpam-4520	345	3	is	be	AUX
ejpam-4520	345	4	even	even	ADV
ejpam-4520	345	5	,	,	PUNCT
ejpam-4520	345	6	n	n	CCONJ
ejpam-4520	345	7	≡	≡	PROPN
ejpam-4520	345	8	1	1	NUM
ejpam-4520	345	9	mod	mod	PROPN
ejpam-4520	345	10	4	4	NUM
ejpam-4520	345	11	f(xij	f(xij	NOUN
ejpam-4520	345	12	)	)	PUNCT
ejpam-4520	345	13	=	=	PUNCT
ejpam-4520	345	14			X
ejpam-4520	345	15	k(3n	k(3n	PROPN
ejpam-4520	345	16	)	)	PUNCT
ejpam-4520	346	1	+	+	CCONJ
ejpam-4520	347	1	5n+	5n+	NUM
ejpam-4520	347	2	1−	1−	NUM
ejpam-4520	348	1	3i−	3i−	NUM
ejpam-4520	348	2	⌊	⌊	VERB
ejpam-4520	348	3	n	n	ADV
ejpam-4520	348	4	2	2	NUM
ejpam-4520	348	5	⌋	⌋	NOUN
ejpam-4520	348	6	for	for	ADP
ejpam-4520	348	7	1	1	NUM
ejpam-4520	348	8	≤	≤	NUM
ejpam-4520	349	1	i	i	PRON
ejpam-4520	349	2	≤	≤	PUNCT
ejpam-4520	349	3	⌊	⌊	VERB
ejpam-4520	349	4	n	n	ADV
ejpam-4520	349	5	2	2	NUM
ejpam-4520	349	6	⌋	⌋	NOUN
ejpam-4520	350	1	and	and	CCONJ
ejpam-4520	350	2	i	i	PRON
ejpam-4520	350	3	is	be	AUX
ejpam-4520	350	4	odd	odd	ADJ
ejpam-4520	350	5	,	,	PUNCT
ejpam-4520	350	6	n	n	CCONJ
ejpam-4520	350	7	≡	≡	PROPN
ejpam-4520	350	8	3	3	NUM
ejpam-4520	350	9	mod	mod	PROPN
ejpam-4520	350	10	4	4	NUM
ejpam-4520	350	11	k(3n	k(3n	PROPN
ejpam-4520	350	12	)	)	PUNCT
ejpam-4520	351	1	+	+	CCONJ
ejpam-4520	351	2	7n+	7n+	NUM
ejpam-4520	351	3	1−	1−	NUM
ejpam-4520	351	4	3i+	3i+	NUM
ejpam-4520	351	5	⌈n2	⌈n2	NOUN
ejpam-4520	351	6	⌉	⌉	PRON
ejpam-4520	351	7	for	for	ADP
ejpam-4520	351	8	⌈n2	⌈n2	NOUN
ejpam-4520	351	9	⌉	⌉	X
ejpam-4520	351	10	≤	≤	NUM
ejpam-4520	351	11	i	i	PRON
ejpam-4520	351	12	≤	≤	NOUN
ejpam-4520	351	13	n	n	CCONJ
ejpam-4520	352	1	and	and	CCONJ
ejpam-4520	352	2	i	i	PRON
ejpam-4520	352	3	is	be	AUX
ejpam-4520	352	4	odd	odd	ADJ
ejpam-4520	352	5	,	,	PUNCT
ejpam-4520	352	6	n	n	CCONJ
ejpam-4520	352	7	≡	≡	PROPN
ejpam-4520	352	8	3	3	NUM
ejpam-4520	352	9	mod	mod	PROPN
ejpam-4520	352	10	4	4	NUM
ejpam-4520	352	11	k(3n	k(3n	PROPN
ejpam-4520	352	12	)	)	PUNCT
ejpam-4520	352	13	+	+	CCONJ
ejpam-4520	353	1	5n+	5n+	NUM
ejpam-4520	353	2	3−	3−	NUM
ejpam-4520	353	3	3i−	3i−	NUM
ejpam-4520	353	4	⌊	⌊	VERB
ejpam-4520	353	5	n	n	ADV
ejpam-4520	353	6	2	2	NUM
ejpam-4520	353	7	⌋	⌋	NOUN
ejpam-4520	353	8	for	for	ADP
ejpam-4520	353	9	1	1	NUM
ejpam-4520	353	10	≤	≤	NUM
ejpam-4520	354	1	i	i	PRON
ejpam-4520	354	2	≤	≤	PUNCT
ejpam-4520	354	3	⌊	⌊	VERB
ejpam-4520	354	4	n	n	ADV
ejpam-4520	354	5	2	2	NUM
ejpam-4520	354	6	⌋	⌋	NOUN
ejpam-4520	355	1	and	and	CCONJ
ejpam-4520	355	2	i	i	PRON
ejpam-4520	355	3	is	be	AUX
ejpam-4520	355	4	even	even	ADV
ejpam-4520	355	5	,	,	PUNCT
ejpam-4520	355	6	n	n	CCONJ
ejpam-4520	355	7	≡	≡	PROPN
ejpam-4520	355	8	3	3	NUM
ejpam-4520	355	9	mod	mod	PROPN
ejpam-4520	355	10	4	4	NUM
ejpam-4520	355	11	k(3n	k(3n	PROPN
ejpam-4520	355	12	)	)	PUNCT
ejpam-4520	356	1	+	+	CCONJ
ejpam-4520	356	2	7n+	7n+	NUM
ejpam-4520	356	3	3−	3−	NUM
ejpam-4520	356	4	3i+	3i+	NUM
ejpam-4520	356	5	⌈n2	⌈n2	NOUN
ejpam-4520	356	6	⌉	⌉	PRON
ejpam-4520	356	7	for	for	ADP
ejpam-4520	356	8	⌈n2	⌈n2	NOUN
ejpam-4520	356	9	⌉	⌉	X
ejpam-4520	356	10	≤	≤	NUM
ejpam-4520	356	11	i	i	PRON
ejpam-4520	356	12	≤	≤	NOUN
ejpam-4520	356	13	n	n	CCONJ
ejpam-4520	357	1	and	and	CCONJ
ejpam-4520	357	2	i	i	PRON
ejpam-4520	357	3	is	be	AUX
ejpam-4520	357	4	even	even	ADV
ejpam-4520	357	5	,	,	PUNCT
ejpam-4520	357	6	n	n	CCONJ
ejpam-4520	357	7	≡	≡	PROPN
ejpam-4520	357	8	3	3	NUM
ejpam-4520	357	9	mod	mod	PROPN
ejpam-4520	357	10	4	4	NUM
ejpam-4520	357	11	k(3n	k(3n	PROPN
ejpam-4520	357	12	)	)	PUNCT
ejpam-4520	357	13	+	+	CCONJ
ejpam-4520	358	1	5n+	5n+	NUM
ejpam-4520	358	2	1−	1−	NUM
ejpam-4520	359	1	3i−	3i−	NUM
ejpam-4520	359	2	⌊	⌊	VERB
ejpam-4520	359	3	n	n	ADV
ejpam-4520	359	4	2	2	NUM
ejpam-4520	359	5	⌋	⌋	NOUN
ejpam-4520	359	6	for	for	ADP
ejpam-4520	359	7	1	1	NUM
ejpam-4520	359	8	≤	≤	NUM
ejpam-4520	359	9	i	i	PRON
ejpam-4520	359	10	≤	≤	NUM
ejpam-4520	359	11	⌈n2	⌈n2	NOUN
ejpam-4520	359	12	⌉	⌉	PUNCT
ejpam-4520	359	13	and	and	CCONJ
ejpam-4520	359	14	i	i	PRON
ejpam-4520	359	15	is	be	AUX
ejpam-4520	359	16	odd	odd	ADJ
ejpam-4520	359	17	,	,	PUNCT
ejpam-4520	359	18	n	n	CCONJ
ejpam-4520	359	19	≡	≡	PROPN
ejpam-4520	359	20	1	1	NUM
ejpam-4520	359	21	mod	mod	PROPN
ejpam-4520	359	22	4	4	NUM
ejpam-4520	359	23	k(3n	k(3n	PROPN
ejpam-4520	359	24	)	)	PUNCT
ejpam-4520	360	1	+	+	CCONJ
ejpam-4520	360	2	7n+	7n+	NUM
ejpam-4520	360	3	1−	1−	NUM
ejpam-4520	360	4	3i+	3i+	NUM
ejpam-4520	360	5	⌈n2	⌈n2	NOUN
ejpam-4520	360	6	⌉	⌉	PRON
ejpam-4520	360	7	for	for	ADP
ejpam-4520	360	8	⌈n2	⌈n2	NOUN
ejpam-4520	360	9	⌉+	⌉+	NOUN
ejpam-4520	360	10	1	1	NUM
ejpam-4520	360	11	≤	≤	NUM
ejpam-4520	360	12	i	i	PRON
ejpam-4520	360	13	≤	≤	ADJ
ejpam-4520	360	14	n	n	CCONJ
ejpam-4520	361	1	and	and	CCONJ
ejpam-4520	361	2	i	i	PRON
ejpam-4520	361	3	is	be	AUX
ejpam-4520	361	4	odd	odd	ADJ
ejpam-4520	361	5	,	,	PUNCT
ejpam-4520	361	6	n	n	CCONJ
ejpam-4520	361	7	≡	≡	PROPN
ejpam-4520	361	8	1	1	NUM
ejpam-4520	361	9	mod	mod	PROPN
ejpam-4520	361	10	4	4	NUM
ejpam-4520	361	11	k(3n	k(3n	PROPN
ejpam-4520	361	12	)	)	PUNCT
ejpam-4520	361	13	+	+	CCONJ
ejpam-4520	362	1	5n+	5n+	NUM
ejpam-4520	362	2	3−	3−	NUM
ejpam-4520	362	3	3i−	3i−	NUM
ejpam-4520	362	4	⌊	⌊	VERB
ejpam-4520	362	5	n	n	ADV
ejpam-4520	362	6	2	2	NUM
ejpam-4520	362	7	⌋	⌋	NOUN
ejpam-4520	362	8	for	for	ADP
ejpam-4520	362	9	1	1	NUM
ejpam-4520	362	10	≤	≤	NUM
ejpam-4520	362	11	i	i	PRON
ejpam-4520	362	12	≤	≤	NUM
ejpam-4520	362	13	⌈n2	⌈n2	NOUN
ejpam-4520	362	14	⌉	⌉	PUNCT
ejpam-4520	362	15	and	and	CCONJ
ejpam-4520	362	16	i	i	PRON
ejpam-4520	362	17	is	be	AUX
ejpam-4520	362	18	even	even	ADV
ejpam-4520	362	19	,	,	PUNCT
ejpam-4520	362	20	n	n	CCONJ
ejpam-4520	362	21	≡	≡	PROPN
ejpam-4520	362	22	1	1	NUM
ejpam-4520	362	23	mod	mod	PROPN
ejpam-4520	362	24	4	4	NUM
ejpam-4520	362	25	k(3n	k(3n	PROPN
ejpam-4520	362	26	)	)	PUNCT
ejpam-4520	363	1	+	+	CCONJ
ejpam-4520	363	2	7n+	7n+	NUM
ejpam-4520	363	3	3−	3−	NUM
ejpam-4520	363	4	3i+	3i+	NUM
ejpam-4520	363	5	⌈n2	⌈n2	NOUN
ejpam-4520	363	6	⌉	⌉	PRON
ejpam-4520	363	7	for	for	ADP
ejpam-4520	363	8	⌈n2	⌈n2	NOUN
ejpam-4520	363	9	⌉+	⌉+	NOUN
ejpam-4520	363	10	1	1	NUM
ejpam-4520	363	11	≤	≤	NUM
ejpam-4520	363	12	i	i	PRON
ejpam-4520	363	13	≤	≤	ADJ
ejpam-4520	363	14	n	n	CCONJ
ejpam-4520	364	1	and	and	CCONJ
ejpam-4520	364	2	i	i	PRON
ejpam-4520	364	3	is	be	AUX
ejpam-4520	364	4	even	even	ADV
ejpam-4520	364	5	,	,	PUNCT
ejpam-4520	364	6	n	n	CCONJ
ejpam-4520	364	7	≡	≡	PROPN
ejpam-4520	364	8	1	1	NUM
ejpam-4520	364	9	mod	mod	PROPN
ejpam-4520	364	10	4	4	NUM
ejpam-4520	364	11	f(yij	f(yij	NOUN
ejpam-4520	364	12	)	)	PUNCT
ejpam-4520	364	13	=	=	PRON
ejpam-4520	364	14	{	{	PUNCT
ejpam-4520	364	15	k(3n	k(3n	PROPN
ejpam-4520	364	16	)	)	PUNCT
ejpam-4520	365	1	+	+	CCONJ
ejpam-4520	365	2	4n+	4n+	NUM
ejpam-4520	365	3	⌈n2	⌈n2	NOUN
ejpam-4520	365	4	⌉+	⌉+	NOUN
ejpam-4520	365	5	2−	2−	NUM
ejpam-4520	365	6	3i	3i	NOUN
ejpam-4520	365	7	for	for	ADP
ejpam-4520	365	8	1	1	NUM
ejpam-4520	365	9	≤	≤	NUM
ejpam-4520	365	10	i	i	PRON
ejpam-4520	365	11	≤	≤	NUM
ejpam-4520	365	12	⌈n2	⌈n2	NOUN
ejpam-4520	365	13	⌉	⌉	NOUN
ejpam-4520	365	14	,	,	PUNCT
ejpam-4520	365	15	1	1	NUM
ejpam-4520	365	16	≤≤	≤≤	NUM
ejpam-4520	365	17	m	m	VERB
ejpam-4520	365	18	k(3n	k(3n	NOUN
ejpam-4520	365	19	)	)	PUNCT
ejpam-4520	366	1	+	+	CCONJ
ejpam-4520	366	2	7n+	7n+	NUM
ejpam-4520	366	3	⌈n2	⌈n2	NOUN
ejpam-4520	366	4	⌉+	⌉+	NOUN
ejpam-4520	366	5	2−	2−	NUM
ejpam-4520	366	6	3i	3i	NOUN
ejpam-4520	366	7	for	for	ADP
ejpam-4520	366	8	⌈n2	⌈n2	NOUN
ejpam-4520	366	9	⌉+	⌉+	NOUN
ejpam-4520	366	10	1	1	NUM
ejpam-4520	366	11	≤	≤	NUM
ejpam-4520	366	12	i	i	PRON
ejpam-4520	366	13	≤	≤	PROPN
ejpam-4520	366	14	n	n	CCONJ
ejpam-4520	366	15	,	,	PUNCT
ejpam-4520	366	16	1	1	NUM
ejpam-4520	366	17	≤	≤	NUM
ejpam-4520	366	18	j	j	PROPN
ejpam-4520	366	19	≤	≤	NUM
ejpam-4520	366	20	m	m	VERB
ejpam-4520	366	21	f(zij	f(zij	PROPN
ejpam-4520	366	22	)	)	PUNCT
ejpam-4520	366	23	=	=	PUNCT
ejpam-4520	366	24			NUM
ejpam-4520	366	25	k(3n	k(3n	PROPN
ejpam-4520	366	26	)	)	PUNCT
ejpam-4520	366	27	+	+	CCONJ
ejpam-4520	367	1	5n+	5n+	NUM
ejpam-4520	367	2	3−	3−	NUM
ejpam-4520	367	3	3i−	3i−	NUM
ejpam-4520	367	4	⌊	⌊	VERB
ejpam-4520	367	5	n	n	ADV
ejpam-4520	367	6	2	2	NUM
ejpam-4520	367	7	⌋	⌋	NOUN
ejpam-4520	367	8	for	for	ADP
ejpam-4520	367	9	1	1	NUM
ejpam-4520	367	10	≤	≤	NUM
ejpam-4520	368	1	i	i	PRON
ejpam-4520	368	2	≤	≤	PUNCT
ejpam-4520	368	3	⌊	⌊	VERB
ejpam-4520	368	4	n	n	ADV
ejpam-4520	368	5	2	2	NUM
ejpam-4520	368	6	⌋	⌋	NOUN
ejpam-4520	369	1	and	and	CCONJ
ejpam-4520	369	2	i	i	PRON
ejpam-4520	369	3	is	be	AUX
ejpam-4520	369	4	odd	odd	ADJ
ejpam-4520	369	5	,	,	PUNCT
ejpam-4520	369	6	n	n	CCONJ
ejpam-4520	369	7	≡	≡	PROPN
ejpam-4520	369	8	3	3	NUM
ejpam-4520	369	9	mod	mod	PROPN
ejpam-4520	369	10	4	4	NUM
ejpam-4520	369	11	k(3n	k(3n	PROPN
ejpam-4520	369	12	)	)	PUNCT
ejpam-4520	370	1	+	+	CCONJ
ejpam-4520	370	2	7n+	7n+	NUM
ejpam-4520	370	3	3−	3−	NUM
ejpam-4520	370	4	3i+	3i+	NUM
ejpam-4520	370	5	⌈n2	⌈n2	NOUN
ejpam-4520	370	6	⌉	⌉	PRON
ejpam-4520	370	7	for	for	ADP
ejpam-4520	370	8	⌈n2	⌈n2	NOUN
ejpam-4520	370	9	⌉	⌉	X
ejpam-4520	370	10	≤	≤	NUM
ejpam-4520	370	11	i	i	PRON
ejpam-4520	370	12	≤	≤	NOUN
ejpam-4520	370	13	n	n	CCONJ
ejpam-4520	371	1	and	and	CCONJ
ejpam-4520	371	2	i	i	PRON
ejpam-4520	371	3	is	be	AUX
ejpam-4520	371	4	odd	odd	ADJ
ejpam-4520	371	5	,	,	PUNCT
ejpam-4520	371	6	n	n	CCONJ
ejpam-4520	371	7	≡	≡	PROPN
ejpam-4520	371	8	3	3	NUM
ejpam-4520	371	9	mod	mod	PROPN
ejpam-4520	371	10	4	4	NUM
ejpam-4520	371	11	k(3n	k(3n	PROPN
ejpam-4520	371	12	)	)	PUNCT
ejpam-4520	371	13	+	+	CCONJ
ejpam-4520	372	1	5n+	5n+	NUM
ejpam-4520	372	2	2−	2−	NUM
ejpam-4520	372	3	3i−	3i−	NUM
ejpam-4520	372	4	⌊	⌊	PROPN
ejpam-4520	372	5	n	n	ADV
ejpam-4520	372	6	2	2	NUM
ejpam-4520	372	7	⌋	⌋	NOUN
ejpam-4520	372	8	for	for	ADP
ejpam-4520	372	9	1	1	NUM
ejpam-4520	372	10	≤	≤	NUM
ejpam-4520	373	1	i	i	PRON
ejpam-4520	373	2	≤	≤	PUNCT
ejpam-4520	373	3	⌊	⌊	VERB
ejpam-4520	373	4	n	n	ADV
ejpam-4520	373	5	2	2	NUM
ejpam-4520	373	6	⌋	⌋	NOUN
ejpam-4520	374	1	and	and	CCONJ
ejpam-4520	374	2	i	i	PRON
ejpam-4520	374	3	is	be	AUX
ejpam-4520	374	4	even	even	ADV
ejpam-4520	374	5	,	,	PUNCT
ejpam-4520	374	6	n	n	CCONJ
ejpam-4520	374	7	≡	≡	PROPN
ejpam-4520	374	8	3	3	NUM
ejpam-4520	374	9	mod	mod	PROPN
ejpam-4520	374	10	4	4	NUM
ejpam-4520	374	11	k(3n	k(3n	PROPN
ejpam-4520	374	12	)	)	PUNCT
ejpam-4520	375	1	+	+	CCONJ
ejpam-4520	375	2	7n+	7n+	NUM
ejpam-4520	375	3	1−	1−	NUM
ejpam-4520	375	4	3i+	3i+	NUM
ejpam-4520	375	5	⌈n2	⌈n2	NOUN
ejpam-4520	375	6	⌉	⌉	PRON
ejpam-4520	375	7	for	for	ADP
ejpam-4520	375	8	⌈n2	⌈n2	NOUN
ejpam-4520	375	9	⌉	⌉	X
ejpam-4520	375	10	≤	≤	NUM
ejpam-4520	375	11	i	i	PRON
ejpam-4520	375	12	≤	≤	NOUN
ejpam-4520	375	13	n	n	CCONJ
ejpam-4520	376	1	and	and	CCONJ
ejpam-4520	376	2	i	i	PRON
ejpam-4520	376	3	is	be	AUX
ejpam-4520	376	4	even	even	ADV
ejpam-4520	376	5	,	,	PUNCT
ejpam-4520	376	6	n	n	CCONJ
ejpam-4520	376	7	≡	≡	PROPN
ejpam-4520	376	8	3	3	NUM
ejpam-4520	376	9	mod	mod	PROPN
ejpam-4520	376	10	4	4	NUM
ejpam-4520	376	11	k(3n	k(3n	PROPN
ejpam-4520	376	12	)	)	PUNCT
ejpam-4520	376	13	+	+	CCONJ
ejpam-4520	377	1	5n+	5n+	NUM
ejpam-4520	377	2	3−	3−	NUM
ejpam-4520	377	3	3i−	3i−	NUM
ejpam-4520	377	4	⌊	⌊	VERB
ejpam-4520	377	5	n	n	ADV
ejpam-4520	377	6	2	2	NUM
ejpam-4520	377	7	⌋	⌋	NOUN
ejpam-4520	377	8	for	for	ADP
ejpam-4520	377	9	1	1	NUM
ejpam-4520	377	10	≤	≤	NUM
ejpam-4520	377	11	i	i	PRON
ejpam-4520	377	12	≤	≤	NUM
ejpam-4520	377	13	⌈n2	⌈n2	NOUN
ejpam-4520	377	14	⌉	⌉	PUNCT
ejpam-4520	377	15	and	and	CCONJ
ejpam-4520	377	16	i	i	PRON
ejpam-4520	377	17	is	be	AUX
ejpam-4520	377	18	odd	odd	ADJ
ejpam-4520	377	19	,	,	PUNCT
ejpam-4520	377	20	n	n	CCONJ
ejpam-4520	377	21	≡	≡	PROPN
ejpam-4520	377	22	1	1	NUM
ejpam-4520	377	23	mod	mod	PROPN
ejpam-4520	377	24	4	4	NUM
ejpam-4520	377	25	k(3n	k(3n	PROPN
ejpam-4520	377	26	)	)	PUNCT
ejpam-4520	378	1	+	+	CCONJ
ejpam-4520	378	2	7n+	7n+	NUM
ejpam-4520	378	3	3−	3−	NUM
ejpam-4520	378	4	3i+	3i+	NUM
ejpam-4520	378	5	⌈n2	⌈n2	NOUN
ejpam-4520	378	6	⌉	⌉	PRON
ejpam-4520	378	7	for	for	ADP
ejpam-4520	378	8	⌈n2	⌈n2	NOUN
ejpam-4520	378	9	⌉+	⌉+	NOUN
ejpam-4520	378	10	1	1	NUM
ejpam-4520	378	11	≤	≤	NUM
ejpam-4520	378	12	i	i	PRON
ejpam-4520	378	13	≤	≤	ADJ
ejpam-4520	378	14	n	n	CCONJ
ejpam-4520	379	1	and	and	CCONJ
ejpam-4520	379	2	i	i	PRON
ejpam-4520	379	3	is	be	AUX
ejpam-4520	379	4	odd	odd	ADJ
ejpam-4520	379	5	,	,	PUNCT
ejpam-4520	379	6	n	n	CCONJ
ejpam-4520	379	7	≡	≡	PROPN
ejpam-4520	379	8	1	1	NUM
ejpam-4520	379	9	mod	mod	PROPN
ejpam-4520	379	10	4	4	NUM
ejpam-4520	379	11	k(3n	k(3n	PROPN
ejpam-4520	379	12	)	)	PUNCT
ejpam-4520	379	13	+	+	CCONJ
ejpam-4520	380	1	5n+	5n+	NUM
ejpam-4520	380	2	2−	2−	NUM
ejpam-4520	380	3	3i−	3i−	NUM
ejpam-4520	380	4	⌊	⌊	PROPN
ejpam-4520	380	5	n	n	ADV
ejpam-4520	380	6	2	2	NUM
ejpam-4520	380	7	⌋	⌋	NOUN
ejpam-4520	380	8	for	for	ADP
ejpam-4520	380	9	1	1	NUM
ejpam-4520	380	10	≤	≤	NUM
ejpam-4520	380	11	i	i	PRON
ejpam-4520	380	12	≤	≤	NUM
ejpam-4520	380	13	⌈n2	⌈n2	NOUN
ejpam-4520	380	14	⌉	⌉	PUNCT
ejpam-4520	380	15	and	and	CCONJ
ejpam-4520	380	16	i	i	PRON
ejpam-4520	380	17	is	be	AUX
ejpam-4520	380	18	even	even	ADV
ejpam-4520	380	19	,	,	PUNCT
ejpam-4520	380	20	n	n	CCONJ
ejpam-4520	380	21	≡	≡	PROPN
ejpam-4520	380	22	1	1	NUM
ejpam-4520	380	23	mod	mod	PROPN
ejpam-4520	380	24	4	4	NUM
ejpam-4520	380	25	k(3n	k(3n	PROPN
ejpam-4520	380	26	)	)	PUNCT
ejpam-4520	381	1	+	+	CCONJ
ejpam-4520	381	2	7n+	7n+	NUM
ejpam-4520	381	3	1−	1−	NUM
ejpam-4520	381	4	3i+	3i+	NUM
ejpam-4520	381	5	⌈n2	⌈n2	NOUN
ejpam-4520	381	6	⌉	⌉	PRON
ejpam-4520	381	7	for	for	ADP
ejpam-4520	381	8	⌈n2	⌈n2	NOUN
ejpam-4520	381	9	⌉+	⌉+	NOUN
ejpam-4520	381	10	1	1	NUM
ejpam-4520	381	11	≤	≤	NUM
ejpam-4520	381	12	i	i	PRON
ejpam-4520	381	13	≤	≤	ADJ
ejpam-4520	381	14	n	n	CCONJ
ejpam-4520	382	1	and	and	CCONJ
ejpam-4520	382	2	i	i	PRON
ejpam-4520	382	3	is	be	AUX
ejpam-4520	382	4	even	even	ADV
ejpam-4520	382	5	,	,	PUNCT
ejpam-4520	382	6	n	n	CCONJ
ejpam-4520	382	7	≡	≡	PROPN
ejpam-4520	382	8	1	1	NUM
ejpam-4520	382	9	mod	mod	NOUN
ejpam-4520	382	10	4	4	NUM
ejpam-4520	382	11	susilowati	susilowati	NOUN
ejpam-4520	382	12	et	et	NOUN
ejpam-4520	382	13	.	.	PUNCT
ejpam-4520	383	1	al	al	PROPN
ejpam-4520	383	2	/	/	PUNCT
ejpam-4520	383	3	eur	eur	PROPN
ejpam-4520	383	4	.	.	PUNCT
ejpam-4520	384	1	j.	j.	PROPN
ejpam-4520	384	2	pure	pure	PROPN
ejpam-4520	384	3	appl	appl	PROPN
ejpam-4520	384	4	.	.	PROPN
ejpam-4520	384	5	math	math	PROPN
ejpam-4520	384	6	,	,	PUNCT
ejpam-4520	384	7	16	16	NUM
ejpam-4520	384	8	(	(	PUNCT
ejpam-4520	384	9	1	1	NUM
ejpam-4520	384	10	)	)	PUNCT
ejpam-4520	384	11	(	(	PUNCT
ejpam-4520	384	12	2023	2023	NUM
ejpam-4520	384	13	)	)	PUNCT
ejpam-4520	384	14	,	,	PUNCT
ejpam-4520	384	15	271	271	NUM
ejpam-4520	384	16	-	-	SYM
ejpam-4520	384	17	285	285	NUM
ejpam-4520	384	18	282	282	NUM
ejpam-4520	384	19	the	the	DET
ejpam-4520	384	20	edge	edge	NOUN
ejpam-4520	384	21	weights	weight	NOUN
ejpam-4520	384	22	of	of	ADP
ejpam-4520	384	23	the	the	DET
ejpam-4520	384	24	above	above	ADJ
ejpam-4520	384	25	vertex	vertex	NOUN
ejpam-4520	384	26	labeling	labeling	NOUN
ejpam-4520	384	27	f	f	PROPN
ejpam-4520	384	28	can	can	AUX
ejpam-4520	384	29	be	be	AUX
ejpam-4520	384	30	presented	present	VERB
ejpam-4520	384	31	as	as	ADP
ejpam-4520	384	32	w(xixi+1	w(xixi+1	PROPN
ejpam-4520	384	33	)	)	PUNCT
ejpam-4520	384	34	=	=	PUNCT
ejpam-4520	384	35	3n+	3n+	NUM
ejpam-4520	384	36	6i	6i	NUM
ejpam-4520	384	37	,	,	PUNCT
ejpam-4520	384	38	for	for	ADP
ejpam-4520	384	39	1	1	NUM
ejpam-4520	384	40	≤	≤	NUM
ejpam-4520	384	41	i	i	PRON
ejpam-4520	384	42	≤	≤	ADJ
ejpam-4520	384	43	n−	n−	NOUN
ejpam-4520	384	44	1	1	NUM
ejpam-4520	384	45	w(xiyi	w(xiyi	NOUN
ejpam-4520	384	46	)	)	PUNCT
ejpam-4520	384	47	=	=	PRON
ejpam-4520	384	48	{	{	PUNCT
ejpam-4520	385	1	6i+	6i+	NUM
ejpam-4520	385	2	2n+	2n+	NUM
ejpam-4520	385	3	2	2	NUM
ejpam-4520	385	4	(	(	PUNCT
ejpam-4520	385	5	⌊	⌊	VERB
ejpam-4520	385	6	n	n	PRON
ejpam-4520	385	7	2	2	NUM
ejpam-4520	385	8	⌋	⌋	NOUN
ejpam-4520	385	9	)	)	PUNCT
ejpam-4520	386	1	−	−	PROPN
ejpam-4520	386	2	1	1	NUM
ejpam-4520	386	3	for	for	ADP
ejpam-4520	386	4	1	1	NUM
ejpam-4520	386	5	≤	≤	NUM
ejpam-4520	386	6	i	i	PRON
ejpam-4520	386	7	≤	≤	ADJ
ejpam-4520	386	8	n	n	CCONJ
ejpam-4520	387	1	and	and	CCONJ
ejpam-4520	387	2	i	i	PRON
ejpam-4520	387	3	is	be	AUX
ejpam-4520	387	4	odd	odd	ADJ
ejpam-4520	387	5	6i+	6i+	NUM
ejpam-4520	387	6	2n+	2n+	NUM
ejpam-4520	387	7	2	2	NUM
ejpam-4520	387	8	(	(	PUNCT
ejpam-4520	387	9	⌊	⌊	VERB
ejpam-4520	387	10	n	n	PRON
ejpam-4520	387	11	2	2	NUM
ejpam-4520	387	12	⌋	⌋	NOUN
ejpam-4520	387	13	)	)	PUNCT
ejpam-4520	388	1	−	−	ADP
ejpam-4520	388	2	4	4	NUM
ejpam-4520	388	3	for	for	ADP
ejpam-4520	388	4	1	1	NUM
ejpam-4520	388	5	≤	≤	NUM
ejpam-4520	388	6	i	i	PRON
ejpam-4520	388	7	≤	≤	ADJ
ejpam-4520	389	1	n	n	CCONJ
ejpam-4520	390	1	and	and	CCONJ
ejpam-4520	390	2	i	i	PRON
ejpam-4520	390	3	is	be	AUX
ejpam-4520	390	4	even	even	ADV
ejpam-4520	390	5	w(yizi	w(yizi	ADJ
ejpam-4520	390	6	)	)	PUNCT
ejpam-4520	391	1	=	=	PRON
ejpam-4520	391	2	{	{	PUNCT
ejpam-4520	391	3	6i+	6i+	NUM
ejpam-4520	391	4	2n+	2n+	NUM
ejpam-4520	391	5	2	2	NUM
ejpam-4520	391	6	(	(	PUNCT
ejpam-4520	391	7	⌊	⌊	VERB
ejpam-4520	391	8	n	n	PRON
ejpam-4520	391	9	2	2	NUM
ejpam-4520	391	10	⌋	⌋	NOUN
ejpam-4520	391	11	)	)	PUNCT
ejpam-4520	391	12	−	−	PROPN
ejpam-4520	391	13	3	3	NUM
ejpam-4520	391	14	for	for	ADP
ejpam-4520	391	15	1	1	NUM
ejpam-4520	391	16	≤	≤	NUM
ejpam-4520	391	17	i	i	PRON
ejpam-4520	391	18	≤	≤	ADJ
ejpam-4520	392	1	n	n	CCONJ
ejpam-4520	393	1	and	and	CCONJ
ejpam-4520	393	2	i	i	PRON
ejpam-4520	393	3	is	be	AUX
ejpam-4520	393	4	odd	odd	ADJ
ejpam-4520	393	5	6i+	6i+	NUM
ejpam-4520	393	6	2n+	2n+	NUM
ejpam-4520	393	7	2	2	NUM
ejpam-4520	393	8	(	(	PUNCT
ejpam-4520	393	9	⌊	⌊	VERB
ejpam-4520	393	10	n	n	PRON
ejpam-4520	393	11	2	2	NUM
ejpam-4520	393	12	⌋	⌋	NOUN
ejpam-4520	393	13	)	)	PUNCT
ejpam-4520	394	1	−	−	PROPN
ejpam-4520	394	2	2	2	NUM
ejpam-4520	394	3	for	for	ADP
ejpam-4520	394	4	1	1	NUM
ejpam-4520	394	5	≤	≤	NUM
ejpam-4520	394	6	i	i	PRON
ejpam-4520	394	7	≤	≤	ADJ
ejpam-4520	395	1	n	n	CCONJ
ejpam-4520	396	1	and	and	CCONJ
ejpam-4520	396	2	i	i	PRON
ejpam-4520	396	3	is	be	AUX
ejpam-4520	396	4	even	even	ADV
ejpam-4520	396	5	w(xix0i	w(xix0i	NOUN
ejpam-4520	396	6	)	)	PUNCT
ejpam-4520	397	1	=	=	SYM
ejpam-4520	397	2			NUM
ejpam-4520	397	3	6i+	6i+	NUM
ejpam-4520	397	4	2	2	NUM
ejpam-4520	397	5	(	(	PUNCT
ejpam-4520	397	6	⌊	⌊	VERB
ejpam-4520	397	7	n	n	PRON
ejpam-4520	397	8	2	2	NUM
ejpam-4520	397	9	⌋	⌋	NOUN
ejpam-4520	397	10	)	)	PUNCT
ejpam-4520	398	1	+	+	CCONJ
ejpam-4520	398	2	5n	5n	NOUN
ejpam-4520	398	3	for	for	ADP
ejpam-4520	398	4	1	1	NUM
ejpam-4520	398	5	≤	≤	NUM
ejpam-4520	399	1	i	i	PRON
ejpam-4520	399	2	≤	≤	PUNCT
ejpam-4520	399	3	⌊	⌊	VERB
ejpam-4520	399	4	n	n	ADV
ejpam-4520	399	5	2	2	NUM
ejpam-4520	399	6	⌋	⌋	NOUN
ejpam-4520	400	1	and	and	CCONJ
ejpam-4520	400	2	i	i	PRON
ejpam-4520	400	3	is	be	AUX
ejpam-4520	400	4	odd	odd	ADJ
ejpam-4520	400	5	,	,	PUNCT
ejpam-4520	400	6	n	n	CCONJ
ejpam-4520	400	7	≡	≡	PROPN
ejpam-4520	400	8	3	3	NUM
ejpam-4520	400	9	mod	mod	NOUN
ejpam-4520	400	10	4	4	NUM
ejpam-4520	400	11	6i−	6i−	NOUN
ejpam-4520	400	12	1	1	NUM
ejpam-4520	400	13	for	for	ADP
ejpam-4520	400	14	⌈n2	⌈n2	NOUN
ejpam-4520	400	15	⌉	⌉	X
ejpam-4520	400	16	≤	≤	NUM
ejpam-4520	400	17	i	i	PRON
ejpam-4520	400	18	≤	≤	NOUN
ejpam-4520	400	19	n	n	CCONJ
ejpam-4520	401	1	and	and	CCONJ
ejpam-4520	401	2	i	i	PRON
ejpam-4520	401	3	is	be	AUX
ejpam-4520	401	4	odd	odd	ADJ
ejpam-4520	401	5	,	,	PUNCT
ejpam-4520	401	6	n	n	CCONJ
ejpam-4520	401	7	≡	≡	PROPN
ejpam-4520	401	8	3	3	NUM
ejpam-4520	401	9	mod	mod	NOUN
ejpam-4520	401	10	4	4	NUM
ejpam-4520	401	11	6i+	6i+	NUM
ejpam-4520	401	12	2	2	NUM
ejpam-4520	401	13	(	(	PUNCT
ejpam-4520	401	14	⌊	⌊	VERB
ejpam-4520	401	15	n	n	PRON
ejpam-4520	401	16	2	2	NUM
ejpam-4520	401	17	⌋	⌋	NOUN
ejpam-4520	401	18	)	)	PUNCT
ejpam-4520	402	1	+	+	PUNCT
ejpam-4520	402	2	5n−	5n−	NUM
ejpam-4520	402	3	4	4	NUM
ejpam-4520	402	4	for	for	ADP
ejpam-4520	402	5	1	1	NUM
ejpam-4520	402	6	≤	≤	NUM
ejpam-4520	402	7	i	i	PRON
ejpam-4520	402	8	≤	≤	PUNCT
ejpam-4520	402	9	⌊	⌊	VERB
ejpam-4520	402	10	n	n	ADV
ejpam-4520	402	11	2	2	NUM
ejpam-4520	402	12	⌋	⌋	NOUN
ejpam-4520	403	1	and	and	CCONJ
ejpam-4520	403	2	i	i	PRON
ejpam-4520	403	3	is	be	AUX
ejpam-4520	403	4	even	even	ADV
ejpam-4520	403	5	,	,	PUNCT
ejpam-4520	403	6	n	n	CCONJ
ejpam-4520	403	7	≡	≡	PROPN
ejpam-4520	403	8	3	3	NUM
ejpam-4520	403	9	mod	mod	NOUN
ejpam-4520	403	10	4	4	NUM
ejpam-4520	403	11	6i−	6i−	NUM
ejpam-4520	403	12	5	5	NUM
ejpam-4520	403	13	for	for	ADP
ejpam-4520	403	14	⌈n2	⌈n2	NOUN
ejpam-4520	403	15	⌉	⌉	X
ejpam-4520	403	16	≤	≤	NUM
ejpam-4520	403	17	i	i	PRON
ejpam-4520	403	18	≤	≤	NOUN
ejpam-4520	403	19	n	n	CCONJ
ejpam-4520	404	1	and	and	CCONJ
ejpam-4520	404	2	i	i	PRON
ejpam-4520	404	3	is	be	AUX
ejpam-4520	404	4	even	even	ADV
ejpam-4520	404	5	,	,	PUNCT
ejpam-4520	404	6	n	n	CCONJ
ejpam-4520	404	7	≡	≡	PROPN
ejpam-4520	404	8	3	3	NUM
ejpam-4520	404	9	mod	mod	NOUN
ejpam-4520	404	10	4	4	NUM
ejpam-4520	404	11	6i+	6i+	NUM
ejpam-4520	404	12	2	2	NUM
ejpam-4520	404	13	(	(	PUNCT
ejpam-4520	404	14	⌊	⌊	VERB
ejpam-4520	404	15	n	n	PRON
ejpam-4520	404	16	2	2	NUM
ejpam-4520	404	17	⌋	⌋	NOUN
ejpam-4520	404	18	)	)	PUNCT
ejpam-4520	405	1	+	+	CCONJ
ejpam-4520	405	2	5n	5n	NOUN
ejpam-4520	405	3	for	for	ADP
ejpam-4520	405	4	1	1	NUM
ejpam-4520	405	5	≤	≤	NUM
ejpam-4520	405	6	i	i	PRON
ejpam-4520	405	7	≤	≤	NUM
ejpam-4520	405	8	⌈n2	⌈n2	NOUN
ejpam-4520	405	9	⌉	⌉	PUNCT
ejpam-4520	405	10	and	and	CCONJ
ejpam-4520	405	11	i	i	PRON
ejpam-4520	405	12	is	be	AUX
ejpam-4520	405	13	odd	odd	ADJ
ejpam-4520	405	14	,	,	PUNCT
ejpam-4520	405	15	n	n	CCONJ
ejpam-4520	405	16	≡	≡	PROPN
ejpam-4520	405	17	1	1	NUM
ejpam-4520	405	18	mod	mod	NOUN
ejpam-4520	405	19	4	4	NUM
ejpam-4520	405	20	6i−	6i−	NOUN
ejpam-4520	405	21	1	1	NUM
ejpam-4520	405	22	for	for	ADP
ejpam-4520	405	23	⌈n2	⌈n2	NOUN
ejpam-4520	405	24	⌉+	⌉+	NOUN
ejpam-4520	405	25	1	1	NUM
ejpam-4520	405	26	≤	≤	NUM
ejpam-4520	405	27	i	i	PRON
ejpam-4520	405	28	≤	≤	ADJ
ejpam-4520	405	29	n	n	CCONJ
ejpam-4520	406	1	and	and	CCONJ
ejpam-4520	406	2	i	i	PRON
ejpam-4520	406	3	is	be	AUX
ejpam-4520	406	4	odd	odd	ADJ
ejpam-4520	406	5	,	,	PUNCT
ejpam-4520	406	6	n	n	CCONJ
ejpam-4520	406	7	≡	≡	PROPN
ejpam-4520	406	8	1	1	NUM
ejpam-4520	406	9	mod	mod	NOUN
ejpam-4520	406	10	4	4	NUM
ejpam-4520	406	11	6i+	6i+	NUM
ejpam-4520	406	12	2	2	NUM
ejpam-4520	406	13	(	(	PUNCT
ejpam-4520	406	14	⌊	⌊	VERB
ejpam-4520	406	15	n	n	PRON
ejpam-4520	406	16	2	2	NUM
ejpam-4520	406	17	⌋	⌋	NOUN
ejpam-4520	406	18	)	)	PUNCT
ejpam-4520	407	1	+	+	PUNCT
ejpam-4520	408	1	5n−	5n−	NUM
ejpam-4520	408	2	4	4	NUM
ejpam-4520	408	3	for	for	ADP
ejpam-4520	408	4	1	1	NUM
ejpam-4520	408	5	≤	≤	NUM
ejpam-4520	408	6	i	i	PRON
ejpam-4520	408	7	≤	≤	NUM
ejpam-4520	408	8	⌈n2	⌈n2	NOUN
ejpam-4520	408	9	⌉	⌉	PUNCT
ejpam-4520	408	10	and	and	CCONJ
ejpam-4520	408	11	i	i	PRON
ejpam-4520	408	12	is	be	AUX
ejpam-4520	408	13	even	even	ADV
ejpam-4520	408	14	,	,	PUNCT
ejpam-4520	408	15	n	n	CCONJ
ejpam-4520	408	16	≡	≡	PROPN
ejpam-4520	408	17	1	1	NUM
ejpam-4520	408	18	mod	mod	NOUN
ejpam-4520	408	19	4	4	NUM
ejpam-4520	408	20	6i−	6i−	NUM
ejpam-4520	408	21	5	5	NUM
ejpam-4520	408	22	for	for	ADP
ejpam-4520	408	23	⌈n2	⌈n2	NOUN
ejpam-4520	408	24	⌉+	⌉+	NOUN
ejpam-4520	408	25	1	1	NUM
ejpam-4520	408	26	≤	≤	NUM
ejpam-4520	408	27	i	i	PRON
ejpam-4520	408	28	≤	≤	ADJ
ejpam-4520	408	29	n	n	CCONJ
ejpam-4520	409	1	and	and	CCONJ
ejpam-4520	409	2	i	i	PRON
ejpam-4520	409	3	is	be	AUX
ejpam-4520	409	4	even	even	ADV
ejpam-4520	409	5	,	,	PUNCT
ejpam-4520	409	6	n	n	CCONJ
ejpam-4520	409	7	≡	≡	PROPN
ejpam-4520	409	8	1	1	NUM
ejpam-4520	409	9	mod	mod	PROPN
ejpam-4520	409	10	4	4	NUM
ejpam-4520	409	11	w(yiy0i	w(yiy0i	NOUN
ejpam-4520	409	12	)	)	PUNCT
ejpam-4520	409	13	=	=	PRON
ejpam-4520	409	14	{	{	PUNCT
ejpam-4520	409	15	6i+	6i+	NUM
ejpam-4520	409	16	5n+	5n+	NUM
ejpam-4520	409	17	⌊	⌊	PROPN
ejpam-4520	409	18	n	n	CCONJ
ejpam-4520	409	19	2	2	NUM
ejpam-4520	409	20	⌋	⌋	NOUN
ejpam-4520	409	21	−	−	NOUN
ejpam-4520	409	22	2	2	NUM
ejpam-4520	409	23	for	for	ADP
ejpam-4520	409	24	1	1	NUM
ejpam-4520	409	25	≤	≤	NUM
ejpam-4520	409	26	i	i	PRON
ejpam-4520	409	27	≤	≤	NUM
ejpam-4520	409	28	⌈n2	⌈n2	NOUN
ejpam-4520	409	29	⌉	⌉	PRON
ejpam-4520	409	30	6i−	6i−	PROPN
ejpam-4520	409	31	3	3	NUM
ejpam-4520	409	32	for	for	ADP
ejpam-4520	409	33	⌈n2	⌈n2	NOUN
ejpam-4520	409	34	⌉+	⌉+	NOUN
ejpam-4520	409	35	1	1	NUM
ejpam-4520	409	36	≤	≤	NUM
ejpam-4520	409	37	i	i	PRON
ejpam-4520	409	38	≤	≤	PROPN
ejpam-4520	409	39	n	n	PRON
ejpam-4520	409	40	w(ziz0i	w(ziz0i	PUNCT
ejpam-4520	409	41	)	)	PUNCT
ejpam-4520	409	42	=	=	SYM
ejpam-4520	409	43			NUM
ejpam-4520	409	44	6i+	6i+	NUM
ejpam-4520	409	45	2	2	NUM
ejpam-4520	409	46	(	(	PUNCT
ejpam-4520	409	47	⌊	⌊	VERB
ejpam-4520	409	48	n	n	PRON
ejpam-4520	409	49	2	2	NUM
ejpam-4520	409	50	⌋	⌋	NOUN
ejpam-4520	409	51	)	)	PUNCT
ejpam-4520	410	1	+	+	PUNCT
ejpam-4520	410	2	5n−	5n−	NUM
ejpam-4520	410	3	4	4	NUM
ejpam-4520	410	4	for	for	ADP
ejpam-4520	410	5	1	1	NUM
ejpam-4520	410	6	≤	≤	NUM
ejpam-4520	410	7	i	i	PRON
ejpam-4520	410	8	≤	≤	PUNCT
ejpam-4520	410	9	⌊	⌊	VERB
ejpam-4520	410	10	n	n	ADV
ejpam-4520	410	11	2	2	NUM
ejpam-4520	410	12	⌋	⌋	NOUN
ejpam-4520	411	1	and	and	CCONJ
ejpam-4520	411	2	i	i	PRON
ejpam-4520	411	3	is	be	AUX
ejpam-4520	411	4	odd	odd	ADJ
ejpam-4520	411	5	,	,	PUNCT
ejpam-4520	411	6	n	n	CCONJ
ejpam-4520	411	7	≡	≡	PROPN
ejpam-4520	411	8	3	3	NUM
ejpam-4520	411	9	mod	mod	NOUN
ejpam-4520	411	10	4	4	NUM
ejpam-4520	411	11	6i−	6i−	NUM
ejpam-4520	411	12	5	5	NUM
ejpam-4520	411	13	for	for	ADP
ejpam-4520	411	14	⌈n2	⌈n2	NOUN
ejpam-4520	411	15	⌉	⌉	X
ejpam-4520	411	16	≤	≤	NUM
ejpam-4520	411	17	i	i	PRON
ejpam-4520	411	18	≤	≤	NOUN
ejpam-4520	411	19	n	n	CCONJ
ejpam-4520	412	1	and	and	CCONJ
ejpam-4520	412	2	i	i	PRON
ejpam-4520	412	3	is	be	AUX
ejpam-4520	412	4	odd	odd	ADJ
ejpam-4520	412	5	,	,	PUNCT
ejpam-4520	412	6	n	n	CCONJ
ejpam-4520	412	7	≡	≡	PROPN
ejpam-4520	412	8	3	3	NUM
ejpam-4520	412	9	mod	mod	NOUN
ejpam-4520	412	10	4	4	NUM
ejpam-4520	412	11	6i+	6i+	NUM
ejpam-4520	412	12	2	2	NUM
ejpam-4520	412	13	(	(	PUNCT
ejpam-4520	412	14	⌊	⌊	VERB
ejpam-4520	412	15	n	n	PRON
ejpam-4520	412	16	2	2	NUM
ejpam-4520	412	17	⌋	⌋	NOUN
ejpam-4520	412	18	)	)	PUNCT
ejpam-4520	413	1	+	+	PUNCT
ejpam-4520	413	2	5n−	5n−	NUM
ejpam-4520	413	3	1	1	NUM
ejpam-4520	413	4	for	for	ADP
ejpam-4520	413	5	1	1	NUM
ejpam-4520	413	6	≤	≤	NUM
ejpam-4520	413	7	i	i	PRON
ejpam-4520	413	8	≤	≤	PUNCT
ejpam-4520	413	9	⌊	⌊	VERB
ejpam-4520	413	10	n	n	ADV
ejpam-4520	413	11	2	2	NUM
ejpam-4520	413	12	⌋	⌋	NOUN
ejpam-4520	414	1	and	and	CCONJ
ejpam-4520	414	2	i	i	PRON
ejpam-4520	414	3	is	be	AUX
ejpam-4520	414	4	even	even	ADV
ejpam-4520	414	5	,	,	PUNCT
ejpam-4520	414	6	n	n	CCONJ
ejpam-4520	414	7	≡	≡	PROPN
ejpam-4520	414	8	3	3	NUM
ejpam-4520	414	9	mod	mod	NOUN
ejpam-4520	414	10	4	4	NUM
ejpam-4520	414	11	6i−	6i−	PROPN
ejpam-4520	414	12	3	3	NUM
ejpam-4520	414	13	for	for	ADP
ejpam-4520	414	14	⌈n2	⌈n2	NOUN
ejpam-4520	414	15	⌉	⌉	X
ejpam-4520	414	16	≤	≤	NUM
ejpam-4520	414	17	i	i	PRON
ejpam-4520	414	18	≤	≤	NOUN
ejpam-4520	414	19	n	n	CCONJ
ejpam-4520	415	1	and	and	CCONJ
ejpam-4520	415	2	i	i	PRON
ejpam-4520	415	3	is	be	AUX
ejpam-4520	415	4	even	even	ADV
ejpam-4520	415	5	,	,	PUNCT
ejpam-4520	415	6	n	n	CCONJ
ejpam-4520	415	7	≡	≡	PROPN
ejpam-4520	415	8	3	3	NUM
ejpam-4520	415	9	mod	mod	NOUN
ejpam-4520	415	10	4	4	NUM
ejpam-4520	415	11	6i+	6i+	NUM
ejpam-4520	415	12	2	2	NUM
ejpam-4520	415	13	(	(	PUNCT
ejpam-4520	415	14	⌊	⌊	VERB
ejpam-4520	415	15	n	n	PRON
ejpam-4520	415	16	2	2	NUM
ejpam-4520	415	17	⌋	⌋	NOUN
ejpam-4520	415	18	)	)	PUNCT
ejpam-4520	416	1	+	+	PUNCT
ejpam-4520	417	1	5n−	5n−	NUM
ejpam-4520	417	2	4	4	NUM
ejpam-4520	417	3	for	for	ADP
ejpam-4520	417	4	1	1	NUM
ejpam-4520	417	5	≤	≤	NUM
ejpam-4520	417	6	i	i	PRON
ejpam-4520	417	7	≤	≤	NUM
ejpam-4520	417	8	⌈n2	⌈n2	NOUN
ejpam-4520	417	9	⌉	⌉	PUNCT
ejpam-4520	417	10	and	and	CCONJ
ejpam-4520	417	11	i	i	PRON
ejpam-4520	417	12	is	be	AUX
ejpam-4520	417	13	odd	odd	ADJ
ejpam-4520	417	14	,	,	PUNCT
ejpam-4520	417	15	n	n	CCONJ
ejpam-4520	417	16	≡	≡	PROPN
ejpam-4520	417	17	1	1	NUM
ejpam-4520	417	18	mod	mod	NOUN
ejpam-4520	417	19	4	4	NUM
ejpam-4520	417	20	6i−	6i−	NUM
ejpam-4520	417	21	5	5	NUM
ejpam-4520	417	22	for	for	ADP
ejpam-4520	417	23	⌈n2	⌈n2	NOUN
ejpam-4520	417	24	⌉+	⌉+	NOUN
ejpam-4520	417	25	1	1	NUM
ejpam-4520	417	26	≤	≤	NUM
ejpam-4520	417	27	i	i	PRON
ejpam-4520	417	28	≤	≤	ADJ
ejpam-4520	417	29	n	n	CCONJ
ejpam-4520	418	1	and	and	CCONJ
ejpam-4520	418	2	i	i	PRON
ejpam-4520	418	3	is	be	AUX
ejpam-4520	418	4	odd	odd	ADJ
ejpam-4520	418	5	,	,	PUNCT
ejpam-4520	418	6	n	n	CCONJ
ejpam-4520	418	7	≡	≡	PROPN
ejpam-4520	418	8	1	1	NUM
ejpam-4520	418	9	mod	mod	NOUN
ejpam-4520	418	10	4	4	NUM
ejpam-4520	418	11	6i+	6i+	NUM
ejpam-4520	418	12	2	2	NUM
ejpam-4520	418	13	(	(	PUNCT
ejpam-4520	418	14	⌊	⌊	VERB
ejpam-4520	418	15	n	n	PRON
ejpam-4520	418	16	2	2	NUM
ejpam-4520	418	17	⌋	⌋	NOUN
ejpam-4520	418	18	)	)	PUNCT
ejpam-4520	419	1	+	+	PUNCT
ejpam-4520	420	1	5n−	5n−	NUM
ejpam-4520	420	2	1	1	NUM
ejpam-4520	420	3	for	for	ADP
ejpam-4520	420	4	1	1	NUM
ejpam-4520	420	5	≤	≤	NUM
ejpam-4520	420	6	i	i	PRON
ejpam-4520	420	7	≤	≤	NUM
ejpam-4520	420	8	⌈n2	⌈n2	NOUN
ejpam-4520	420	9	⌉	⌉	PUNCT
ejpam-4520	420	10	and	and	CCONJ
ejpam-4520	420	11	i	i	PRON
ejpam-4520	420	12	is	be	AUX
ejpam-4520	420	13	even	even	ADV
ejpam-4520	420	14	,	,	PUNCT
ejpam-4520	420	15	n	n	CCONJ
ejpam-4520	420	16	≡	≡	PROPN
ejpam-4520	420	17	1	1	NUM
ejpam-4520	420	18	mod	mod	NOUN
ejpam-4520	420	19	4	4	NUM
ejpam-4520	420	20	6i−	6i−	PROPN
ejpam-4520	420	21	3	3	NUM
ejpam-4520	420	22	for	for	ADP
ejpam-4520	420	23	⌈n2	⌈n2	NOUN
ejpam-4520	420	24	⌉+	⌉+	NOUN
ejpam-4520	420	25	1	1	NUM
ejpam-4520	420	26	≤	≤	NUM
ejpam-4520	420	27	i	i	PRON
ejpam-4520	420	28	≤	≤	ADJ
ejpam-4520	420	29	n	n	CCONJ
ejpam-4520	421	1	and	and	CCONJ
ejpam-4520	421	2	i	i	PRON
ejpam-4520	421	3	is	be	AUX
ejpam-4520	421	4	even	even	ADV
ejpam-4520	421	5	,	,	PUNCT
ejpam-4520	421	6	n	n	CCONJ
ejpam-4520	421	7	≡	≡	PROPN
ejpam-4520	421	8	1	1	NUM
ejpam-4520	421	9	mod	mod	PROPN
ejpam-4520	421	10	4	4	NUM
ejpam-4520	421	11	w(xixij	w(xixij	NOUN
ejpam-4520	421	12	)	)	PUNCT
ejpam-4520	421	13	=	=	SYM
ejpam-4520	421	14			X
ejpam-4520	421	15	k(3n	k(3n	PROPN
ejpam-4520	421	16	)	)	PUNCT
ejpam-4520	422	1	+	+	CCONJ
ejpam-4520	422	2	6n+	6n+	NUM
ejpam-4520	422	3	1	1	NUM
ejpam-4520	422	4	for	for	ADP
ejpam-4520	422	5	1	1	NUM
ejpam-4520	422	6	≤	≤	NUM
ejpam-4520	422	7	i	i	PRON
ejpam-4520	422	8	≤	≤	NUM
ejpam-4520	422	9	⌈n2	⌈n2	NOUN
ejpam-4520	422	10	⌉	⌉	PRON
ejpam-4520	422	11	and	and	CCONJ
ejpam-4520	422	12	n	n	PRON
ejpam-4520	422	13	≡	≡	PROPN
ejpam-4520	422	14	3	3	NUM
ejpam-4520	422	15	mod	mod	PROPN
ejpam-4520	422	16	4	4	NUM
ejpam-4520	422	17	k(3n	k(3n	PROPN
ejpam-4520	422	18	)	)	PUNCT
ejpam-4520	422	19	+	+	CCONJ
ejpam-4520	422	20	9n+	9n+	NUM
ejpam-4520	422	21	1	1	NUM
ejpam-4520	422	22	for	for	ADP
ejpam-4520	422	23	⌈n2	⌈n2	NOUN
ejpam-4520	422	24	⌉+	⌉+	NOUN
ejpam-4520	422	25	1	1	NUM
ejpam-4520	422	26	≤	≤	NUM
ejpam-4520	422	27	i	i	PRON
ejpam-4520	422	28	≤	≤	ADJ
ejpam-4520	422	29	n	n	CCONJ
ejpam-4520	422	30	and	and	CCONJ
ejpam-4520	422	31	n	n	CCONJ
ejpam-4520	422	32	≡	≡	PROPN
ejpam-4520	422	33	3	3	NUM
ejpam-4520	422	34	mod	mod	PROPN
ejpam-4520	422	35	4	4	NUM
ejpam-4520	422	36	k(3n	k(3n	PROPN
ejpam-4520	422	37	)	)	PUNCT
ejpam-4520	423	1	+	+	CCONJ
ejpam-4520	423	2	6n+	6n+	NUM
ejpam-4520	423	3	1	1	NUM
ejpam-4520	423	4	for	for	ADP
ejpam-4520	423	5	1	1	NUM
ejpam-4520	423	6	≤	≤	NUM
ejpam-4520	423	7	i	i	PRON
ejpam-4520	423	8	≤	≤	PUNCT
ejpam-4520	423	9	⌊	⌊	VERB
ejpam-4520	423	10	n	n	ADV
ejpam-4520	423	11	2	2	NUM
ejpam-4520	423	12	⌋	⌋	NOUN
ejpam-4520	423	13	and	and	CCONJ
ejpam-4520	423	14	n	n	CCONJ
ejpam-4520	423	15	≡	≡	PROPN
ejpam-4520	423	16	1	1	NUM
ejpam-4520	423	17	mod	mod	PROPN
ejpam-4520	423	18	4	4	NUM
ejpam-4520	423	19	k(3n	k(3n	PROPN
ejpam-4520	423	20	)	)	PUNCT
ejpam-4520	424	1	+	+	CCONJ
ejpam-4520	424	2	9n+	9n+	NUM
ejpam-4520	424	3	1	1	NUM
ejpam-4520	424	4	for	for	ADP
ejpam-4520	424	5	⌈n2	⌈n2	NOUN
ejpam-4520	424	6	⌉	⌉	X
ejpam-4520	424	7	≤	≤	NUM
ejpam-4520	424	8	i	i	NOUN
ejpam-4520	424	9	≤	≤	ADJ
ejpam-4520	424	10	n	n	CCONJ
ejpam-4520	424	11	and	and	CCONJ
ejpam-4520	424	12	n	n	CCONJ
ejpam-4520	424	13	≡	≡	PROPN
ejpam-4520	424	14	1	1	NUM
ejpam-4520	424	15	mod	mod	PROPN
ejpam-4520	424	16	4	4	NUM
ejpam-4520	424	17	w(x0ixij	w(x0ixij	NOUN
ejpam-4520	424	18	)	)	PUNCT
ejpam-4520	424	19	=	=	PUNCT
ejpam-4520	424	20			X
ejpam-4520	424	21	k(3n	k(3n	PROPN
ejpam-4520	424	22	)	)	PUNCT
ejpam-4520	425	1	+	+	CCONJ
ejpam-4520	425	2	9n+	9n+	NUM
ejpam-4520	425	3	1	1	NUM
ejpam-4520	425	4	for	for	ADP
ejpam-4520	425	5	1	1	NUM
ejpam-4520	425	6	≤	≤	NUM
ejpam-4520	425	7	i	i	PRON
ejpam-4520	425	8	≤	≤	NUM
ejpam-4520	425	9	⌈n2	⌈n2	NOUN
ejpam-4520	425	10	⌉	⌉	PRON
ejpam-4520	425	11	and	and	CCONJ
ejpam-4520	425	12	n	n	PRON
ejpam-4520	425	13	≡	≡	PROPN
ejpam-4520	425	14	3	3	NUM
ejpam-4520	425	15	mod	mod	PROPN
ejpam-4520	425	16	4	4	NUM
ejpam-4520	425	17	k(3n	k(3n	PROPN
ejpam-4520	425	18	)	)	PUNCT
ejpam-4520	426	1	+	+	CCONJ
ejpam-4520	426	2	6n+	6n+	NUM
ejpam-4520	426	3	1	1	NUM
ejpam-4520	426	4	for	for	ADP
ejpam-4520	426	5	⌈n2	⌈n2	NOUN
ejpam-4520	426	6	⌉+	⌉+	NOUN
ejpam-4520	426	7	1	1	NUM
ejpam-4520	426	8	≤	≤	NUM
ejpam-4520	426	9	i	i	PRON
ejpam-4520	427	1	≤	≤	ADJ
ejpam-4520	427	2	n	n	CCONJ
ejpam-4520	427	3	and	and	CCONJ
ejpam-4520	427	4	n	n	CCONJ
ejpam-4520	427	5	≡	≡	PROPN
ejpam-4520	427	6	3	3	NUM
ejpam-4520	427	7	mod	mod	PROPN
ejpam-4520	427	8	4	4	NUM
ejpam-4520	427	9	k(3n	k(3n	PROPN
ejpam-4520	427	10	)	)	PUNCT
ejpam-4520	427	11	+	+	CCONJ
ejpam-4520	427	12	9n+	9n+	NUM
ejpam-4520	427	13	1	1	NUM
ejpam-4520	427	14	for	for	ADP
ejpam-4520	427	15	1	1	NUM
ejpam-4520	427	16	≤	≤	NUM
ejpam-4520	427	17	i	i	PRON
ejpam-4520	427	18	≤	≤	PUNCT
ejpam-4520	427	19	⌊	⌊	VERB
ejpam-4520	427	20	n	n	ADV
ejpam-4520	427	21	2	2	NUM
ejpam-4520	427	22	⌋	⌋	NOUN
ejpam-4520	427	23	and	and	CCONJ
ejpam-4520	427	24	n	n	CCONJ
ejpam-4520	427	25	≡	≡	PROPN
ejpam-4520	427	26	1	1	NUM
ejpam-4520	427	27	mod	mod	PROPN
ejpam-4520	427	28	4	4	NUM
ejpam-4520	427	29	k(3n	k(3n	PROPN
ejpam-4520	427	30	)	)	PUNCT
ejpam-4520	428	1	+	+	CCONJ
ejpam-4520	428	2	6n+	6n+	NUM
ejpam-4520	428	3	1	1	NUM
ejpam-4520	428	4	for	for	ADP
ejpam-4520	428	5	⌈n2	⌈n2	NOUN
ejpam-4520	428	6	⌉	⌉	X
ejpam-4520	428	7	≤	≤	NUM
ejpam-4520	428	8	i	i	NOUN
ejpam-4520	428	9	≤	≤	ADJ
ejpam-4520	428	10	n	n	CCONJ
ejpam-4520	428	11	and	and	CCONJ
ejpam-4520	428	12	n	n	CCONJ
ejpam-4520	428	13	≡	≡	PROPN
ejpam-4520	428	14	1	1	NUM
ejpam-4520	428	15	mod	mod	PROPN
ejpam-4520	428	16	4	4	NUM
ejpam-4520	428	17	w(yiyij	w(yiyij	NOUN
ejpam-4520	428	18	)	)	PUNCT
ejpam-4520	428	19	=	=	PRON
ejpam-4520	428	20	{	{	PUNCT
ejpam-4520	428	21	k(3n	k(3n	PROPN
ejpam-4520	428	22	)	)	PUNCT
ejpam-4520	429	1	+	+	CCONJ
ejpam-4520	429	2	6n+	6n+	NUM
ejpam-4520	429	3	1	1	NUM
ejpam-4520	429	4	for	for	ADP
ejpam-4520	429	5	1	1	NUM
ejpam-4520	429	6	≤	≤	NUM
ejpam-4520	429	7	i	i	PRON
ejpam-4520	429	8	≤	≤	NUM
ejpam-4520	429	9	⌈n2	⌈n2	NOUN
ejpam-4520	429	10	⌉	⌉	NOUN
ejpam-4520	429	11	,	,	PUNCT
ejpam-4520	429	12	1	1	NUM
ejpam-4520	429	13	≤≤	≤≤	NUM
ejpam-4520	429	14	m	m	VERB
ejpam-4520	429	15	k(3n	k(3n	NOUN
ejpam-4520	429	16	)	)	PUNCT
ejpam-4520	430	1	+	+	CCONJ
ejpam-4520	430	2	9n+	9n+	NUM
ejpam-4520	430	3	1	1	NUM
ejpam-4520	430	4	for	for	ADP
ejpam-4520	430	5	⌈n2	⌈n2	NOUN
ejpam-4520	430	6	⌉+	⌉+	NOUN
ejpam-4520	430	7	1	1	NUM
ejpam-4520	430	8	≤	≤	NUM
ejpam-4520	430	9	i	i	PRON
ejpam-4520	430	10	≤	≤	PROPN
ejpam-4520	430	11	n	n	CCONJ
ejpam-4520	430	12	,	,	PUNCT
ejpam-4520	430	13	1	1	NUM
ejpam-4520	430	14	≤	≤	NUM
ejpam-4520	430	15	j	j	PROPN
ejpam-4520	430	16	≤	≤	PROPN
ejpam-4520	430	17	m	m	VERB
ejpam-4520	430	18	w(zizij	w(zizij	PROPN
ejpam-4520	430	19	)	)	PUNCT
ejpam-4520	430	20	=	=	SYM
ejpam-4520	431	1			X
ejpam-4520	431	2	k(3n	k(3n	PROPN
ejpam-4520	431	3	)	)	PUNCT
ejpam-4520	432	1	+	+	CCONJ
ejpam-4520	432	2	6n+	6n+	NUM
ejpam-4520	432	3	1	1	NUM
ejpam-4520	432	4	for	for	ADP
ejpam-4520	432	5	1	1	NUM
ejpam-4520	432	6	≤	≤	NUM
ejpam-4520	432	7	i	i	PRON
ejpam-4520	432	8	≤	≤	PUNCT
ejpam-4520	432	9	⌊	⌊	VERB
ejpam-4520	432	10	n	n	ADV
ejpam-4520	432	11	2	2	NUM
ejpam-4520	432	12	⌋	⌋	NOUN
ejpam-4520	432	13	and	and	CCONJ
ejpam-4520	432	14	n	n	PRON
ejpam-4520	432	15	≡	≡	PROPN
ejpam-4520	432	16	3	3	NUM
ejpam-4520	432	17	mod	mod	PROPN
ejpam-4520	432	18	4	4	NUM
ejpam-4520	432	19	k(3n	k(3n	PROPN
ejpam-4520	432	20	)	)	PUNCT
ejpam-4520	432	21	+	+	CCONJ
ejpam-4520	433	1	9n+	9n+	NUM
ejpam-4520	433	2	1	1	NUM
ejpam-4520	433	3	for	for	ADP
ejpam-4520	433	4	⌈n2	⌈n2	NOUN
ejpam-4520	433	5	⌉	⌉	X
ejpam-4520	433	6	≤	≤	NUM
ejpam-4520	433	7	i	i	NOUN
ejpam-4520	433	8	≤	≤	ADJ
ejpam-4520	433	9	n	n	CCONJ
ejpam-4520	433	10	and	and	CCONJ
ejpam-4520	433	11	n	n	CCONJ
ejpam-4520	433	12	≡	≡	PROPN
ejpam-4520	433	13	3	3	NUM
ejpam-4520	433	14	mod	mod	PROPN
ejpam-4520	433	15	4	4	NUM
ejpam-4520	433	16	k(3n	k(3n	PROPN
ejpam-4520	433	17	)	)	PUNCT
ejpam-4520	433	18	+	+	CCONJ
ejpam-4520	433	19	6n+	6n+	NUM
ejpam-4520	433	20	1	1	NUM
ejpam-4520	433	21	for	for	ADP
ejpam-4520	433	22	1	1	NUM
ejpam-4520	433	23	≤	≤	NUM
ejpam-4520	433	24	i	i	PRON
ejpam-4520	433	25	≤	≤	NUM
ejpam-4520	433	26	⌈n2	⌈n2	NOUN
ejpam-4520	433	27	⌉	⌉	PRON
ejpam-4520	433	28	and	and	CCONJ
ejpam-4520	433	29	n	n	PRON
ejpam-4520	433	30	≡	≡	PROPN
ejpam-4520	433	31	1	1	NUM
ejpam-4520	433	32	mod	mod	PROPN
ejpam-4520	433	33	4	4	NUM
ejpam-4520	433	34	k(3n	k(3n	PROPN
ejpam-4520	433	35	)	)	PUNCT
ejpam-4520	434	1	+	+	CCONJ
ejpam-4520	434	2	9n+	9n+	NUM
ejpam-4520	434	3	1	1	NUM
ejpam-4520	434	4	for	for	ADP
ejpam-4520	434	5	⌈n2	⌈n2	NOUN
ejpam-4520	434	6	⌉+	⌉+	NOUN
ejpam-4520	434	7	1	1	NUM
ejpam-4520	434	8	≤	≤	NUM
ejpam-4520	434	9	i	i	PRON
ejpam-4520	434	10	≤	≤	ADJ
ejpam-4520	434	11	n	n	CCONJ
ejpam-4520	434	12	and	and	CCONJ
ejpam-4520	434	13	n	n	CCONJ
ejpam-4520	434	14	≡	≡	PROPN
ejpam-4520	434	15	1	1	NUM
ejpam-4520	434	16	mod	mod	NOUN
ejpam-4520	434	17	4	4	NUM
ejpam-4520	434	18	references	reference	NOUN
ejpam-4520	434	19	283	283	NUM
ejpam-4520	434	20	w(z0izij	w(z0izij	NOUN
ejpam-4520	434	21	)	)	PUNCT
ejpam-4520	434	22	=	=	PUNCT
ejpam-4520	434	23			X
ejpam-4520	434	24	k(3n	k(3n	PROPN
ejpam-4520	434	25	)	)	PUNCT
ejpam-4520	435	1	+	+	CCONJ
ejpam-4520	435	2	9n+	9n+	NUM
ejpam-4520	435	3	1	1	NUM
ejpam-4520	435	4	for	for	ADP
ejpam-4520	435	5	1	1	NUM
ejpam-4520	435	6	≤	≤	NUM
ejpam-4520	435	7	i	i	PRON
ejpam-4520	435	8	≤	≤	PUNCT
ejpam-4520	435	9	⌊	⌊	VERB
ejpam-4520	435	10	n	n	ADV
ejpam-4520	435	11	2	2	NUM
ejpam-4520	435	12	⌋	⌋	NOUN
ejpam-4520	435	13	and	and	CCONJ
ejpam-4520	435	14	n	n	PRON
ejpam-4520	435	15	≡	≡	PROPN
ejpam-4520	435	16	3	3	NUM
ejpam-4520	435	17	mod	mod	PROPN
ejpam-4520	435	18	4	4	NUM
ejpam-4520	435	19	k(3n	k(3n	PROPN
ejpam-4520	435	20	)	)	PUNCT
ejpam-4520	436	1	+	+	CCONJ
ejpam-4520	436	2	6n+	6n+	NUM
ejpam-4520	436	3	1	1	NUM
ejpam-4520	436	4	for	for	ADP
ejpam-4520	436	5	⌈n2	⌈n2	NOUN
ejpam-4520	436	6	⌉	⌉	X
ejpam-4520	436	7	≤	≤	NUM
ejpam-4520	436	8	i	i	NOUN
ejpam-4520	436	9	≤	≤	ADJ
ejpam-4520	436	10	n	n	CCONJ
ejpam-4520	436	11	and	and	CCONJ
ejpam-4520	436	12	n	n	CCONJ
ejpam-4520	436	13	≡	≡	PROPN
ejpam-4520	436	14	3	3	NUM
ejpam-4520	436	15	mod	mod	PROPN
ejpam-4520	436	16	4	4	NUM
ejpam-4520	436	17	k(3n	k(3n	PROPN
ejpam-4520	436	18	)	)	PUNCT
ejpam-4520	437	1	+	+	CCONJ
ejpam-4520	437	2	9n+	9n+	NUM
ejpam-4520	437	3	1	1	NUM
ejpam-4520	437	4	for	for	ADP
ejpam-4520	437	5	1	1	NUM
ejpam-4520	437	6	≤	≤	NUM
ejpam-4520	437	7	i	i	PRON
ejpam-4520	437	8	≤	≤	NUM
ejpam-4520	437	9	⌈n2	⌈n2	NOUN
ejpam-4520	437	10	⌉	⌉	PRON
ejpam-4520	437	11	and	and	CCONJ
ejpam-4520	437	12	n	n	PRON
ejpam-4520	437	13	≡	≡	PROPN
ejpam-4520	437	14	1	1	NUM
ejpam-4520	437	15	mod	mod	PROPN
ejpam-4520	437	16	4	4	NUM
ejpam-4520	437	17	k(3n	k(3n	PROPN
ejpam-4520	437	18	)	)	PUNCT
ejpam-4520	438	1	+	+	CCONJ
ejpam-4520	438	2	6n+	6n+	NUM
ejpam-4520	438	3	1	1	NUM
ejpam-4520	438	4	for	for	ADP
ejpam-4520	438	5	⌈n2	⌈n2	NOUN
ejpam-4520	438	6	⌉+	⌉+	NOUN
ejpam-4520	438	7	1	1	NUM
ejpam-4520	438	8	≤	≤	NUM
ejpam-4520	438	9	i	i	PRON
ejpam-4520	438	10	≤	≤	ADJ
ejpam-4520	438	11	n	n	CCONJ
ejpam-4520	438	12	and	and	CCONJ
ejpam-4520	438	13	n	n	CCONJ
ejpam-4520	438	14	≡	≡	PROPN
ejpam-4520	438	15	1	1	NUM
ejpam-4520	438	16	mod	mod	NOUN
ejpam-4520	438	17	4	4	NUM
ejpam-4520	438	18	based	base	VERB
ejpam-4520	438	19	on	on	ADP
ejpam-4520	438	20	theorem	theorem	ADJ
ejpam-4520	438	21	3	3	NUM
ejpam-4520	438	22	,	,	PUNCT
ejpam-4520	438	23	rac(fn,3	rac(fn,3	PROPN
ejpam-4520	438	24	)	)	PUNCT
ejpam-4520	438	25	=	=	SYM
ejpam-4520	439	1	3n	3n	NUM
ejpam-4520	439	2	−	−	NOUN
ejpam-4520	439	3	1	1	X
ejpam-4520	439	4	.	.	PUNCT
ejpam-4520	439	5	since	since	SCONJ
ejpam-4520	439	6	e(fn,3	e(fn,3	NUM
ejpam-4520	439	7	)	)	PUNCT
ejpam-4520	440	1	=	=	SYM
ejpam-4520	440	2	3n	3n	NUM
ejpam-4520	441	1	−	−	NUM
ejpam-4520	441	2	1	1	NUM
ejpam-4520	441	3	,	,	PUNCT
ejpam-4520	441	4	for	for	ADP
ejpam-4520	441	5	u	u	NOUN
ejpam-4520	441	6	,	,	PUNCT
ejpam-4520	441	7	v	v	PROPN
ejpam-4520	441	8	∈	∈	PROPN
ejpam-4520	441	9	e(fn,3	e(fn,3	NUM
ejpam-4520	441	10	)	)	PUNCT
ejpam-4520	441	11	has	have	VERB
ejpam-4520	441	12	a	a	DET
ejpam-4520	441	13	different	different	ADJ
ejpam-4520	441	14	colors	color	NOUN
ejpam-4520	441	15	.	.	PUNCT
ejpam-4520	442	1	therefore	therefore	ADV
ejpam-4520	442	2	,	,	PUNCT
ejpam-4520	442	3	the	the	DET
ejpam-4520	442	4	sum	sum	NOUN
ejpam-4520	442	5	of	of	ADP
ejpam-4520	442	6	the	the	DET
ejpam-4520	442	7	weights	weight	NOUN
ejpam-4520	442	8	of	of	ADP
ejpam-4520	442	9	graph	graph	NOUN
ejpam-4520	442	10	fn,3	fn,3	NOUN
ejpam-4520	442	11	is	be	AUX
ejpam-4520	442	12	3n	3n	NUM
ejpam-4520	442	13	−	−	NUM
ejpam-4520	442	14	1	1	NUM
ejpam-4520	442	15	.	.	PUNCT
ejpam-4520	442	16	based	base	VERB
ejpam-4520	442	17	on	on	ADP
ejpam-4520	442	18	theorem	theorem	NOUN
ejpam-4520	442	19	5	5	NUM
ejpam-4520	442	20	,	,	PUNCT
ejpam-4520	442	21	we	we	PRON
ejpam-4520	442	22	have	have	VERB
ejpam-4520	442	23	rac(k1	rac(k1	PROPN
ejpam-4520	442	24	+	+	CCONJ
ejpam-4520	442	25	sm	sm	NOUN
ejpam-4520	442	26	)	)	PUNCT
ejpam-4520	442	27	=	=	PUNCT
ejpam-4520	443	1	m+	m+	NUM
ejpam-4520	443	2	2	2	NUM
ejpam-4520	443	3	.	.	PUNCT
ejpam-4520	443	4	based	base	VERB
ejpam-4520	443	5	on	on	ADP
ejpam-4520	443	6	the	the	DET
ejpam-4520	443	7	description	description	NOUN
ejpam-4520	443	8	above	above	ADV
ejpam-4520	444	1	,	,	PUNCT
ejpam-4520	444	2	we	we	PRON
ejpam-4520	444	3	have	have	VERB
ejpam-4520	444	4	that	that	SCONJ
ejpam-4520	444	5	the	the	DET
ejpam-4520	444	6	distinct	distinct	ADJ
ejpam-4520	444	7	weight	weight	NOUN
ejpam-4520	444	8	of	of	ADP
ejpam-4520	444	9	graph	graph	NOUN
ejpam-4520	444	10	(	(	PUNCT
ejpam-4520	444	11	fn,3	fn,3	NOUN
ejpam-4520	444	12	⊙sm	⊙sm	NOUN
ejpam-4520	444	13	)	)	PUNCT
ejpam-4520	444	14	is	be	AUX
ejpam-4520	444	15	3n+m+1	3n+m+1	NUM
ejpam-4520	444	16	.	.	PUNCT
ejpam-4520	445	1	it	it	PRON
ejpam-4520	445	2	implies	imply	VERB
ejpam-4520	445	3	the	the	DET
ejpam-4520	445	4	edge	edge	NOUN
ejpam-4520	445	5	weights	weight	NOUN
ejpam-4520	445	6	of	of	ADP
ejpam-4520	445	7	f	f	NOUN
ejpam-4520	445	8	:	:	PUNCT
ejpam-4520	445	9	v	v	X
ejpam-4520	445	10	(	(	PUNCT
ejpam-4520	445	11	fn,3⊙sm	fn,3⊙sm	NOUN
ejpam-4520	445	12	)	)	PUNCT
ejpam-4520	445	13	→	→	SYM
ejpam-4520	445	14	{	{	PUNCT
ejpam-4520	445	15	1	1	NUM
ejpam-4520	445	16	,	,	PUNCT
ejpam-4520	445	17	2	2	NUM
ejpam-4520	445	18	,	,	PUNCT
ejpam-4520	445	19	...	...	PUNCT
ejpam-4520	445	20	,	,	PUNCT
ejpam-4520	445	21	6n+3	6n+3	PROPN
ejpam-4520	445	22	nm	nm	NOUN
ejpam-4520	445	23	}	}	PUNCT
ejpam-4520	445	24	induces	induce	VERB
ejpam-4520	445	25	a	a	DET
ejpam-4520	445	26	rainbow	rainbow	NOUN
ejpam-4520	445	27	antimagic	antimagic	ADJ
ejpam-4520	445	28	coloring	coloring	NOUN
ejpam-4520	445	29	of	of	ADP
ejpam-4520	445	30	3n+m+1	3n+m+1	NUM
ejpam-4520	445	31	colors	color	NOUN
ejpam-4520	445	32	.	.	PUNCT
ejpam-4520	446	1	thus	thus	ADV
ejpam-4520	446	2	rac(fn,3⊙sm	rac(fn,3⊙sm	NOUN
ejpam-4520	446	3	)	)	PUNCT
ejpam-4520	446	4	≤	≤	NUM
ejpam-4520	446	5	3n+m+1	3n+m+1	NUM
ejpam-4520	446	6	.	.	PUNCT
ejpam-4520	447	1	comparing	compare	VERB
ejpam-4520	447	2	the	the	DET
ejpam-4520	447	3	two	two	NUM
ejpam-4520	447	4	bounds	bound	NOUN
ejpam-4520	447	5	,	,	PUNCT
ejpam-4520	447	6	we	we	PRON
ejpam-4520	447	7	have	have	VERB
ejpam-4520	447	8	the	the	DET
ejpam-4520	447	9	exact	exact	ADJ
ejpam-4520	447	10	value	value	NOUN
ejpam-4520	447	11	of	of	ADP
ejpam-4520	447	12	rac(fn,3	rac(fn,3	PROPN
ejpam-4520	447	13	⊙	⊙	NOUN
ejpam-4520	447	14	sm	sm	INTJ
ejpam-4520	447	15	)	)	PUNCT
ejpam-4520	447	16	=	=	PUNCT
ejpam-4520	448	1	3n+m+	3n+m+	NUM
ejpam-4520	448	2	1	1	NUM
ejpam-4520	448	3	.	.	PUNCT
ejpam-4520	449	1	the	the	DET
ejpam-4520	449	2	next	next	ADJ
ejpam-4520	449	3	step	step	NOUN
ejpam-4520	449	4	,	,	PUNCT
ejpam-4520	449	5	evaluate	evaluate	VERB
ejpam-4520	449	6	to	to	PART
ejpam-4520	449	7	prove	prove	VERB
ejpam-4520	449	8	the	the	DET
ejpam-4520	449	9	existence	existence	NOUN
ejpam-4520	449	10	of	of	ADP
ejpam-4520	449	11	a	a	DET
ejpam-4520	449	12	rainbow	rainbow	NOUN
ejpam-4520	449	13	u	u	NOUN
ejpam-4520	449	14	−	−	PROPN
ejpam-4520	449	15	v	v	ADP
ejpam-4520	449	16	path	path	NOUN
ejpam-4520	449	17	fn,3	fn,3	PROPN
ejpam-4520	449	18	⊙	⊙	PROPN
ejpam-4520	450	1	sm	sm	PROPN
ejpam-4520	450	2	.	.	PROPN
ejpam-4520	451	1	based	base	VERB
ejpam-4520	451	2	on	on	ADP
ejpam-4520	451	3	the	the	DET
ejpam-4520	451	4	definition	definition	NOUN
ejpam-4520	451	5	of	of	ADP
ejpam-4520	451	6	the	the	DET
ejpam-4520	451	7	graph	graph	NOUN
ejpam-4520	451	8	fn,3	fn,3	PROPN
ejpam-4520	451	9	⊙	⊙	PROPN
ejpam-4520	452	1	sm	sm	PROPN
ejpam-4520	452	2	,	,	PUNCT
ejpam-4520	452	3	then	then	ADV
ejpam-4520	452	4	the	the	DET
ejpam-4520	452	5	graph	graph	NOUN
ejpam-4520	452	6	fn,3	fn,3	PROPN
ejpam-4520	452	7	⊙	⊙	PROPN
ejpam-4520	452	8	sm	sm	PROPN
ejpam-4520	452	9	contains	contain	VERB
ejpam-4520	452	10	one	one	NUM
ejpam-4520	452	11	graph	graph	NOUN
ejpam-4520	452	12	fn,3	fn,3	NOUN
ejpam-4520	452	13	and	and	CCONJ
ejpam-4520	452	14	|v	|v	PROPN
ejpam-4520	452	15	(	(	PUNCT
ejpam-4520	452	16	fn,3)|	fn,3)|	NUM
ejpam-4520	452	17	copies	copy	NOUN
ejpam-4520	452	18	of	of	ADP
ejpam-4520	452	19	k1	k1	PROPN
ejpam-4520	452	20	+	+	CCONJ
ejpam-4520	452	21	sm	sm	PROPN
ejpam-4520	452	22	,	,	PUNCT
ejpam-4520	452	23	so	so	SCONJ
ejpam-4520	452	24	that	that	SCONJ
ejpam-4520	452	25	we	we	PRON
ejpam-4520	452	26	can	can	AUX
ejpam-4520	452	27	evaluate	evaluate	VERB
ejpam-4520	452	28	the	the	DET
ejpam-4520	452	29	rainbow	rainbow	NOUN
ejpam-4520	452	30	u	u	NOUN
ejpam-4520	452	31	−	−	PROPN
ejpam-4520	452	32	v	v	ADP
ejpam-4520	452	33	path	path	NOUN
ejpam-4520	452	34	of	of	ADP
ejpam-4520	452	35	the	the	DET
ejpam-4520	452	36	graph	graph	NOUN
ejpam-4520	452	37	fn,3	fn,3	NOUN
ejpam-4520	452	38	⊙	⊙	PROPN
ejpam-4520	453	1	sm	sm	INTJ
ejpam-4520	453	2	by	by	ADP
ejpam-4520	453	3	evaluating	evaluate	VERB
ejpam-4520	453	4	the	the	DET
ejpam-4520	453	5	rainbow	rainbow	NOUN
ejpam-4520	453	6	u−	u−	PROPN
ejpam-4520	453	7	v	v	ADP
ejpam-4520	453	8	path	path	NOUN
ejpam-4520	453	9	on	on	ADP
ejpam-4520	453	10	the	the	DET
ejpam-4520	453	11	graph	graph	NOUN
ejpam-4520	453	12	fn,3	fn,3	NOUN
ejpam-4520	453	13	and	and	CCONJ
ejpam-4520	453	14	the	the	DET
ejpam-4520	453	15	graph	graph	NOUN
ejpam-4520	453	16	k1	k1	NOUN
ejpam-4520	453	17	+	+	CCONJ
ejpam-4520	453	18	sm	sm	PROPN
ejpam-4520	453	19	.	.	PUNCT
ejpam-4520	454	1	since	since	SCONJ
ejpam-4520	454	2	diam(k1	diam(k1	PROPN
ejpam-4520	454	3	+	+	CCONJ
ejpam-4520	454	4	sm	sm	NOUN
ejpam-4520	454	5	)	)	PUNCT
ejpam-4520	454	6	=	=	SYM
ejpam-4520	454	7	2	2	NUM
ejpam-4520	454	8	,	,	PUNCT
ejpam-4520	454	9	based	base	VERB
ejpam-4520	454	10	on	on	ADP
ejpam-4520	454	11	theorem	theorem	NOUN
ejpam-4520	454	12	2	2	NUM
ejpam-4520	454	13	,	,	PUNCT
ejpam-4520	454	14	there	there	PRON
ejpam-4520	454	15	is	be	VERB
ejpam-4520	454	16	a	a	DET
ejpam-4520	454	17	rainbow	rainbow	NOUN
ejpam-4520	454	18	u−	u−	NOUN
ejpam-4520	454	19	v	v	NUM
ejpam-4520	454	20	path	path	NOUN
ejpam-4520	454	21	for	for	ADP
ejpam-4520	454	22	every	every	DET
ejpam-4520	454	23	u	u	NOUN
ejpam-4520	454	24	,	,	PUNCT
ejpam-4520	454	25	v	v	PROPN
ejpam-4520	454	26	∈	∈	PROPN
ejpam-4520	454	27	v	v	NOUN
ejpam-4520	454	28	(	(	PUNCT
ejpam-4520	454	29	k1	k1	NOUN
ejpam-4520	454	30	+	+	CCONJ
ejpam-4520	454	31	sm	sm	NOUN
ejpam-4520	454	32	)	)	PUNCT
ejpam-4520	454	33	.	.	PUNCT
ejpam-4520	455	1	based	base	VERB
ejpam-4520	455	2	on	on	ADP
ejpam-4520	455	3	theorem	theorem	ADJ
ejpam-4520	455	4	3	3	NUM
ejpam-4520	455	5	,	,	PUNCT
ejpam-4520	455	6	rac(fn,3	rac(fn,3	PROPN
ejpam-4520	455	7	)	)	PUNCT
ejpam-4520	455	8	=	=	SYM
ejpam-4520	456	1	3n−	3n−	NUM
ejpam-4520	456	2	1	1	NUM
ejpam-4520	456	3	.	.	PUNCT
ejpam-4520	457	1	since	since	SCONJ
ejpam-4520	457	2	fn,3	fn,3	NOUN
ejpam-4520	457	3	has	have	VERB
ejpam-4520	457	4	3n−	3n−	PROPN
ejpam-4520	457	5	1	1	NUM
ejpam-4520	457	6	edges	edge	NOUN
ejpam-4520	457	7	,	,	PUNCT
ejpam-4520	457	8	there	there	PRON
ejpam-4520	457	9	is	be	VERB
ejpam-4520	457	10	a	a	DET
ejpam-4520	457	11	rainbow	rainbow	NOUN
ejpam-4520	457	12	u−	u−	NOUN
ejpam-4520	457	13	v	v	NUM
ejpam-4520	457	14	path	path	NOUN
ejpam-4520	457	15	for	for	ADP
ejpam-4520	457	16	every	every	DET
ejpam-4520	457	17	u	u	NOUN
ejpam-4520	457	18	,	,	PUNCT
ejpam-4520	457	19	v	v	PROPN
ejpam-4520	457	20	∈	∈	PROPN
ejpam-4520	457	21	v	v	NOUN
ejpam-4520	457	22	(	(	PUNCT
ejpam-4520	457	23	fn,3	fn,3	NOUN
ejpam-4520	457	24	)	)	PUNCT
ejpam-4520	457	25	.	.	PUNCT
ejpam-4520	458	1	therefore	therefore	ADV
ejpam-4520	458	2	,	,	PUNCT
ejpam-4520	458	3	according	accord	VERB
ejpam-4520	458	4	to	to	ADP
ejpam-4520	458	5	the	the	DET
ejpam-4520	458	6	explanation	explanation	NOUN
ejpam-4520	458	7	,	,	PUNCT
ejpam-4520	458	8	it	it	PRON
ejpam-4520	458	9	can	can	AUX
ejpam-4520	458	10	be	be	AUX
ejpam-4520	458	11	seen	see	VERB
ejpam-4520	458	12	that	that	SCONJ
ejpam-4520	458	13	there	there	PRON
ejpam-4520	458	14	is	be	VERB
ejpam-4520	458	15	a	a	DET
ejpam-4520	458	16	rainbow	rainbow	NOUN
ejpam-4520	458	17	u	u	NOUN
ejpam-4520	458	18	−	−	PROPN
ejpam-4520	458	19	v	v	ADP
ejpam-4520	458	20	path	path	NOUN
ejpam-4520	458	21	for	for	ADP
ejpam-4520	458	22	every	every	DET
ejpam-4520	458	23	u	u	NOUN
ejpam-4520	458	24	,	,	PUNCT
ejpam-4520	458	25	v	v	PROPN
ejpam-4520	458	26	∈	∈	PROPN
ejpam-4520	458	27	v	v	NOUN
ejpam-4520	458	28	(	(	PUNCT
ejpam-4520	458	29	fn,3	fn,3	PROPN
ejpam-4520	458	30	⊙	⊙	PROPN
ejpam-4520	458	31	sm	sm	PROPN
ejpam-4520	458	32	)	)	PUNCT
ejpam-4520	458	33	.	.	PUNCT
ejpam-4520	459	1	4	4	X
ejpam-4520	459	2	.	.	X
ejpam-4520	459	3	concluding	conclude	VERB
ejpam-4520	459	4	remarks	remark	NOUN
ejpam-4520	459	5	we	we	PRON
ejpam-4520	459	6	have	have	AUX
ejpam-4520	459	7	studied	study	VERB
ejpam-4520	459	8	the	the	DET
ejpam-4520	459	9	rainbow	rainbow	NOUN
ejpam-4520	459	10	antimagic	antimagic	ADJ
ejpam-4520	459	11	coloring	coloring	NOUN
ejpam-4520	459	12	of	of	ADP
ejpam-4520	459	13	the	the	DET
ejpam-4520	459	14	corona	corona	NOUN
ejpam-4520	459	15	product	product	NOUN
ejpam-4520	459	16	on	on	ADP
ejpam-4520	459	17	a	a	DET
ejpam-4520	459	18	graph	graph	NOUN
ejpam-4520	459	19	with	with	ADP
ejpam-4520	459	20	a	a	DET
ejpam-4520	459	21	star	star	NOUN
ejpam-4520	459	22	graph	graph	NOUN
ejpam-4520	459	23	.	.	PUNCT
ejpam-4520	460	1	based	base	VERB
ejpam-4520	460	2	on	on	ADP
ejpam-4520	460	3	the	the	DET
ejpam-4520	460	4	results	result	NOUN
ejpam-4520	460	5	we	we	PRON
ejpam-4520	460	6	have	have	VERB
ejpam-4520	460	7	the	the	DET
ejpam-4520	460	8	exact	exact	ADJ
ejpam-4520	460	9	value	value	NOUN
ejpam-4520	460	10	of	of	ADP
ejpam-4520	460	11	the	the	DET
ejpam-4520	460	12	rainbow	rainbow	NOUN
ejpam-4520	460	13	antimagic	antimagic	ADJ
ejpam-4520	460	14	connection	connection	NOUN
ejpam-4520	460	15	number	number	NOUN
ejpam-4520	460	16	of	of	ADP
ejpam-4520	460	17	graph	graph	NOUN
ejpam-4520	460	18	tn	tn	PROPN
ejpam-4520	460	19	⊙	⊙	PROPN
ejpam-4520	460	20	sm	sm	PROPN
ejpam-4520	460	21	where	where	SCONJ
ejpam-4520	460	22	tn	tn	PROPN
ejpam-4520	460	23	is	be	AUX
ejpam-4520	460	24	path	path	PROPN
ejpam-4520	460	25	pn	pn	PROPN
ejpam-4520	460	26	,	,	PUNCT
ejpam-4520	460	27	star	star	PROPN
ejpam-4520	460	28	sn	sn	PROPN
ejpam-4520	460	29	,	,	PUNCT
ejpam-4520	460	30	double	double	PROPN
ejpam-4520	460	31	star	star	PROPN
ejpam-4520	460	32	sn	sn	PROPN
ejpam-4520	460	33	,	,	PUNCT
ejpam-4520	460	34	p	p	NOUN
ejpam-4520	460	35	and	and	CCONJ
ejpam-4520	460	36	fire	fire	NOUN
ejpam-4520	460	37	craker	craker	NOUN
ejpam-4520	460	38	fn,3	fn,3	NOUN
ejpam-4520	460	39	.	.	PUNCT
ejpam-4520	461	1	however	however	ADV
ejpam-4520	461	2	,	,	PUNCT
ejpam-4520	461	3	if	if	SCONJ
ejpam-4520	461	4	tn	tn	NOUN
ejpam-4520	461	5	is	be	AUX
ejpam-4520	461	6	not	not	PART
ejpam-4520	461	7	a	a	DET
ejpam-4520	461	8	tree	tree	NOUN
ejpam-4520	461	9	graph	graph	NOUN
ejpam-4520	461	10	,	,	PUNCT
ejpam-4520	461	11	it	it	PRON
ejpam-4520	461	12	is	be	AUX
ejpam-4520	461	13	still	still	ADV
ejpam-4520	461	14	difficult	difficult	ADJ
ejpam-4520	461	15	to	to	PART
ejpam-4520	461	16	determine	determine	VERB
ejpam-4520	461	17	the	the	DET
ejpam-4520	461	18	exact	exact	ADJ
ejpam-4520	461	19	value	value	NOUN
ejpam-4520	461	20	of	of	ADP
ejpam-4520	461	21	the	the	DET
ejpam-4520	461	22	rainbow	rainbow	NOUN
ejpam-4520	461	23	antimagic	antimagic	ADJ
ejpam-4520	461	24	connection	connection	NOUN
ejpam-4520	461	25	number	number	NOUN
ejpam-4520	461	26	.	.	PUNCT
ejpam-4520	462	1	therefore	therefore	ADV
ejpam-4520	462	2	,	,	PUNCT
ejpam-4520	462	3	this	this	DET
ejpam-4520	462	4	study	study	NOUN
ejpam-4520	462	5	raises	raise	VERB
ejpam-4520	462	6	an	an	DET
ejpam-4520	462	7	open	open	ADJ
ejpam-4520	462	8	problem	problem	NOUN
ejpam-4520	462	9	.	.	PUNCT
ejpam-4520	463	1	determine	determine	VERB
ejpam-4520	463	2	the	the	DET
ejpam-4520	463	3	exact	exact	ADJ
ejpam-4520	463	4	value	value	NOUN
ejpam-4520	463	5	of	of	ADP
ejpam-4520	463	6	the	the	DET
ejpam-4520	463	7	rainbow	rainbow	NOUN
ejpam-4520	463	8	antimagic	antimagic	ADJ
ejpam-4520	463	9	connection	connection	NOUN
ejpam-4520	463	10	number	number	NOUN
ejpam-4520	463	11	of	of	ADP
ejpam-4520	463	12	graph	graph	NOUN
ejpam-4520	463	13	g⊙sm	g⊙sm	NOUN
ejpam-4520	463	14	where	where	SCONJ
ejpam-4520	463	15	g	g	PROPN
ejpam-4520	463	16	is	be	AUX
ejpam-4520	463	17	not	not	PART
ejpam-4520	463	18	tree	tree	NOUN
ejpam-4520	463	19	.	.	PUNCT
ejpam-4520	464	1	acknowledgements	acknowledgement	NOUN
ejpam-4520	464	2	we	we	PRON
ejpam-4520	464	3	would	would	AUX
ejpam-4520	464	4	like	like	VERB
ejpam-4520	464	5	to	to	PART
ejpam-4520	464	6	earnestly	earnestly	ADV
ejpam-4520	464	7	acknowledge	acknowledge	VERB
ejpam-4520	464	8	the	the	DET
ejpam-4520	464	9	sincere	sincere	ADJ
ejpam-4520	464	10	efforts	effort	NOUN
ejpam-4520	464	11	and	and	CCONJ
ejpam-4520	464	12	valuable	valuable	ADJ
ejpam-4520	464	13	guidance	guidance	NOUN
ejpam-4520	464	14	given	give	VERB
ejpam-4520	464	15	by	by	ADP
ejpam-4520	464	16	the	the	DET
ejpam-4520	464	17	research	research	NOUN
ejpam-4520	464	18	teams	team	NOUN
ejpam-4520	464	19	of	of	ADP
ejpam-4520	464	20	pui	pui	PROPN
ejpam-4520	464	21	-	-	PUNCT
ejpam-4520	464	22	pt	pt	NOUN
ejpam-4520	464	23	combinatorics	combinatoric	NOUN
ejpam-4520	464	24	and	and	CCONJ
ejpam-4520	464	25	graph	graph	NOUN
ejpam-4520	464	26	,	,	PUNCT
ejpam-4520	464	27	cgant	cgant	ADJ
ejpam-4520	464	28	,	,	PUNCT
ejpam-4520	464	29	university	university	NOUN
ejpam-4520	464	30	of	of	ADP
ejpam-4520	464	31	jember	jember	PROPN
ejpam-4520	464	32	,	,	PUNCT
ejpam-4520	464	33	indonesia	indonesia	PROPN
ejpam-4520	464	34	and	and	CCONJ
ejpam-4520	464	35	the	the	DET
ejpam-4520	464	36	postgraduate	postgraduate	NOUN
ejpam-4520	464	37	program	program	NOUN
ejpam-4520	464	38	researchers	researcher	NOUN
ejpam-4520	464	39	of	of	ADP
ejpam-4520	464	40	airlangga	airlangga	PROPN
ejpam-4520	464	41	university	university	PROPN
ejpam-4520	464	42	.	.	PUNCT
ejpam-4520	465	1	references	reference	NOUN
ejpam-4520	465	2	[	[	X
ejpam-4520	465	3	1	1	NUM
ejpam-4520	465	4	]	]	X
ejpam-4520	465	5	s	s	VERB
ejpam-4520	465	6	arumugam	arumugam	NOUN
ejpam-4520	465	7	,	,	PUNCT
ejpam-4520	465	8	k	k	PROPN
ejpam-4520	465	9	premalatha	premalatha	PROPN
ejpam-4520	465	10	,	,	PUNCT
ejpam-4520	466	1	m	m	VERB
ejpam-4520	466	2	bača	bača	ADJ
ejpam-4520	466	3	,	,	PUNCT
ejpam-4520	466	4	and	and	CCONJ
ejpam-4520	466	5	a	a	DET
ejpam-4520	466	6	semaničová	semaničová	X
ejpam-4520	466	7	-	-	PUNCT
ejpam-4520	466	8	feňovčíková	feňovčíková	PROPN
ejpam-4520	466	9	.	.	PUNCT
ejpam-4520	467	1	local	local	ADJ
ejpam-4520	467	2	antimagic	antimagic	ADJ
ejpam-4520	467	3	vertex	vertex	NOUN
ejpam-4520	467	4	coloring	coloring	NOUN
ejpam-4520	467	5	of	of	ADP
ejpam-4520	467	6	a	a	DET
ejpam-4520	467	7	graph	graph	NOUN
ejpam-4520	467	8	.	.	PUNCT
ejpam-4520	468	1	graphs	graph	NOUN
ejpam-4520	468	2	and	and	CCONJ
ejpam-4520	468	3	combinatorics	combinatoric	NOUN
ejpam-4520	468	4	,	,	PUNCT
ejpam-4520	468	5	33(2):275–285	33(2):275–285	PROPN
ejpam-4520	468	6	,	,	PUNCT
ejpam-4520	468	7	2017	2017	NUM
ejpam-4520	468	8	.	.	PUNCT
ejpam-4520	469	1	references	reference	NOUN
ejpam-4520	469	2	284	284	NUM
ejpam-4520	470	1	[	[	X
ejpam-4520	470	2	2	2	NUM
ejpam-4520	470	3	]	]	PUNCT
ejpam-4520	470	4	m	m	VERB
ejpam-4520	470	5	bača	bača	ADJ
ejpam-4520	470	6	,	,	PUNCT
ejpam-4520	470	7	e	e	PROPN
ejpam-4520	470	8	t	t	PROPN
ejpam-4520	470	9	baskoro	baskoro	PROPN
ejpam-4520	470	10	,	,	PUNCT
ejpam-4520	470	11	s	s	VERB
ejpam-4520	470	12	jendrol	jendrol	NOUN
ejpam-4520	470	13	,	,	PUNCT
ejpam-4520	470	14	and	and	CCONJ
ejpam-4520	470	15	m	m	NOUN
ejpam-4520	470	16	miler	miler	NOUN
ejpam-4520	470	17	.	.	PUNCT
ejpam-4520	471	1	antimagic	antimagic	ADJ
ejpam-4520	471	2	labelings	labeling	NOUN
ejpam-4520	471	3	of	of	ADP
ejpam-4520	471	4	hexagonal	hexagonal	ADJ
ejpam-4520	471	5	plane	plane	NOUN
ejpam-4520	471	6	maps	map	NOUN
ejpam-4520	471	7	.	.	PUNCT
ejpam-4520	472	1	utilitas	utilitas	PROPN
ejpam-4520	472	2	mathematica	mathematica	PROPN
ejpam-4520	472	3	,	,	PUNCT
ejpam-4520	472	4	66:231–238	66:231–238	PROPN
ejpam-4520	472	5	,	,	PUNCT
ejpam-4520	472	6	2004	2004	NUM
ejpam-4520	472	7	.	.	PUNCT
ejpam-4520	473	1	[	[	X
ejpam-4520	473	2	3	3	X
ejpam-4520	473	3	]	]	X
ejpam-4520	473	4	m	m	VERB
ejpam-4520	473	5	bača	bača	ADJ
ejpam-4520	473	6	,	,	PUNCT
ejpam-4520	473	7	y	y	PROPN
ejpam-4520	473	8	lin	lin	PROPN
ejpam-4520	473	9	,	,	PUNCT
ejpam-4520	473	10	and	and	CCONJ
ejpam-4520	473	11	m	m	NOUN
ejpam-4520	473	12	miler	miler	NOUN
ejpam-4520	473	13	.	.	PUNCT
ejpam-4520	474	1	antimagic	antimagic	ADJ
ejpam-4520	474	2	labelings	labeling	NOUN
ejpam-4520	474	3	of	of	ADP
ejpam-4520	474	4	grids	grid	NOUN
ejpam-4520	474	5	.	.	PUNCT
ejpam-4520	475	1	utilitas	utilitas	PROPN
ejpam-4520	475	2	mathematica	mathematica	PROPN
ejpam-4520	475	3	,	,	PUNCT
ejpam-4520	475	4	72:65–75	72:65–75	PROPN
ejpam-4520	475	5	,	,	PUNCT
ejpam-4520	475	6	2007	2007	NUM
ejpam-4520	475	7	.	.	PUNCT
ejpam-4520	476	1	[	[	X
ejpam-4520	476	2	4	4	NUM
ejpam-4520	476	3	]	]	X
ejpam-4520	476	4	m	m	VERB
ejpam-4520	476	5	bača	bača	ADJ
ejpam-4520	476	6	,	,	PUNCT
ejpam-4520	476	7	m	m	NOUN
ejpam-4520	476	8	miler	miler	NOUN
ejpam-4520	476	9	,	,	PUNCT
ejpam-4520	476	10	and	and	CCONJ
ejpam-4520	476	11	j	j	PROPN
ejpam-4520	476	12	ryan	ryan	PROPN
ejpam-4520	476	13	.	.	PUNCT
ejpam-4520	477	1	antimagic	antimagic	ADJ
ejpam-4520	477	2	labelings	labeling	NOUN
ejpam-4520	477	3	of	of	ADP
ejpam-4520	477	4	disjoint	disjoint	PROPN
ejpam-4520	477	5	union	union	NOUN
ejpam-4520	477	6	of	of	ADP
ejpam-4520	477	7	s	s	NOUN
ejpam-4520	477	8	-	-	PUNCT
ejpam-4520	477	9	crowns	crowns	NOUN
ejpam-4520	477	10	.	.	PUNCT
ejpam-4520	478	1	utilitas	utilitas	PROPN
ejpam-4520	478	2	mathematica	mathematica	PROPN
ejpam-4520	478	3	,	,	PUNCT
ejpam-4520	478	4	79:193–205	79:193–205	PROPN
ejpam-4520	478	5	,	,	PUNCT
ejpam-4520	478	6	2009	2009	NUM
ejpam-4520	478	7	.	.	PUNCT
ejpam-4520	479	1	[	[	X
ejpam-4520	479	2	5	5	NUM
ejpam-4520	479	3	]	]	X
ejpam-4520	479	4	h	h	PROPN
ejpam-4520	479	5	s	s	PROPN
ejpam-4520	479	6	budi	budi	PROPN
ejpam-4520	479	7	,	,	PUNCT
ejpam-4520	479	8	dafik	dafik	PROPN
ejpam-4520	479	9	,	,	PUNCT
ejpam-4520	479	10	i	i	PRON
ejpam-4520	479	11	m	m	VERB
ejpam-4520	479	12	tirta	tirta	ADJ
ejpam-4520	479	13	,	,	PUNCT
ejpam-4520	479	14	i	i	PROPN
ejpam-4520	479	15	h	h	PROPN
ejpam-4520	479	16	agustin	agustin	PROPN
ejpam-4520	479	17	,	,	PUNCT
ejpam-4520	479	18	and	and	CCONJ
ejpam-4520	479	19	a	a	DET
ejpam-4520	479	20	i	i	PROPN
ejpam-4520	479	21	kristiana	kristiana	PROPN
ejpam-4520	479	22	.	.	PUNCT
ejpam-4520	480	1	on	on	ADP
ejpam-4520	480	2	rainbow	rainbow	NOUN
ejpam-4520	480	3	antimagic	antimagic	ADJ
ejpam-4520	480	4	coloring	coloring	NOUN
ejpam-4520	480	5	of	of	ADP
ejpam-4520	480	6	graphs	graph	NOUN
ejpam-4520	480	7	.	.	PUNCT
ejpam-4520	481	1	volume	volume	NOUN
ejpam-4520	481	2	1832	1832	NUM
ejpam-4520	481	3	,	,	PUNCT
ejpam-4520	481	4	page	page	NOUN
ejpam-4520	481	5	012016	012016	NUM
ejpam-4520	481	6	,	,	PUNCT
ejpam-4520	481	7	2021	2021	NUM
ejpam-4520	481	8	.	.	PUNCT
ejpam-4520	482	1	[	[	X
ejpam-4520	482	2	6	6	NUM
ejpam-4520	482	3	]	]	X
ejpam-4520	482	4	f	f	PROPN
ejpam-4520	482	5	chang	chang	PROPN
ejpam-4520	482	6	,	,	PUNCT
ejpam-4520	482	7	y	y	PROPN
ejpam-4520	482	8	c	c	PROPN
ejpam-4520	482	9	liang	liang	PROPN
ejpam-4520	482	10	,	,	PUNCT
ejpam-4520	482	11	z	z	PROPN
ejpam-4520	482	12	pan	pan	PROPN
ejpam-4520	482	13	,	,	PUNCT
ejpam-4520	482	14	and	and	CCONJ
ejpam-4520	482	15	x	x	X
ejpam-4520	482	16	zhu	zhu	PROPN
ejpam-4520	482	17	.	.	PUNCT
ejpam-4520	483	1	antimagic	antimagic	ADJ
ejpam-4520	483	2	labeling	labeling	NOUN
ejpam-4520	483	3	of	of	ADP
ejpam-4520	483	4	reguler	reguler	NOUN
ejpam-4520	483	5	graphs	graph	NOUN
ejpam-4520	483	6	.	.	PUNCT
ejpam-4520	484	1	journal	journal	NOUN
ejpam-4520	484	2	of	of	ADP
ejpam-4520	484	3	graph	graph	NOUN
ejpam-4520	484	4	theory	theory	NOUN
ejpam-4520	484	5	,	,	PUNCT
ejpam-4520	484	6	82(4):339–349	82(4):339–349	NUM
ejpam-4520	484	7	,	,	PUNCT
ejpam-4520	484	8	2016	2016	NUM
ejpam-4520	484	9	.	.	PUNCT
ejpam-4520	485	1	[	[	X
ejpam-4520	485	2	7	7	X
ejpam-4520	485	3	]	]	X
ejpam-4520	485	4	g	g	PROPN
ejpam-4520	485	5	chartrand	chartrand	NOUN
ejpam-4520	485	6	,	,	PUNCT
ejpam-4520	485	7	g	g	PROPN
ejpam-4520	485	8	l	l	PROPN
ejpam-4520	485	9	johns	johns	PROPN
ejpam-4520	485	10	,	,	PUNCT
ejpam-4520	485	11	k	k	PROPN
ejpam-4520	485	12	a	a	DET
ejpam-4520	485	13	mckeon	mckeon	NOUN
ejpam-4520	485	14	,	,	PUNCT
ejpam-4520	485	15	and	and	CCONJ
ejpam-4520	485	16	p	p	PROPN
ejpam-4520	485	17	zhang	zhang	PROPN
ejpam-4520	485	18	.	.	PUNCT
ejpam-4520	485	19	rainbow	rainbow	PROPN
ejpam-4520	485	20	connection	connection	NOUN
ejpam-4520	485	21	in	in	ADP
ejpam-4520	485	22	graphs	graph	NOUN
ejpam-4520	485	23	.	.	PUNCT
ejpam-4520	486	1	math	math	NOUN
ejpam-4520	486	2	.	.	PUNCT
ejpam-4520	487	1	bohemica	bohemica	PROPN
ejpam-4520	487	2	,	,	PUNCT
ejpam-4520	487	3	133:85–98	133:85–98	NUM
ejpam-4520	487	4	,	,	PUNCT
ejpam-4520	487	5	2008	2008	NUM
ejpam-4520	487	6	.	.	PUNCT
ejpam-4520	488	1	[	[	X
ejpam-4520	488	2	8	8	NUM
ejpam-4520	488	3	]	]	X
ejpam-4520	488	4	g	g	PROPN
ejpam-4520	488	5	chartrand	chartrand	NOUN
ejpam-4520	488	6	,	,	PUNCT
ejpam-4520	488	7	l	l	PROPN
ejpam-4520	488	8	lesniak	lesniak	PROPN
ejpam-4520	488	9	,	,	PUNCT
ejpam-4520	488	10	and	and	CCONJ
ejpam-4520	488	11	p	p	PROPN
ejpam-4520	488	12	zhang	zhang	PROPN
ejpam-4520	488	13	.	.	PUNCT
ejpam-4520	488	14	graphs	graph	NOUN
ejpam-4520	488	15	&	&	CCONJ
ejpam-4520	488	16	digraphs	digraph	NOUN
ejpam-4520	488	17	.	.	PUNCT
ejpam-4520	489	1	taylor	taylor	PROPN
ejpam-4520	489	2	&	&	CCONJ
ejpam-4520	489	3	francis	francis	PROPN
ejpam-4520	489	4	group	group	PROPN
ejpam-4520	489	5	,	,	PUNCT
ejpam-4520	489	6	new	new	PROPN
ejpam-4520	489	7	york	york	PROPN
ejpam-4520	489	8	,	,	PUNCT
ejpam-4520	489	9	2016	2016	NUM
ejpam-4520	489	10	.	.	PUNCT
ejpam-4520	490	1	[	[	X
ejpam-4520	490	2	9	9	NUM
ejpam-4520	490	3	]	]	X
ejpam-4520	490	4	d	d	PROPN
ejpam-4520	490	5	w	w	PROPN
ejpam-4520	490	6	cranston	cranston	PROPN
ejpam-4520	490	7	.	.	PUNCT
ejpam-4520	491	1	reguler	reguler	PROPN
ejpam-4520	491	2	bipartite	bipartite	PROPN
ejpam-4520	491	3	graphs	graph	NOUN
ejpam-4520	491	4	are	be	AUX
ejpam-4520	491	5	antimagic	antimagic	ADJ
ejpam-4520	491	6	.	.	PUNCT
ejpam-4520	492	1	journal	journal	NOUN
ejpam-4520	492	2	of	of	ADP
ejpam-4520	492	3	graph	graph	NOUN
ejpam-4520	492	4	theory	theory	NOUN
ejpam-4520	492	5	,	,	PUNCT
ejpam-4520	492	6	60(3):173–182	60(3):173–182	PROPN
ejpam-4520	492	7	,	,	PUNCT
ejpam-4520	492	8	2009	2009	NUM
ejpam-4520	492	9	.	.	PUNCT
ejpam-4520	493	1	[	[	X
ejpam-4520	493	2	10	10	NUM
ejpam-4520	493	3	]	]	X
ejpam-4520	493	4	dafik	dafik	NOUN
ejpam-4520	493	5	,	,	PUNCT
ejpam-4520	493	6	m	m	NOUN
ejpam-4520	493	7	miler	miler	NOUN
ejpam-4520	493	8	,	,	PUNCT
ejpam-4520	493	9	j	j	PROPN
ejpam-4520	493	10	ryan	ryan	PROPN
ejpam-4520	493	11	,	,	PUNCT
ejpam-4520	493	12	and	and	CCONJ
ejpam-4520	493	13	m	m	NOUN
ejpam-4520	493	14	bača	bača	ADJ
ejpam-4520	493	15	.	.	PUNCT
ejpam-4520	494	1	antimagic	antimagic	ADJ
ejpam-4520	494	2	labeling	labeling	NOUN
ejpam-4520	494	3	of	of	ADP
ejpam-4520	494	4	the	the	DET
ejpam-4520	494	5	union	union	NOUN
ejpam-4520	494	6	of	of	ADP
ejpam-4520	494	7	two	two	NUM
ejpam-4520	494	8	stars	star	NOUN
ejpam-4520	494	9	.	.	PUNCT
ejpam-4520	495	1	australasian	australasian	ADJ
ejpam-4520	495	2	journal	journal	NOUN
ejpam-4520	495	3	of	of	ADP
ejpam-4520	495	4	combinatorics	combinatoric	NOUN
ejpam-4520	495	5	,	,	PUNCT
ejpam-4520	495	6	42:35–44	42:35–44	NUM
ejpam-4520	495	7	,	,	PUNCT
ejpam-4520	495	8	2018	2018	NUM
ejpam-4520	495	9	.	.	PUNCT
ejpam-4520	496	1	[	[	X
ejpam-4520	496	2	11	11	NUM
ejpam-4520	496	3	]	]	PUNCT
ejpam-4520	496	4	dafik	dafik	NOUN
ejpam-4520	496	5	,	,	PUNCT
ejpam-4520	496	6	f	f	PROPN
ejpam-4520	496	7	susanto	susanto	NOUN
ejpam-4520	496	8	,	,	PUNCT
ejpam-4520	496	9	r	r	NOUN
ejpam-4520	496	10	alfarisi	alfarisi	PROPN
ejpam-4520	496	11	,	,	PUNCT
ejpam-4520	496	12	b	b	PROPN
ejpam-4520	496	13	j	j	PROPN
ejpam-4520	496	14	septory	septory	ADJ
ejpam-4520	496	15	,	,	PUNCT
ejpam-4520	496	16	i	i	PROPN
ejpam-4520	496	17	h	h	PROPN
ejpam-4520	496	18	agustin	agustin	PROPN
ejpam-4520	496	19	,	,	PUNCT
ejpam-4520	496	20	and	and	CCONJ
ejpam-4520	496	21	m	m	AUX
ejpam-4520	496	22	venkatachalam	venkatachalam	ADJ
ejpam-4520	496	23	.	.	PUNCT
ejpam-4520	497	1	on	on	ADP
ejpam-4520	497	2	rainbow	rainbow	NOUN
ejpam-4520	497	3	antimagic	antimagic	ADJ
ejpam-4520	497	4	coloring	coloring	NOUN
ejpam-4520	497	5	of	of	ADP
ejpam-4520	497	6	graphs	graph	NOUN
ejpam-4520	497	7	.	.	PUNCT
ejpam-4520	498	1	advanced	advanced	ADJ
ejpam-4520	498	2	mathematical	mathematical	ADJ
ejpam-4520	498	3	models	model	NOUN
ejpam-4520	498	4	and	and	CCONJ
ejpam-4520	498	5	aplication	aplication	NOUN
ejpam-4520	498	6	,	,	PUNCT
ejpam-4520	498	7	6(3):278–291	6(3):278–291	NOUN
ejpam-4520	498	8	,	,	PUNCT
ejpam-4520	498	9	2021	2021	NUM
ejpam-4520	498	10	.	.	PUNCT
ejpam-4520	499	1	[	[	X
ejpam-4520	499	2	12	12	NUM
ejpam-4520	499	3	]	]	X
ejpam-4520	499	4	r	r	NOUN
ejpam-4520	499	5	frucht	frucht	NOUN
ejpam-4520	499	6	and	and	CCONJ
ejpam-4520	499	7	f	f	PROPN
ejpam-4520	499	8	harary	harary	NOUN
ejpam-4520	499	9	.	.	PUNCT
ejpam-4520	500	1	on	on	ADP
ejpam-4520	500	2	the	the	DET
ejpam-4520	500	3	corona	corona	NOUN
ejpam-4520	500	4	of	of	ADP
ejpam-4520	500	5	two	two	NUM
ejpam-4520	500	6	graphs	graph	NOUN
ejpam-4520	500	7	.	.	PUNCT
ejpam-4520	501	1	aequationes	aequatione	NOUN
ejpam-4520	501	2	math	math	PROPN
ejpam-4520	501	3	,	,	PUNCT
ejpam-4520	501	4	4:322–325	4:322–325	PROPN
ejpam-4520	501	5	,	,	PUNCT
ejpam-4520	501	6	1970	1970	NUM
ejpam-4520	501	7	.	.	PUNCT
ejpam-4520	502	1	[	[	X
ejpam-4520	502	2	13	13	NUM
ejpam-4520	502	3	]	]	PUNCT
ejpam-4520	502	4	n	n	CCONJ
ejpam-4520	502	5	hartsfield	hartsfield	NOUN
ejpam-4520	502	6	and	and	CCONJ
ejpam-4520	502	7	g	g	PROPN
ejpam-4520	502	8	ringel	ringel	NOUN
ejpam-4520	502	9	.	.	PUNCT
ejpam-4520	503	1	pearls	pearl	NOUN
ejpam-4520	503	2	in	in	ADP
ejpam-4520	503	3	graph	graph	NOUN
ejpam-4520	503	4	theory	theory	NOUN
ejpam-4520	503	5	.	.	PUNCT
ejpam-4520	504	1	academic	academic	ADJ
ejpam-4520	504	2	press	press	NOUN
ejpam-4520	504	3	,	,	PUNCT
ejpam-4520	504	4	san	san	PROPN
ejpam-4520	504	5	diego	diego	PROPN
ejpam-4520	504	6	,	,	PUNCT
ejpam-4520	504	7	1990	1990	NUM
ejpam-4520	504	8	.	.	PUNCT
ejpam-4520	505	1	[	[	X
ejpam-4520	505	2	14	14	NUM
ejpam-4520	505	3	]	]	X
ejpam-4520	505	4	m	m	PROPN
ejpam-4520	505	5	s	s	PROPN
ejpam-4520	505	6	hasan	hasan	PROPN
ejpam-4520	505	7	,	,	PUNCT
ejpam-4520	505	8	slamin	slamin	PROPN
ejpam-4520	505	9	,	,	PUNCT
ejpam-4520	505	10	dafik	dafik	NOUN
ejpam-4520	505	11	,	,	PUNCT
ejpam-4520	505	12	i	i	PROPN
ejpam-4520	505	13	h	h	PROPN
ejpam-4520	505	14	agustin	agustin	PROPN
ejpam-4520	505	15	,	,	PUNCT
ejpam-4520	505	16	and	and	CCONJ
ejpam-4520	505	17	r	r	NOUN
ejpam-4520	505	18	alfarisi	alfarisi	VERB
ejpam-4520	505	19	.	.	PUNCT
ejpam-4520	506	1	on	on	ADP
ejpam-4520	506	2	the	the	DET
ejpam-4520	506	3	total	total	ADJ
ejpam-4520	506	4	rainbow	rainbow	NOUN
ejpam-4520	506	5	connection	connection	NOUN
ejpam-4520	506	6	of	of	ADP
ejpam-4520	506	7	the	the	DET
ejpam-4520	506	8	wheel	wheel	NOUN
ejpam-4520	506	9	related	relate	VERB
ejpam-4520	506	10	graphs	graph	NOUN
ejpam-4520	506	11	.	.	PUNCT
ejpam-4520	507	1	journal	journal	PROPN
ejpam-4520	507	2	of	of	ADP
ejpam-4520	507	3	physics	physics	PROPN
ejpam-4520	507	4	:	:	PUNCT
ejpam-4520	507	5	conf	conf	PROPN
ejpam-4520	507	6	.	.	PUNCT
ejpam-4520	508	1	series	series	PROPN
ejpam-4520	508	2	,	,	PUNCT
ejpam-4520	508	3	1008:012954	1008:012954	NUM
ejpam-4520	508	4	,	,	PUNCT
ejpam-4520	508	5	2018	2018	NUM
ejpam-4520	508	6	.	.	PUNCT
ejpam-4520	509	1	[	[	X
ejpam-4520	509	2	15	15	NUM
ejpam-4520	509	3	]	]	X
ejpam-4520	509	4	j	j	PROPN
ejpam-4520	509	5	c	c	PROPN
ejpam-4520	509	6	joedo	joedo	PROPN
ejpam-4520	509	7	,	,	PUNCT
ejpam-4520	509	8	dafik	dafik	PROPN
ejpam-4520	509	9	,	,	PUNCT
ejpam-4520	509	10	a	a	DET
ejpam-4520	509	11	i	i	PRON
ejpam-4520	509	12	kristiana	kristiana	PROPN
ejpam-4520	509	13	,	,	PUNCT
ejpam-4520	509	14	i	i	PROPN
ejpam-4520	509	15	h	h	PROPN
ejpam-4520	509	16	agustin	agustin	PROPN
ejpam-4520	509	17	,	,	PUNCT
ejpam-4520	509	18	and	and	CCONJ
ejpam-4520	509	19	r	r	NOUN
ejpam-4520	509	20	nisviasari	nisviasari	NOUN
ejpam-4520	509	21	.	.	PUNCT
ejpam-4520	510	1	on	on	ADP
ejpam-4520	510	2	the	the	DET
ejpam-4520	510	3	rainbow	rainbow	NOUN
ejpam-4520	510	4	antimagic	antimagic	ADJ
ejpam-4520	510	5	coloring	coloring	NOUN
ejpam-4520	510	6	of	of	ADP
ejpam-4520	510	7	vertex	vertex	NOUN
ejpam-4520	510	8	almagamation	almagamation	NOUN
ejpam-4520	510	9	of	of	ADP
ejpam-4520	510	10	graphs	graph	NOUN
ejpam-4520	510	11	.	.	PUNCT
ejpam-4520	511	1	journal	journal	PROPN
ejpam-4520	511	2	of	of	ADP
ejpam-4520	511	3	physics	physics	PROPN
ejpam-4520	511	4	:	:	PUNCT
ejpam-4520	511	5	conf	conf	PROPN
ejpam-4520	511	6	.	.	PUNCT
ejpam-4520	512	1	series	series	PROPN
ejpam-4520	512	2	,	,	PUNCT
ejpam-4520	512	3	2157:012014	2157:012014	NUM
ejpam-4520	512	4	,	,	PUNCT
ejpam-4520	512	5	2022	2022	NUM
ejpam-4520	512	6	.	.	PUNCT
ejpam-4520	513	1	[	[	X
ejpam-4520	513	2	16	16	NUM
ejpam-4520	513	3	]	]	X
ejpam-4520	513	4	m	m	VERB
ejpam-4520	513	5	krivelevich	krivelevich	NOUN
ejpam-4520	513	6	and	and	CCONJ
ejpam-4520	513	7	r	r	NOUN
ejpam-4520	513	8	yuster	yuster	NOUN
ejpam-4520	513	9	.	.	PUNCT
ejpam-4520	514	1	the	the	DET
ejpam-4520	514	2	rainbow	rainbow	NOUN
ejpam-4520	514	3	connection	connection	NOUN
ejpam-4520	514	4	of	of	ADP
ejpam-4520	514	5	a	a	DET
ejpam-4520	514	6	graph	graph	NOUN
ejpam-4520	514	7	is	be	AUX
ejpam-4520	514	8	(	(	PUNCT
ejpam-4520	514	9	at	at	ADP
ejpam-4520	514	10	most	most	ADJ
ejpam-4520	514	11	)	)	PUNCT
ejpam-4520	514	12	reciprocal	reciprocal	ADJ
ejpam-4520	514	13	to	to	ADP
ejpam-4520	514	14	its	its	PRON
ejpam-4520	514	15	minimum	minimum	NOUN
ejpam-4520	514	16	degree	degree	NOUN
ejpam-4520	514	17	.	.	PUNCT
ejpam-4520	515	1	j.	j.	PROPN
ejpam-4520	515	2	graph	graph	PROPN
ejpam-4520	515	3	theory	theory	NOUN
ejpam-4520	515	4	,	,	PUNCT
ejpam-4520	515	5	63(3):185–191	63(3):185–191	PROPN
ejpam-4520	515	6	,	,	PUNCT
ejpam-4520	515	7	2010	2010	NUM
ejpam-4520	515	8	.	.	PUNCT
ejpam-4520	516	1	references	reference	NOUN
ejpam-4520	516	2	285	285	NUM
ejpam-4520	516	3	[	[	X
ejpam-4520	516	4	17	17	NUM
ejpam-4520	516	5	]	]	X
ejpam-4520	516	6	h	h	PROPN
ejpam-4520	516	7	li	li	PROPN
ejpam-4520	516	8	,	,	PUNCT
ejpam-4520	516	9	x	x	PROPN
ejpam-4520	516	10	li	li	PROPN
ejpam-4520	516	11	,	,	PUNCT
ejpam-4520	516	12	and	and	CCONJ
ejpam-4520	516	13	s	s	VERB
ejpam-4520	516	14	liu	liu	PROPN
ejpam-4520	516	15	.	.	PUNCT
ejpam-4520	517	1	rainbow	rainbow	PROPN
ejpam-4520	517	2	connection	connection	NOUN
ejpam-4520	517	3	of	of	ADP
ejpam-4520	517	4	graphs	graph	NOUN
ejpam-4520	517	5	with	with	ADP
ejpam-4520	517	6	diameter	diameter	NOUN
ejpam-4520	517	7	2	2	NUM
ejpam-4520	517	8	.	.	PUNCT
ejpam-4520	517	9	discrete	discrete	ADJ
ejpam-4520	517	10	mathematics	mathematic	NOUN
ejpam-4520	517	11	,	,	PUNCT
ejpam-4520	517	12	312(8):1453–1457	312(8):1453–1457	NUM
ejpam-4520	517	13	,	,	PUNCT
ejpam-4520	517	14	2012	2012	NUM
ejpam-4520	517	15	.	.	PUNCT
ejpam-4520	518	1	[	[	X
ejpam-4520	518	2	18	18	NUM
ejpam-4520	518	3	]	]	X
ejpam-4520	518	4	h	h	NOUN
ejpam-4520	518	5	li	li	PROPN
ejpam-4520	518	6	,	,	PUNCT
ejpam-4520	518	7	x	x	PROPN
ejpam-4520	518	8	li	li	PROPN
ejpam-4520	518	9	,	,	PUNCT
ejpam-4520	518	10	and	and	CCONJ
ejpam-4520	518	11	y	y	PROPN
ejpam-4520	518	12	sun	sun	PROPN
ejpam-4520	518	13	.	.	PUNCT
ejpam-4520	518	14	rainbow	rainbow	PROPN
ejpam-4520	518	15	connection	connection	NOUN
ejpam-4520	518	16	of	of	ADP
ejpam-4520	518	17	graphs	graph	NOUN
ejpam-4520	518	18	with	with	ADP
ejpam-4520	518	19	diameter	diameter	NOUN
ejpam-4520	518	20	3	3	NUM
ejpam-4520	518	21	.	.	PUNCT
ejpam-4520	519	1	discussiones	discussione	NOUN
ejpam-4520	519	2	mathematicae	mathematicae	PROPN
ejpam-4520	519	3	graph	graph	NOUN
ejpam-4520	519	4	theory	theory	NOUN
ejpam-4520	519	5	,	,	PUNCT
ejpam-4520	519	6	37(2):141–154	37(2):141–154	PROPN
ejpam-4520	519	7	,	,	PUNCT
ejpam-4520	519	8	2017	2017	NUM
ejpam-4520	519	9	.	.	PUNCT
ejpam-4520	520	1	[	[	X
ejpam-4520	520	2	19	19	NUM
ejpam-4520	520	3	]	]	X
ejpam-4520	520	4	x	x	X
ejpam-4520	520	5	li	li	PROPN
ejpam-4520	520	6	and	and	CCONJ
ejpam-4520	520	7	y	y	PROPN
ejpam-4520	520	8	shi	shi	PROPN
ejpam-4520	520	9	.	.	PUNCT
ejpam-4520	521	1	on	on	ADP
ejpam-4520	521	2	the	the	DET
ejpam-4520	521	3	rainbow	rainbow	NOUN
ejpam-4520	521	4	vertex	vertex	NOUN
ejpam-4520	521	5	connection	connection	NOUN
ejpam-4520	521	6	.	.	PUNCT
ejpam-4520	522	1	graph	graph	NOUN
ejpam-4520	522	2	theory	theory	NOUN
ejpam-4520	522	3	,	,	PUNCT
ejpam-4520	522	4	33:307–313	33:307–313	NUM
ejpam-4520	522	5	,	,	PUNCT
ejpam-4520	522	6	2013	2013	NUM
ejpam-4520	522	7	.	.	PUNCT
ejpam-4520	523	1	[	[	X
ejpam-4520	523	2	20	20	NUM
ejpam-4520	523	3	]	]	PUNCT
ejpam-4520	523	4	x	x	X
ejpam-4520	523	5	li	li	PROPN
ejpam-4520	523	6	and	and	CCONJ
ejpam-4520	523	7	y	y	PROPN
ejpam-4520	523	8	sun	sun	PROPN
ejpam-4520	523	9	.	.	PUNCT
ejpam-4520	524	1	an	an	DET
ejpam-4520	524	2	updated	update	VERB
ejpam-4520	524	3	survey	survey	NOUN
ejpam-4520	524	4	on	on	ADP
ejpam-4520	524	5	rainbow	rainbow	NOUN
ejpam-4520	524	6	connections	connection	NOUN
ejpam-4520	524	7	of	of	ADP
ejpam-4520	524	8	graphs	graph	NOUN
ejpam-4520	524	9	.	.	PUNCT
ejpam-4520	525	1	theory	theory	NOUN
ejpam-4520	525	2	and	and	CCONJ
ejpam-4520	525	3	application	application	NOUN
ejpam-4520	525	4	of	of	ADP
ejpam-4520	525	5	graph	graph	NOUN
ejpam-4520	525	6	,	,	PUNCT
ejpam-4520	525	7	0(1):article	0(1):article	NOUN
ejpam-4520	525	8	3	3	NUM
ejpam-4520	525	9	,	,	PUNCT
ejpam-4520	525	10	2017	2017	NUM
ejpam-4520	525	11	.	.	PUNCT
ejpam-4520	526	1	[	[	X
ejpam-4520	526	2	21	21	NUM
ejpam-4520	526	3	]	]	X
ejpam-4520	526	4	i	i	PRON
ejpam-4520	526	5	schiermeyer	schiermeyer	PROPN
ejpam-4520	526	6	.	.	PUNCT
ejpam-4520	527	1	bounds	bound	VERB
ejpam-4520	527	2	for	for	ADP
ejpam-4520	527	3	the	the	DET
ejpam-4520	527	4	rainbow	rainbow	NOUN
ejpam-4520	527	5	connection	connection	NOUN
ejpam-4520	527	6	number	number	NOUN
ejpam-4520	527	7	of	of	ADP
ejpam-4520	527	8	graph	graph	NOUN
ejpam-4520	527	9	.	.	PUNCT
ejpam-4520	528	1	discussiones	discussione	NOUN
ejpam-4520	528	2	mathematicae	mathematicae	PROPN
ejpam-4520	528	3	graph	graph	NOUN
ejpam-4520	528	4	theory	theory	NOUN
ejpam-4520	528	5	,	,	PUNCT
ejpam-4520	528	6	31:387–395	31:387–395	PROPN
ejpam-4520	528	7	,	,	PUNCT
ejpam-4520	528	8	2011	2011	NUM
ejpam-4520	528	9	.	.	PUNCT
ejpam-4520	529	1	[	[	X
ejpam-4520	529	2	22	22	NUM
ejpam-4520	529	3	]	]	SYM
ejpam-4520	529	4	b	b	X
ejpam-4520	529	5	j	j	PROPN
ejpam-4520	529	6	septory	septory	ADJ
ejpam-4520	529	7	,	,	PUNCT
ejpam-4520	529	8	m	m	VERB
ejpam-4520	529	9	i	i	PRON
ejpam-4520	529	10	utoyo	utoyo	NOUN
ejpam-4520	529	11	,	,	PUNCT
ejpam-4520	529	12	dafik	dafik	PROPN
ejpam-4520	529	13	,	,	PUNCT
ejpam-4520	529	14	b	b	NOUN
ejpam-4520	529	15	sulistiyono	sulistiyono	NOUN
ejpam-4520	529	16	,	,	PUNCT
ejpam-4520	529	17	and	and	CCONJ
ejpam-4520	529	18	i	i	PRON
ejpam-4520	529	19	h	h	PROPN
ejpam-4520	529	20	agustin	agustin	PROPN
ejpam-4520	529	21	.	.	PUNCT
ejpam-4520	530	1	on	on	ADP
ejpam-4520	530	2	rainbow	rainbow	NOUN
ejpam-4520	530	3	antimagic	antimagic	ADJ
ejpam-4520	530	4	coloring	coloring	NOUN
ejpam-4520	530	5	of	of	ADP
ejpam-4520	530	6	special	special	ADJ
ejpam-4520	530	7	graphs	graph	NOUN
ejpam-4520	530	8	.	.	PUNCT
ejpam-4520	531	1	journal	journal	PROPN
ejpam-4520	531	2	of	of	ADP
ejpam-4520	531	3	physics	physics	PROPN
ejpam-4520	531	4	:	:	PUNCT
ejpam-4520	531	5	conference	conference	NOUN
ejpam-4520	531	6	series	series	NOUN
ejpam-4520	531	7	,	,	PUNCT
ejpam-4520	531	8	1836:012016	1836:012016	NUM
ejpam-4520	531	9	,	,	PUNCT
ejpam-4520	531	10	2021	2021	NUM
ejpam-4520	531	11	.	.	PUNCT
ejpam-4520	532	1	[	[	X
ejpam-4520	532	2	23	23	NUM
ejpam-4520	532	3	]	]	X
ejpam-4520	532	4	d	d	X
ejpam-4520	532	5	n	n	SYM
ejpam-4520	532	6	s	s	PART
ejpam-4520	532	7	simamora	simamora	PROPN
ejpam-4520	532	8	and	and	CCONJ
ejpam-4520	532	9	a	a	DET
ejpam-4520	532	10	n	n	NOUN
ejpam-4520	532	11	m	m	PROPN
ejpam-4520	532	12	salman	salman	PROPN
ejpam-4520	532	13	.	.	PUNCT
ejpam-4520	533	1	the	the	DET
ejpam-4520	533	2	rainbow	rainbow	NOUN
ejpam-4520	533	3	(	(	PUNCT
ejpam-4520	533	4	vertex	vertex	NOUN
ejpam-4520	533	5	)	)	PUNCT
ejpam-4520	533	6	connection	connection	NOUN
ejpam-4520	533	7	number	number	NOUN
ejpam-4520	533	8	of	of	ADP
ejpam-4520	533	9	pencil	pencil	NOUN
ejpam-4520	533	10	graphs	graph	NOUN
ejpam-4520	533	11	.	.	PUNCT
ejpam-4520	534	1	procedia	procedia	NOUN
ejpam-4520	534	2	computer	computer	NOUN
ejpam-4520	534	3	science	science	NOUN
ejpam-4520	534	4	,	,	PUNCT
ejpam-4520	534	5	74:138–142	74:138–142	PROPN
ejpam-4520	534	6	,	,	PUNCT
ejpam-4520	534	7	2010	2010	NUM
ejpam-4520	534	8	.	.	PUNCT
ejpam-4520	535	1	[	[	X
ejpam-4520	535	2	24	24	NUM
ejpam-4520	535	3	]	]	X
ejpam-4520	535	4	y	y	PROPN
ejpam-4520	535	5	sun	sun	PROPN
ejpam-4520	535	6	.	.	PUNCT
ejpam-4520	536	1	on	on	ADP
ejpam-4520	536	2	rainbow	rainbow	PROPN
ejpam-4520	536	3	total	total	ADJ
ejpam-4520	536	4	coloring	coloring	NOUN
ejpam-4520	536	5	of	of	ADP
ejpam-4520	536	6	a	a	DET
ejpam-4520	536	7	graph	graph	NOUN
ejpam-4520	536	8	.	.	PUNCT
ejpam-4520	537	1	discrete	discrete	ADJ
ejpam-4520	537	2	applied	apply	VERB
ejpam-4520	537	3	mathematics	mathematic	NOUN
ejpam-4520	537	4	,	,	PUNCT
ejpam-4520	537	5	194:171	194:171	NUM
ejpam-4520	537	6	–	–	PUNCT
ejpam-4520	537	7	177	177	NUM
ejpam-4520	537	8	,	,	PUNCT
ejpam-4520	537	9	2015	2015	NUM
ejpam-4520	537	10	.	.	PUNCT
ejpam-4520	538	1	[	[	X
ejpam-4520	538	2	25	25	NUM
ejpam-4520	538	3	]	]	X
ejpam-4520	538	4	w	w	PROPN
ejpam-4520	538	5	d	d	X
ejpam-4520	538	6	wallis	wallis	PROPN
ejpam-4520	538	7	.	.	PUNCT
ejpam-4520	539	1	magic	magic	ADJ
ejpam-4520	539	2	graphs	graph	NOUN
ejpam-4520	539	3	.	.	PUNCT
ejpam-4520	540	1	springer	springer	NOUN
ejpam-4520	540	2	science	science	PROPN
ejpam-4520	540	3	&	&	CCONJ
ejpam-4520	540	4	business	business	NOUN
ejpam-4520	540	5	media	medium	NOUN
ejpam-4520	540	6	,	,	PUNCT
ejpam-4520	540	7	boston	boston	PROPN
ejpam-4520	540	8	,	,	PUNCT
ejpam-4520	540	9	2001	2001	NUM
ejpam-4520	540	10	.	.	PUNCT