id	sid	tid	token	lemma	pos
easat-4161	1	1	edelweiss	edelweiss	PROPN
easat-4161	1	2	applied	apply	VERB
easat-4161	1	3	science	science	NOUN
easat-4161	1	4	and	and	CCONJ
easat-4161	1	5	technology	technology	NOUN
easat-4161	1	6	issn	issn	PROPN
easat-4161	1	7	:	:	PUNCT
easat-4161	1	8	2576	2576	NUM
easat-4161	1	9	-	-	SYM
easat-4161	1	10	8484	8484	NUM
easat-4161	1	11	vol	vol	NOUN
easat-4161	1	12	.	.	PROPN
easat-4161	2	1	9	9	NUM
easat-4161	2	2	,	,	PUNCT
easat-4161	2	3	no	no	INTJ
easat-4161	2	4	.	.	NOUN
easat-4161	2	5	1	1	NUM
easat-4161	2	6	,	,	PUNCT
easat-4161	2	7	481	481	NUM
easat-4161	2	8	-	-	SYM
easat-4161	2	9	492	492	NUM
easat-4161	2	10	2025	2025	NUM
easat-4161	2	11	publisher	publisher	NOUN
easat-4161	2	12	:	:	PUNCT
easat-4161	2	13	learning	learn	VERB
easat-4161	2	14	gate	gate	NOUN
easat-4161	2	15	doi	doi	PROPN
easat-4161	2	16	:	:	PUNCT
easat-4161	2	17	10.55214/25768484.v9i1.4161	10.55214/25768484.v9i1.4161	NUM
easat-4161	2	18	©	©	PROPN
easat-4161	2	19	2025	2025	NUM
easat-4161	2	20	by	by	ADP
easat-4161	2	21	the	the	DET
easat-4161	2	22	authors	author	NOUN
easat-4161	2	23	;	;	PUNCT
easat-4161	3	1	licensee	licensee	PROPN
easat-4161	3	2	learning	learning	NOUN
easat-4161	3	3	gate	gate	NOUN
easat-4161	3	4	©	©	PROPN
easat-4161	3	5	2025	2025	NUM
easat-4161	3	6	by	by	ADP
easat-4161	3	7	the	the	DET
easat-4161	3	8	authors	author	NOUN
easat-4161	3	9	;	;	PUNCT
easat-4161	3	10	licensee	licensee	PROPN
easat-4161	3	11	learning	learning	NOUN
easat-4161	3	12	gate	gate	NOUN
easat-4161	3	13	history	history	NOUN
easat-4161	3	14	:	:	PUNCT
easat-4161	3	15	received	receive	VERB
easat-4161	3	16	:	:	PUNCT
easat-4161	3	17	28	28	NUM
easat-4161	3	18	november	november	PROPN
easat-4161	3	19	2024	2024	NUM
easat-4161	3	20	;	;	PUNCT
easat-4161	3	21	revised	revise	VERB
easat-4161	3	22	:	:	PUNCT
easat-4161	3	23	26	26	NUM
easat-4161	3	24	december	december	PROPN
easat-4161	3	25	2024	2024	NUM
easat-4161	3	26	;	;	PUNCT
easat-4161	3	27	accepted	accept	VERB
easat-4161	3	28	:	:	PUNCT
easat-4161	3	29	3	3	NUM
easat-4161	3	30	january	january	NOUN
easat-4161	3	31	2025	2025	NUM
easat-4161	3	32	;	;	PUNCT
easat-4161	3	33	published	publish	VERB
easat-4161	3	34	:	:	PUNCT
easat-4161	4	1	9	9	NUM
easat-4161	4	2	january	january	NOUN
easat-4161	4	3	2025	2025	NUM
easat-4161	4	4	*	*	PUNCT
easat-4161	4	5	correspondence	correspondence	NOUN
easat-4161	4	6	:	:	PUNCT
easat-4161	4	7	nurdin1701@unhas.ac.id	nurdin1701@unhas.ac.id	PROPN
easat-4161	4	8	development	development	NOUN
easat-4161	4	9	of	of	ADP
easat-4161	4	10	navigation	navigation	NOUN
easat-4161	4	11	systems	system	NOUN
easat-4161	4	12	in	in	ADP
easat-4161	4	13	optimal	optimal	ADJ
easat-4161	4	14	utilization	utilization	NOUN
easat-4161	4	15	of	of	ADP
easat-4161	4	16	transportation	transportation	NOUN
easat-4161	4	17	routes	route	NOUN
easat-4161	4	18	in	in	ADP
easat-4161	4	19	topology	topology	NOUN
easat-4161	4	20	helm	helm	NOUN
easat-4161	4	21	graphs	graph	NOUN
easat-4161	4	22	using	use	VERB
easat-4161	4	23	graph	graph	NOUN
easat-4161	4	24	labeling	label	VERB
easat-4161	4	25	nurdin	nurdin	NOUN
easat-4161	4	26	hinding1	hinding1	NOUN
easat-4161	4	27	*	*	SYM
easat-4161	4	28	,	,	PUNCT
easat-4161	4	29	nurtiti	nurtiti	ADJ
easat-4161	4	30	sunusi2	sunusi2	NOUN
easat-4161	4	31	,	,	PUNCT
easat-4161	4	32	yuni	yuni	PROPN
easat-4161	4	33	syahrani3	syahrani3	PROPN
easat-4161	4	34	,	,	PUNCT
easat-4161	4	35	harry	harry	PROPN
easat-4161	4	36	maulana	maulana	PROPN
easat-4161	4	37	buhari4	buhari4	PROPN
easat-4161	5	1	1graph	1graph	NUM
easat-4161	5	2	theory	theory	NOUN
easat-4161	5	3	research	research	NOUN
easat-4161	5	4	group	group	NOUN
easat-4161	5	5	,	,	PUNCT
easat-4161	5	6	department	department	NOUN
easat-4161	5	7	of	of	ADP
easat-4161	5	8	mathematics	mathematic	NOUN
easat-4161	5	9	,	,	PUNCT
easat-4161	5	10	faculty	faculty	NOUN
easat-4161	5	11	of	of	ADP
easat-4161	5	12	mathematics	mathematic	NOUN
easat-4161	5	13	and	and	CCONJ
easat-4161	5	14	natural	natural	ADJ
easat-4161	5	15	sciences	science	NOUN
easat-4161	5	16	,	,	PUNCT
easat-4161	5	17	hasanuddin	hasanuddin	VERB
easat-4161	5	18	university	university	NOUN
easat-4161	5	19	,	,	PUNCT
easat-4161	5	20	indonesia	indonesia	PROPN
easat-4161	5	21	,	,	PUNCT
easat-4161	5	22	90245	90245	NUM
easat-4161	5	23	;	;	PUNCT
easat-4161	5	24	nurdin1701@unhas.ac.id	nurdin1701@unhas.ac.id	PROPN
easat-4161	5	25	(	(	PUNCT
easat-4161	5	26	n.h	n.h	PROPN
easat-4161	5	27	.	.	PUNCT
easat-4161	5	28	)	)	PUNCT
easat-4161	5	29	.	.	PUNCT
easat-4161	6	1	2stochastic	2stochastic	NUM
easat-4161	6	2	modeling	modeling	NOUN
easat-4161	6	3	research	research	NOUN
easat-4161	6	4	group	group	NOUN
easat-4161	6	5	department	department	PROPN
easat-4161	6	6	of	of	ADP
easat-4161	6	7	statistics	statistic	NOUN
easat-4161	6	8	,	,	PUNCT
easat-4161	6	9	faculty	faculty	NOUN
easat-4161	6	10	of	of	ADP
easat-4161	6	11	mathematics	mathematic	NOUN
easat-4161	6	12	and	and	CCONJ
easat-4161	6	13	natural	natural	ADJ
easat-4161	6	14	sciences	science	NOUN
easat-4161	6	15	,	,	PUNCT
easat-4161	6	16	hasanuddin	hasanuddin	VERB
easat-4161	6	17	university	university	NOUN
easat-4161	6	18	,	,	PUNCT
easat-4161	6	19	indonesia	indonesia	PROPN
easat-4161	6	20	,	,	PUNCT
easat-4161	6	21	90245	90245	NUM
easat-4161	6	22	.	.	PUNCT
easat-4161	7	1	3,4undergraduate	3,4undergraduate	NUM
easat-4161	7	2	’s	’s	PART
easat-4161	7	3	program	program	NOUN
easat-4161	7	4	in	in	ADP
easat-4161	7	5	mathematics	mathematics	PROPN
easat-4161	7	6	,	,	PUNCT
easat-4161	7	7	department	department	NOUN
easat-4161	7	8	of	of	ADP
easat-4161	7	9	mathematics	mathematic	NOUN
easat-4161	7	10	,	,	PUNCT
easat-4161	7	11	faculty	faculty	NOUN
easat-4161	7	12	of	of	ADP
easat-4161	7	13	mathematics	mathematic	NOUN
easat-4161	7	14	and	and	CCONJ
easat-4161	7	15	natural	natural	ADJ
easat-4161	7	16	sciences	science	NOUN
easat-4161	7	17	,	,	PUNCT
easat-4161	7	18	hasanuddin	hasanuddin	VERB
easat-4161	7	19	university	university	NOUN
easat-4161	7	20	,	,	PUNCT
easat-4161	7	21	indonesia	indonesia	PROPN
easat-4161	7	22	,	,	PUNCT
easat-4161	7	23	90245	90245	NUM
easat-4161	7	24	.	.	PUNCT
easat-4161	8	1	abstract	abstract	ADJ
easat-4161	8	2	:	:	PUNCT
easat-4161	8	3	graph	graph	NOUN
easat-4161	8	4	theory	theory	NOUN
easat-4161	8	5	plays	play	VERB
easat-4161	8	6	a	a	DET
easat-4161	8	7	vital	vital	ADJ
easat-4161	8	8	role	role	NOUN
easat-4161	8	9	in	in	ADP
easat-4161	8	10	many	many	ADJ
easat-4161	8	11	fields	field	NOUN
easat-4161	8	12	.	.	PUNCT
easat-4161	9	1	the	the	DET
easat-4161	9	2	graph	graph	NOUN
easat-4161	9	3	concept	concept	NOUN
easat-4161	9	4	models	model	NOUN
easat-4161	9	5	many	many	ADJ
easat-4161	9	6	relationships	relationship	NOUN
easat-4161	9	7	and	and	CCONJ
easat-4161	9	8	processes	process	NOUN
easat-4161	9	9	in	in	ADP
easat-4161	9	10	physical	physical	ADJ
easat-4161	9	11	,	,	PUNCT
easat-4161	9	12	biological	biological	ADJ
easat-4161	9	13	,	,	PUNCT
easat-4161	9	14	social	social	ADJ
easat-4161	9	15	,	,	PUNCT
easat-4161	9	16	transportation	transportation	NOUN
easat-4161	9	17	,	,	PUNCT
easat-4161	9	18	and	and	CCONJ
easat-4161	9	19	information	information	NOUN
easat-4161	9	20	systems	system	NOUN
easat-4161	9	21	.	.	PUNCT
easat-4161	10	1	one	one	NUM
easat-4161	10	2	of	of	ADP
easat-4161	10	3	the	the	DET
easat-4161	10	4	essential	essential	ADJ
easat-4161	10	5	fields	field	NOUN
easat-4161	10	6	in	in	ADP
easat-4161	10	7	graph	graph	NOUN
easat-4161	10	8	theory	theory	NOUN
easat-4161	10	9	is	be	AUX
easat-4161	10	10	graph	graph	NOUN
easat-4161	10	11	labeling	labeling	NOUN
easat-4161	10	12	.	.	PUNCT
easat-4161	11	1	graph	graph	NOUN
easat-4161	11	2	labeling	labeling	NOUN
easat-4161	11	3	is	be	AUX
easat-4161	11	4	widely	widely	ADV
easat-4161	11	5	used	use	VERB
easat-4161	11	6	in	in	ADP
easat-4161	11	7	various	various	ADJ
easat-4161	11	8	applications	application	NOUN
easat-4161	11	9	such	such	ADJ
easat-4161	11	10	as	as	ADP
easat-4161	11	11	coding	code	VERB
easat-4161	11	12	theory	theory	NOUN
easat-4161	11	13	,	,	PUNCT
easat-4161	11	14	x	x	NOUN
easat-4161	11	15	-	-	NOUN
easat-4161	11	16	ray	ray	NOUN
easat-4161	11	17	crystallography	crystallography	NOUN
easat-4161	11	18	,	,	PUNCT
easat-4161	11	19	radar	radar	NOUN
easat-4161	11	20	,	,	PUNCT
easat-4161	11	21	astronomy	astronomy	NOUN
easat-4161	11	22	,	,	PUNCT
easat-4161	11	23	circuit	circuit	NOUN
easat-4161	11	24	design	design	NOUN
easat-4161	11	25	,	,	PUNCT
easat-4161	11	26	addressing	address	VERB
easat-4161	11	27	of	of	ADP
easat-4161	11	28	communication	communication	NOUN
easat-4161	11	29	networks	network	NOUN
easat-4161	11	30	,	,	PUNCT
easat-4161	11	31	database	database	NOUN
easat-4161	11	32	management	management	NOUN
easat-4161	11	33	,	,	PUNCT
easat-4161	11	34	etc	etc	X
easat-4161	11	35	.	.	X
easat-4161	12	1	in	in	ADP
easat-4161	12	2	this	this	DET
easat-4161	12	3	research	research	NOUN
easat-4161	12	4	,	,	PUNCT
easat-4161	12	5	we	we	PRON
easat-4161	12	6	will	will	AUX
easat-4161	12	7	examine	examine	VERB
easat-4161	12	8	a	a	DET
easat-4161	12	9	form	form	NOUN
easat-4161	12	10	of	of	ADP
easat-4161	12	11	topology	topology	NOUN
easat-4161	12	12	of	of	ADP
easat-4161	12	13	transportation	transportation	NOUN
easat-4161	12	14	routes	route	NOUN
easat-4161	12	15	based	base	VERB
easat-4161	12	16	on	on	ADP
easat-4161	12	17	graph	graph	NOUN
easat-4161	12	18	labeling	labeling	NOUN
easat-4161	12	19	.	.	PUNCT
easat-4161	13	1	the	the	DET
easat-4161	13	2	topology	topology	NOUN
easat-4161	13	3	of	of	ADP
easat-4161	13	4	the	the	DET
easat-4161	13	5	transportation	transportation	NOUN
easat-4161	13	6	routes	route	NOUN
easat-4161	13	7	that	that	PRON
easat-4161	13	8	will	will	AUX
easat-4161	13	9	be	be	AUX
easat-4161	13	10	studied	study	VERB
easat-4161	13	11	is	be	AUX
easat-4161	13	12	a	a	DET
easat-4161	13	13	modified	modify	VERB
easat-4161	13	14	of	of	ADP
easat-4161	13	15	helm	helm	NOUN
easat-4161	13	16	graph	graph	NOUN
easat-4161	13	17	.	.	PUNCT
easat-4161	14	1	this	this	DET
easat-4161	14	2	research	research	NOUN
easat-4161	14	3	aims	aim	VERB
easat-4161	14	4	to	to	PART
easat-4161	14	5	determine	determine	VERB
easat-4161	14	6	the	the	DET
easat-4161	14	7	total	total	ADJ
easat-4161	14	8	vertex	vertex	NOUN
easat-4161	14	9	irregularity	irregularity	NOUN
easat-4161	14	10	strength	strength	NOUN
easat-4161	14	11	of	of	ADP
easat-4161	14	12	the	the	DET
easat-4161	14	13	modified	modify	VERB
easat-4161	14	14	helm	helm	NOUN
easat-4161	14	15	graph	graph	NOUN
easat-4161	14	16	denoted	denote	VERB
easat-4161	14	17	by	by	ADP
easat-4161	14	18	𝐻𝑛	𝐻𝑛	PROPN
easat-4161	14	19	for	for	ADP
easat-4161	14	20	𝑛	𝑛	PRON
easat-4161	14	21	≥	≥	NUM
easat-4161	14	22	3	3	NUM
easat-4161	14	23	.	.	PUNCT
easat-4161	15	1	the	the	DET
easat-4161	15	2	lower	lower	ADV
easat-4161	15	3	bound	bind	VERB
easat-4161	15	4	is	be	AUX
easat-4161	15	5	obtained	obtain	VERB
easat-4161	15	6	based	base	VERB
easat-4161	15	7	on	on	ADP
easat-4161	15	8	the	the	DET
easat-4161	15	9	properties	property	NOUN
easat-4161	15	10	of	of	ADP
easat-4161	15	11	the	the	DET
easat-4161	15	12	graph	graph	NOUN
easat-4161	16	1	𝐻𝑛	𝐻𝑛	ADJ
easat-4161	16	2	using	use	VERB
easat-4161	16	3	the	the	DET
easat-4161	16	4	existing	exist	VERB
easat-4161	16	5	supporting	support	VERB
easat-4161	16	6	theorem	theorem	NOUN
easat-4161	16	7	.	.	PUNCT
easat-4161	17	1	the	the	DET
easat-4161	17	2	upper	upper	ADJ
easat-4161	17	3	bound	bind	VERB
easat-4161	17	4	is	be	AUX
easat-4161	17	5	obtained	obtain	VERB
easat-4161	17	6	by	by	ADP
easat-4161	17	7	labeling	label	VERB
easat-4161	17	8	the	the	DET
easat-4161	17	9	vertices	vertex	NOUN
easat-4161	17	10	and	and	CCONJ
easat-4161	17	11	edges	edge	NOUN
easat-4161	17	12	of	of	ADP
easat-4161	17	13	the	the	DET
easat-4161	17	14	graph	graph	NOUN
easat-4161	17	15	𝐻𝑛	𝐻𝑛	VERB
easat-4161	17	16	in	in	ADP
easat-4161	17	17	some	some	DET
easat-4161	17	18	simple	simple	ADJ
easat-4161	17	19	cases	case	NOUN
easat-4161	17	20	.	.	PUNCT
easat-4161	18	1	from	from	ADP
easat-4161	18	2	this	this	DET
easat-4161	18	3	labeling	labeling	NOUN
easat-4161	18	4	,	,	PUNCT
easat-4161	18	5	total	total	ADJ
easat-4161	18	6	vertex	vertex	NOUN
easat-4161	18	7	irregular	irregular	ADJ
easat-4161	18	8	labeling	labeling	NOUN
easat-4161	18	9	will	will	AUX
easat-4161	18	10	be	be	AUX
easat-4161	18	11	constructed	construct	VERB
easat-4161	18	12	for	for	ADP
easat-4161	18	13	any	any	DET
easat-4161	18	14	𝑛.	𝑛.	NOUN
easat-4161	18	15	based	base	VERB
easat-4161	18	16	on	on	ADP
easat-4161	18	17	the	the	DET
easat-4161	18	18	results	result	NOUN
easat-4161	18	19	of	of	ADP
easat-4161	18	20	this	this	DET
easat-4161	18	21	research	research	NOUN
easat-4161	18	22	,	,	PUNCT
easat-4161	18	23	the	the	DET
easat-4161	18	24	total	total	ADJ
easat-4161	18	25	vertex	vertex	NOUN
easat-4161	18	26	irregularity	irregularity	NOUN
easat-4161	18	27	strength	strength	NOUN
easat-4161	18	28	of	of	ADP
easat-4161	18	29	the	the	DET
easat-4161	18	30	graph	graph	NOUN
easat-4161	18	31	𝐻𝑛	𝐻𝑛	PROPN
easat-4161	18	32	is	be	AUX
easat-4161	18	33	𝑡𝑣𝑠(𝐻𝑛	𝑡𝑣𝑠(𝐻𝑛	NOUN
easat-4161	18	34	)	)	PUNCT
easat-4161	18	35	=	=	PUNCT
easat-4161	19	1	⌈	⌈	SYM
easat-4161	19	2	3	3	NUM
easat-4161	19	3	+	+	SYM
easat-4161	19	4	3𝑛	3𝑛	NUM
easat-4161	19	5	4	4	NUM
easat-4161	19	6	⌉	⌉	X
easat-4161	19	7	with	with	ADP
easat-4161	19	8	𝑛	𝑛	DET
easat-4161	19	9	≥	≥	NUM
easat-4161	19	10	3	3	NUM
easat-4161	19	11	.	.	PUNCT
easat-4161	19	12	keywords	keyword	NOUN
easat-4161	19	13	:	:	PUNCT
easat-4161	19	14	helm	helm	NOUN
easat-4161	19	15	graph	graph	NOUN
easat-4161	19	16	,	,	PUNCT
easat-4161	19	17	irregular	irregular	ADJ
easat-4161	19	18	labeling	labeling	NOUN
easat-4161	19	19	,	,	PUNCT
easat-4161	19	20	irregular	irregular	ADJ
easat-4161	19	21	strength	strength	NOUN
easat-4161	19	22	,	,	PUNCT
easat-4161	19	23	transportation	transportation	NOUN
easat-4161	19	24	system	system	NOUN
easat-4161	19	25	.	.	PUNCT
easat-4161	20	1	1	1	X
easat-4161	20	2	.	.	X
easat-4161	20	3	introduction	introduction	NOUN
easat-4161	20	4	one	one	NUM
easat-4161	20	5	of	of	ADP
easat-4161	20	6	the	the	DET
easat-4161	20	7	problems	problem	NOUN
easat-4161	20	8	encountered	encounter	VERB
easat-4161	20	9	in	in	ADP
easat-4161	20	10	big	big	ADJ
easat-4161	20	11	cities	city	NOUN
easat-4161	20	12	,	,	PUNCT
easat-4161	20	13	such	such	ADJ
easat-4161	20	14	as	as	ADP
easat-4161	20	15	jakarta	jakarta	PROPN
easat-4161	20	16	,	,	PUNCT
easat-4161	20	17	surabaya	surabaya	PROPN
easat-4161	20	18	,	,	PUNCT
easat-4161	20	19	and	and	CCONJ
easat-4161	20	20	makassar	makassar	NOUN
easat-4161	20	21	,	,	PUNCT
easat-4161	20	22	is	be	AUX
easat-4161	20	23	the	the	DET
easat-4161	20	24	increase	increase	NOUN
easat-4161	20	25	in	in	ADP
easat-4161	20	26	the	the	DET
easat-4161	20	27	number	number	NOUN
easat-4161	20	28	of	of	ADP
easat-4161	20	29	vehicles	vehicle	NOUN
easat-4161	20	30	,	,	PUNCT
easat-4161	20	31	which	which	PRON
easat-4161	20	32	needs	need	VERB
easat-4161	20	33	to	to	PART
easat-4161	20	34	be	be	AUX
easat-4161	20	35	balanced	balance	VERB
easat-4161	20	36	with	with	ADP
easat-4161	20	37	road	road	NOUN
easat-4161	20	38	infrastructure	infrastructure	NOUN
easat-4161	20	39	development	development	NOUN
easat-4161	20	40	.	.	PUNCT
easat-4161	21	1	this	this	PRON
easat-4161	21	2	will	will	AUX
easat-4161	21	3	lead	lead	VERB
easat-4161	21	4	to	to	ADP
easat-4161	21	5	the	the	DET
easat-4161	21	6	appearance	appearance	NOUN
easat-4161	21	7	of	of	ADP
easat-4161	21	8	congestion	congestion	NOUN
easat-4161	21	9	points	point	NOUN
easat-4161	21	10	on	on	ADP
easat-4161	21	11	the	the	DET
easat-4161	21	12	highway	highway	NOUN
easat-4161	21	13	.	.	PUNCT
easat-4161	22	1	various	various	ADJ
easat-4161	22	2	attempts	attempt	NOUN
easat-4161	22	3	have	have	AUX
easat-4161	22	4	been	be	AUX
easat-4161	22	5	made	make	VERB
easat-4161	22	6	to	to	PART
easat-4161	22	7	resolve	resolve	VERB
easat-4161	22	8	this	this	DET
easat-4161	22	9	problem	problem	NOUN
easat-4161	22	10	.	.	PUNCT
easat-4161	23	1	one	one	NUM
easat-4161	23	2	way	way	NOUN
easat-4161	23	3	is	be	AUX
easat-4161	23	4	to	to	PART
easat-4161	23	5	theoretically	theoretically	ADV
easat-4161	23	6	study	study	VERB
easat-4161	23	7	transportation	transportation	NOUN
easat-4161	23	8	networks	network	NOUN
easat-4161	23	9	using	use	VERB
easat-4161	23	10	graph	graph	NOUN
easat-4161	23	11	models	model	NOUN
easat-4161	23	12	,	,	PUNCT
easat-4161	23	13	especially	especially	ADV
easat-4161	23	14	labeled	label	VERB
easat-4161	23	15	graphs	graph	NOUN
easat-4161	23	16	.	.	PUNCT
easat-4161	24	1	a	a	DET
easat-4161	24	2	labeling	labeling	NOUN
easat-4161	24	3	of	of	ADP
easat-4161	24	4	a	a	DET
easat-4161	24	5	graph	graph	NOUN
easat-4161	24	6	is	be	AUX
easat-4161	24	7	generally	generally	ADV
easat-4161	24	8	defined	define	VERB
easat-4161	24	9	as	as	ADP
easat-4161	24	10	a	a	DET
easat-4161	24	11	function	function	NOUN
easat-4161	24	12	of	of	ADP
easat-4161	24	13	the	the	DET
easat-4161	24	14	subsets	subset	NOUN
easat-4161	24	15	of	of	ADP
easat-4161	24	16	elements	element	NOUN
easat-4161	24	17	from	from	ADP
easat-4161	24	18	g	g	PRON
easat-4161	24	19	to	to	ADP
easat-4161	24	20	a	a	DET
easat-4161	24	21	set	set	NOUN
easat-4161	24	22	of	of	ADP
easat-4161	24	23	numbers	number	NOUN
easat-4161	24	24	,	,	PUNCT
easat-4161	24	25	typically	typically	ADV
easat-4161	24	26	a	a	DET
easat-4161	24	27	set	set	NOUN
easat-4161	24	28	of	of	ADP
easat-4161	24	29	positive	positive	ADJ
easat-4161	24	30	or	or	CCONJ
easat-4161	24	31	non	non	ADJ
easat-4161	24	32	-	-	ADJ
easat-4161	24	33	negative	negative	ADJ
easat-4161	24	34	integers	integer	NOUN
easat-4161	24	35	,	,	PUNCT
easat-4161	24	36	which	which	PRON
easat-4161	24	37	fulfill	fulfill	VERB
easat-4161	24	38	certain	certain	ADJ
easat-4161	24	39	conditions	condition	NOUN
easat-4161	24	40	.	.	PUNCT
easat-4161	25	1	several	several	ADJ
easat-4161	25	2	types	type	NOUN
easat-4161	25	3	of	of	ADP
easat-4161	25	4	graph	graph	NOUN
easat-4161	25	5	labeling	labeling	NOUN
easat-4161	25	6	have	have	AUX
easat-4161	25	7	been	be	AUX
easat-4161	25	8	studied	study	VERB
easat-4161	25	9	,	,	PUNCT
easat-4161	25	10	including	include	VERB
easat-4161	25	11	graceful	graceful	ADJ
easat-4161	25	12	labeling	labeling	NOUN
easat-4161	25	13	,	,	PUNCT
easat-4161	25	14	magic	magic	ADJ
easat-4161	25	15	labeling	labeling	NOUN
easat-4161	25	16	,	,	PUNCT
easat-4161	25	17	anti	anti	ADJ
easat-4161	25	18	-	-	ADJ
easat-4161	25	19	magic	magic	ADJ
easat-4161	25	20	labeling	labeling	NOUN
easat-4161	25	21	,	,	PUNCT
easat-4161	25	22	and	and	CCONJ
easat-4161	25	23	irregular	irregular	ADJ
easat-4161	25	24	labeling	labeling	NOUN
easat-4161	25	25	.	.	PUNCT
easat-4161	26	1	one	one	NUM
easat-4161	26	2	good	good	ADJ
easat-4161	26	3	source	source	NOUN
easat-4161	26	4	of	of	ADP
easat-4161	26	5	information	information	NOUN
easat-4161	26	6	about	about	ADP
easat-4161	26	7	graph	graph	NOUN
easat-4161	26	8	labeling	labeling	NOUN
easat-4161	26	9	is	be	AUX
easat-4161	26	10	"	"	PUNCT
easat-4161	26	11	a	a	DET
easat-4161	26	12	dynamic	dynamic	ADJ
easat-4161	26	13	survey	survey	NOUN
easat-4161	26	14	of	of	ADP
easat-4161	26	15	graph	graph	NOUN
easat-4161	26	16	labeling	labeling	NOUN
easat-4161	26	17	"	"	PUNCT
easat-4161	26	18	[	[	X
easat-4161	26	19	1	1	NUM
easat-4161	26	20	]	]	PUNCT
easat-4161	26	21	.	.	PUNCT
easat-4161	27	1	our	our	PRON
easat-4161	27	2	research	research	NOUN
easat-4161	27	3	topic	topic	NOUN
easat-4161	27	4	is	be	AUX
easat-4161	27	5	focused	focus	VERB
easat-4161	27	6	on	on	ADP
easat-4161	27	7	irregular	irregular	ADJ
easat-4161	27	8	labeling	labeling	NOUN
easat-4161	27	9	.	.	PUNCT
easat-4161	28	1	the	the	DET
easat-4161	28	2	concept	concept	NOUN
easat-4161	28	3	of	of	ADP
easat-4161	28	4	irregular	irregular	ADJ
easat-4161	28	5	labeling	labeling	NOUN
easat-4161	28	6	on	on	ADP
easat-4161	28	7	a	a	DET
easat-4161	28	8	graph	graph	NOUN
easat-4161	28	9	was	be	AUX
easat-4161	28	10	first	first	ADV
easat-4161	28	11	introduced	introduce	VERB
easat-4161	28	12	by	by	ADP
easat-4161	28	13	chartrand	chartrand	PROPN
easat-4161	28	14	,	,	PUNCT
easat-4161	28	15	et	et	PROPN
easat-4161	28	16	al	al	PROPN
easat-4161	28	17	.	.	PUNCT
easat-4161	29	1	[	[	X
easat-4161	29	2	2	2	NUM
easat-4161	29	3	]	]	PUNCT
easat-4161	29	4	.	.	PUNCT
easat-4161	30	1	in	in	ADP
easat-4161	30	2	bac	bac	PROPN
easat-4161	30	3	̆a	̆a	PROPN
easat-4161	30	4	,	,	PUNCT
easat-4161	30	5	et	et	PROPN
easat-4161	30	6	al	al	PROPN
easat-4161	30	7	.	.	PUNCT
easat-4161	31	1	[	[	X
easat-4161	31	2	3	3	X
easat-4161	31	3	]	]	PUNCT
easat-4161	31	4	introduced	introduce	VERB
easat-4161	31	5	another	another	DET
easat-4161	31	6	irregular	irregular	ADJ
easat-4161	31	7	labeling	labeling	NOUN
easat-4161	31	8	based	base	VERB
easat-4161	31	9	on	on	ADP
easat-4161	31	10	total	total	ADJ
easat-4161	31	11	labeling	labeling	NOUN
easat-4161	31	12	,	,	PUNCT
easat-4161	31	13	namely	namely	ADV
easat-4161	31	14	edge	edge	VERB
easat-4161	31	15	irregular	irregular	ADJ
easat-4161	31	16	total	total	ADJ
easat-4161	31	17	labeling	labeling	NOUN
easat-4161	31	18	and	and	CCONJ
easat-4161	31	19	vertex	vertex	NOUN
easat-4161	31	20	total	total	ADJ
easat-4161	31	21	irregular	irregular	ADJ
easat-4161	31	22	labeling	labeling	NOUN
easat-4161	31	23	.	.	PUNCT
easat-4161	32	1	determination	determination	NOUN
easat-4161	32	2	of	of	ADP
easat-4161	32	3	the	the	DET
easat-4161	32	4	vertex	vertex	NOUN
easat-4161	32	5	irregularity	irregularity	NOUN
easat-4161	32	6	strength	strength	NOUN
easat-4161	32	7	,	,	PUNCT
easat-4161	32	8	the	the	DET
easat-4161	32	9	total	total	ADJ
easat-4161	32	10	edge	edge	NOUN
easat-4161	32	11	irregularity	irregularity	NOUN
easat-4161	32	12	strength	strength	NOUN
easat-4161	32	13	,	,	PUNCT
easat-4161	32	14	and	and	CCONJ
easat-4161	32	15	the	the	DET
easat-4161	32	16	total	total	ADJ
easat-4161	32	17	vertex	vertex	NOUN
easat-4161	32	18	irregularity	irregularity	NOUN
easat-4161	32	19	strength	strength	NOUN
easat-4161	32	20	of	of	ADP
easat-4161	32	21	a	a	DET
easat-4161	32	22	graph	graph	NOUN
easat-4161	32	23	can	can	AUX
easat-4161	32	24	only	only	ADV
easat-4161	32	25	be	be	AUX
easat-4161	32	26	done	do	VERB
easat-4161	32	27	partially	partially	ADV
easat-4161	32	28	for	for	ADP
easat-4161	32	29	some	some	DET
easat-4161	32	30	land	land	NOUN
easat-4161	32	31	transportation	transportation	NOUN
easat-4161	32	32	network	network	NOUN
easat-4161	32	33	482	482	NUM
easat-4161	32	34	edelweiss	edelweiss	PROPN
easat-4161	32	35	applied	apply	VERB
easat-4161	32	36	science	science	NOUN
easat-4161	32	37	and	and	CCONJ
easat-4161	32	38	technology	technology	NOUN
easat-4161	32	39	issn	issn	PROPN
easat-4161	32	40	:	:	PUNCT
easat-4161	32	41	2576	2576	NUM
easat-4161	32	42	-	-	SYM
easat-4161	32	43	8484	8484	NUM
easat-4161	32	44	vol	vol	NOUN
easat-4161	32	45	.	.	PROPN
easat-4161	33	1	9	9	NUM
easat-4161	33	2	,	,	PUNCT
easat-4161	33	3	no	no	INTJ
easat-4161	33	4	.	.	NOUN
easat-4161	33	5	1	1	NUM
easat-4161	33	6	:	:	PUNCT
easat-4161	33	7	481	481	NUM
easat-4161	33	8	-	-	SYM
easat-4161	33	9	492	492	NUM
easat-4161	33	10	,	,	PUNCT
easat-4161	33	11	2025	2025	NUM
easat-4161	33	12	doi	doi	NOUN
easat-4161	33	13	:	:	PUNCT
easat-4161	33	14	10.55214/25768484.v9i1.4161	10.55214/25768484.v9i1.4161	NUM
easat-4161	33	15	©	©	PROPN
easat-4161	33	16	2025	2025	NUM
easat-4161	33	17	by	by	ADP
easat-4161	33	18	the	the	DET
easat-4161	33	19	authors	author	NOUN
easat-4161	33	20	;	;	PUNCT
easat-4161	33	21	licensee	licensee	PROPN
easat-4161	33	22	learning	learn	VERB
easat-4161	33	23	gate	gate	NOUN
easat-4161	33	24	models	model	NOUN
easat-4161	33	25	.	.	PUNCT
easat-4161	34	1	several	several	ADJ
easat-4161	34	2	models	model	NOUN
easat-4161	34	3	of	of	ADP
easat-4161	34	4	transportation	transportation	NOUN
easat-4161	34	5	networks	network	NOUN
easat-4161	34	6	are	be	AUX
easat-4161	34	7	still	still	ADV
easat-4161	34	8	open	open	ADJ
easat-4161	34	9	issues	issue	NOUN
easat-4161	34	10	that	that	PRON
easat-4161	34	11	that	that	PRON
easat-4161	34	12	need	need	VERB
easat-4161	34	13	to	to	PART
easat-4161	34	14	be	be	AUX
easat-4161	34	15	resolved	resolve	VERB
easat-4161	34	16	entirely	entirely	ADV
easat-4161	34	17	.	.	PUNCT
easat-4161	35	1	our	our	PRON
easat-4161	35	2	previous	previous	ADJ
easat-4161	35	3	research	research	NOUN
easat-4161	35	4	on	on	ADP
easat-4161	35	5	labeling	label	VERB
easat-4161	35	6	total	total	ADJ
easat-4161	35	7	irregularities	irregularity	NOUN
easat-4161	35	8	of	of	ADP
easat-4161	35	9	vertices	vertex	NOUN
easat-4161	35	10	has	have	AUX
easat-4161	35	11	been	be	AUX
easat-4161	35	12	studied	study	VERB
easat-4161	35	13	for	for	ADP
easat-4161	35	14	graphs	graph	NOUN
easat-4161	35	15	in	in	ADP
easat-4161	35	16	general	general	ADJ
easat-4161	35	17	.	.	PUNCT
easat-4161	36	1	this	this	DET
easat-4161	36	2	research	research	NOUN
easat-4161	36	3	produces	produce	VERB
easat-4161	36	4	a	a	DET
easat-4161	36	5	lower	low	ADJ
easat-4161	36	6	bound	bind	VERB
easat-4161	36	7	on	on	ADP
easat-4161	36	8	the	the	DET
easat-4161	36	9	total	total	ADJ
easat-4161	36	10	vertex	vertex	NOUN
easat-4161	36	11	irregularity	irregularity	NOUN
easat-4161	36	12	strength	strength	NOUN
easat-4161	36	13	,	,	PUNCT
easat-4161	36	14	but	but	CCONJ
easat-4161	36	15	the	the	DET
easat-4161	36	16	exact	exact	ADJ
easat-4161	36	17	value	value	NOUN
easat-4161	36	18	has	have	VERB
easat-4161	36	19	yet	yet	ADV
easat-4161	36	20	to	to	PART
easat-4161	36	21	be	be	AUX
easat-4161	36	22	obtained	obtain	VERB
easat-4161	36	23	.	.	PUNCT
easat-4161	37	1	in	in	ADP
easat-4161	37	2	the	the	DET
easat-4161	37	3	same	same	ADJ
easat-4161	37	4	paper	paper	NOUN
easat-4161	37	5	,	,	PUNCT
easat-4161	37	6	a	a	DET
easat-4161	37	7	conjecture	conjecture	NOUN
easat-4161	37	8	is	be	AUX
easat-4161	37	9	given	give	VERB
easat-4161	37	10	,	,	PUNCT
easat-4161	37	11	which	which	PRON
easat-4161	37	12	has	have	VERB
easat-4161	37	13	yet	yet	ADV
easat-4161	37	14	to	to	PART
easat-4161	37	15	be	be	AUX
easat-4161	37	16	resolved	resolve	VERB
easat-4161	37	17	[	[	PUNCT
easat-4161	37	18	4	4	NUM
easat-4161	37	19	]	]	PUNCT
easat-4161	37	20	.	.	PUNCT
easat-4161	38	1	2	2	X
easat-4161	38	2	.	.	X
easat-4161	38	3	total	total	ADJ
easat-4161	38	4	vertex	vertex	NOUN
easat-4161	38	5	irregular	irregular	ADJ
easat-4161	38	6	graph	graph	NOUN
easat-4161	38	7	historically	historically	ADV
easat-4161	38	8	,	,	PUNCT
easat-4161	38	9	leonhard	leonhard	PROPN
easat-4161	38	10	euler	euler	PROPN
easat-4161	38	11	used	use	VERB
easat-4161	38	12	graphs	graph	NOUN
easat-4161	38	13	to	to	PART
easat-4161	38	14	solve	solve	VERB
easat-4161	38	15	the	the	DET
easat-4161	38	16	konigsberg	konigsberg	PROPN
easat-4161	38	17	bridge	bridge	PROPN
easat-4161	38	18	problem	problem	NOUN
easat-4161	38	19	in	in	ADP
easat-4161	38	20	1736	1736	NUM
easat-4161	38	21	.	.	PUNCT
easat-4161	39	1	one	one	NUM
easat-4161	39	2	of	of	ADP
easat-4161	39	3	the	the	DET
easat-4161	39	4	main	main	ADJ
easat-4161	39	5	points	point	NOUN
easat-4161	39	6	of	of	ADP
easat-4161	39	7	discussion	discussion	NOUN
easat-4161	39	8	in	in	ADP
easat-4161	39	9	graphs	graph	NOUN
easat-4161	39	10	is	be	AUX
easat-4161	39	11	graph	graph	NOUN
easat-4161	39	12	labeling	labeling	NOUN
easat-4161	39	13	.	.	PUNCT
easat-4161	40	1	graph	graph	NOUN
easat-4161	40	2	labeling	labeling	NOUN
easat-4161	40	3	is	be	AUX
easat-4161	40	4	a	a	DET
easat-4161	40	5	function	function	NOUN
easat-4161	40	6	that	that	PRON
easat-4161	40	7	maps	map	VERB
easat-4161	40	8	the	the	DET
easat-4161	40	9	elements	element	NOUN
easat-4161	40	10	of	of	ADP
easat-4161	40	11	a	a	DET
easat-4161	40	12	graph	graph	NOUN
easat-4161	40	13	(	(	PUNCT
easat-4161	40	14	vertices	vertex	NOUN
easat-4161	40	15	or	or	CCONJ
easat-4161	40	16	edges	edge	NOUN
easat-4161	40	17	)	)	PUNCT
easat-4161	40	18	to	to	ADP
easat-4161	40	19	positive	positive	ADJ
easat-4161	40	20	or	or	CCONJ
easat-4161	40	21	non	non	ADJ
easat-4161	40	22	-	-	ADJ
easat-4161	40	23	negative	negative	ADJ
easat-4161	40	24	integers	integer	NOUN
easat-4161	40	25	.	.	PUNCT
easat-4161	41	1	if	if	SCONJ
easat-4161	41	2	the	the	DET
easat-4161	41	3	labeling	labeling	NOUN
easat-4161	41	4	domain	domain	NOUN
easat-4161	41	5	is	be	AUX
easat-4161	41	6	a	a	DET
easat-4161	41	7	set	set	NOUN
easat-4161	41	8	of	of	ADP
easat-4161	41	9	vertices	vertex	NOUN
easat-4161	41	10	,	,	PUNCT
easat-4161	41	11	it	it	PRON
easat-4161	41	12	is	be	AUX
easat-4161	41	13	called	call	VERB
easat-4161	41	14	point	point	NOUN
easat-4161	41	15	labeling	labeling	NOUN
easat-4161	41	16	.	.	PUNCT
easat-4161	42	1	if	if	SCONJ
easat-4161	42	2	the	the	DET
easat-4161	42	3	labeling	labeling	NOUN
easat-4161	42	4	domain	domain	NOUN
easat-4161	42	5	is	be	AUX
easat-4161	42	6	an	an	DET
easat-4161	42	7	edge	edge	NOUN
easat-4161	42	8	set	set	NOUN
easat-4161	42	9	,	,	PUNCT
easat-4161	42	10	then	then	ADV
easat-4161	42	11	it	it	PRON
easat-4161	42	12	is	be	AUX
easat-4161	42	13	called	call	VERB
easat-4161	42	14	an	an	DET
easat-4161	42	15	edge	edge	NOUN
easat-4161	42	16	label	label	NOUN
easat-4161	42	17	,	,	PUNCT
easat-4161	42	18	and	and	CCONJ
easat-4161	42	19	if	if	SCONJ
easat-4161	42	20	the	the	DET
easat-4161	42	21	labeling	labeling	NOUN
easat-4161	42	22	domain	domain	NOUN
easat-4161	42	23	is	be	AUX
easat-4161	42	24	a	a	DET
easat-4161	42	25	set	set	NOUN
easat-4161	42	26	of	of	ADP
easat-4161	42	27	vertices	vertex	NOUN
easat-4161	42	28	and	and	CCONJ
easat-4161	42	29	edges	edge	NOUN
easat-4161	42	30	,	,	PUNCT
easat-4161	42	31	then	then	ADV
easat-4161	42	32	it	it	PRON
easat-4161	42	33	is	be	AUX
easat-4161	42	34	called	call	VERB
easat-4161	42	35	total	total	ADJ
easat-4161	42	36	labeling	labeling	NOUN
easat-4161	43	1	[	[	X
easat-4161	43	2	4	4	NUM
easat-4161	43	3	]	]	PUNCT
easat-4161	43	4	.	.	PUNCT
easat-4161	44	1	definition	definition	NOUN
easat-4161	44	2	1	1	NUM
easat-4161	44	3	.	.	PUNCT
easat-4161	45	1	bac	bac	PROPN
easat-4161	45	2	̆a	̆a	PROPN
easat-4161	45	3	,	,	PUNCT
easat-4161	45	4	et	et	PROPN
easat-4161	45	5	al	al	PROPN
easat-4161	45	6	.	.	PUNCT
easat-4161	46	1	[	[	X
easat-4161	46	2	3	3	X
easat-4161	46	3	]	]	X
easat-4161	46	4	the	the	DET
easat-4161	46	5	vertex	vertex	NOUN
easat-4161	46	6	weight	weight	NOUN
easat-4161	46	7	𝑣	𝑣	X
easat-4161	46	8	on	on	ADP
easat-4161	46	9	the	the	DET
easat-4161	46	10	total	total	ADJ
easat-4161	46	11	labeling	labeling	NOUN
easat-4161	46	12	𝑓	𝑓	PRON
easat-4161	46	13	is	be	AUX
easat-4161	46	14	the	the	DET
easat-4161	46	15	vertex	vertex	NOUN
easat-4161	46	16	label	label	NOUN
easat-4161	46	17	𝑣	𝑣	ADP
easat-4161	46	18	added	add	VERB
easat-4161	46	19	to	to	ADP
easat-4161	46	20	the	the	DET
easat-4161	46	21	sum	sum	NOUN
easat-4161	46	22	of	of	ADP
easat-4161	46	23	all	all	DET
easat-4161	46	24	the	the	DET
easat-4161	46	25	edges	edge	NOUN
easat-4161	46	26	labels	label	VERB
easat-4161	46	27	incident	incident	NOUN
easat-4161	46	28	to	to	ADP
easat-4161	46	29	𝑣	𝑣	ADP
easat-4161	46	30	,	,	PUNCT
easat-4161	46	31	i.e	i.e	PRON
easat-4161	46	32	𝑤𝑡(𝑣	𝑤𝑡(𝑣	NOUN
easat-4161	46	33	)	)	PUNCT
easat-4161	46	34	=	=	SYM
easat-4161	46	35	𝑓(𝑣	𝑓(𝑣	NOUN
easat-4161	46	36	)	)	PUNCT
easat-4161	46	37	+	+	ADJ
easat-4161	46	38	∑	∑	ADJ
easat-4161	46	39	𝑓(𝑢𝑣	𝑓(𝑢𝑣	ADJ
easat-4161	46	40	)	)	PUNCT
easat-4161	46	41	𝑢𝑣∈𝐸	𝑢𝑣∈𝐸	PROPN
easat-4161	46	42	.	.	PUNCT
easat-4161	47	1	definition	definition	NOUN
easat-4161	47	2	2	2	NUM
easat-4161	47	3	.	.	PUNCT
easat-4161	47	4	bac	bac	PROPN
easat-4161	47	5	̆a	̆a	PROPN
easat-4161	47	6	,	,	PUNCT
easat-4161	47	7	et	et	PROPN
easat-4161	47	8	al	al	PROPN
easat-4161	47	9	.	.	PUNCT
easat-4161	48	1	[	[	X
easat-4161	48	2	3]let	3]let	NOUN
easat-4161	48	3	𝐺(𝑉	𝐺(𝑉	NUM
easat-4161	48	4	,	,	PUNCT
easat-4161	48	5	𝐸	𝐸	PROPN
easat-4161	48	6	)	)	PUNCT
easat-4161	48	7	be	be	VERB
easat-4161	48	8	a	a	DET
easat-4161	48	9	simple	simple	ADJ
easat-4161	48	10	graph	graph	NOUN
easat-4161	48	11	.	.	PUNCT
easat-4161	49	1	a	a	DET
easat-4161	49	2	total	total	ADJ
easat-4161	49	3	labeling	labeling	NOUN
easat-4161	49	4	𝑓	𝑓	X
easat-4161	49	5	:	:	PUNCT
easat-4161	49	6	𝑉	𝑉	PROPN
easat-4161	49	7	∪	∪	NOUN
easat-4161	49	8	𝐸	𝐸	PROPN
easat-4161	49	9	→	→	SYM
easat-4161	49	10	{	{	PUNCT
easat-4161	49	11	1,2	1,2	NUM
easat-4161	49	12	,	,	PUNCT
easat-4161	49	13	…	…	PUNCT
easat-4161	49	14	,	,	PUNCT
easat-4161	49	15	𝑘	𝑘	X
easat-4161	49	16	}	}	PUNCT
easat-4161	49	17	is	be	AUX
easat-4161	49	18	a	a	DET
easat-4161	49	19	total	total	ADJ
easat-4161	49	20	vertex	vertex	NOUN
easat-4161	49	21	irregular	irregular	ADJ
easat-4161	49	22	k	k	NOUN
easat-4161	49	23	-	-	NOUN
easat-4161	49	24	labeling	labeling	NOUN
easat-4161	49	25	on	on	ADP
easat-4161	49	26	𝐺	𝐺	PROPN
easat-4161	49	27	if	if	SCONJ
easat-4161	49	28	for	for	ADP
easat-4161	49	29	every	every	DET
easat-4161	49	30	two	two	NUM
easat-4161	49	31	different	different	ADJ
easat-4161	49	32	vertices	vertex	NOUN
easat-4161	49	33	in	in	ADP
easat-4161	49	34	𝑉	𝑉	PROPN
easat-4161	49	35	satisfy	satisfy	NOUN
easat-4161	49	36	𝑤𝑡(𝑥	𝑤𝑡(𝑥	NOUN
easat-4161	49	37	)	)	PUNCT
easat-4161	49	38	≠	≠	PROPN
easat-4161	49	39	𝑤𝑡(𝑦	𝑤𝑡(𝑦	NOUN
easat-4161	49	40	)	)	PUNCT
easat-4161	49	41	,	,	PUNCT
easat-4161	50	1	where	where	SCONJ
easat-4161	50	2	𝑤𝑡(𝑥	𝑤𝑡(𝑥	NUM
easat-4161	50	3	)	)	PUNCT
easat-4161	50	4	=	=	SYM
easat-4161	50	5	𝑓(𝑥	𝑓(𝑥	NOUN
easat-4161	50	6	)	)	PUNCT
easat-4161	51	1	+	+	CCONJ
easat-4161	51	2	∑	∑	PUNCT
easat-4161	51	3	𝑓(𝑥𝑢)𝑥𝑢∈𝐸	𝑓(𝑥𝑢)𝑥𝑢∈𝐸	NOUN
easat-4161	51	4	.	.	PUNCT
easat-4161	52	1	definition	definition	NOUN
easat-4161	52	2	3	3	NUM
easat-4161	52	3	.	.	PUNCT
easat-4161	52	4	bac	bac	PROPN
easat-4161	52	5	̆a	̆a	PROPN
easat-4161	52	6	,	,	PUNCT
easat-4161	52	7	et	et	PROPN
easat-4161	52	8	al	al	PROPN
easat-4161	52	9	.	.	PUNCT
easat-4161	53	1	[	[	X
easat-4161	53	2	3	3	X
easat-4161	53	3	]	]	PUNCT
easat-4161	53	4	let	let	VERB
easat-4161	53	5	𝐺(𝑉	𝐺(𝑉	NUM
easat-4161	53	6	,	,	PUNCT
easat-4161	53	7	𝐸	𝐸	PROPN
easat-4161	53	8	)	)	PUNCT
easat-4161	53	9	be	be	VERB
easat-4161	53	10	a	a	DET
easat-4161	53	11	simple	simple	ADJ
easat-4161	53	12	graph	graph	NOUN
easat-4161	53	13	.	.	PUNCT
easat-4161	54	1	the	the	DET
easat-4161	54	2	total	total	ADJ
easat-4161	54	3	vertex	vertex	NOUN
easat-4161	54	4	irregularity	irregularity	NOUN
easat-4161	54	5	strength	strength	NOUN
easat-4161	54	6	of	of	ADP
easat-4161	54	7	𝐺	𝐺	PROPN
easat-4161	54	8	,	,	PUNCT
easat-4161	54	9	dinoted	dinote	VERB
easat-4161	54	10	by	by	ADP
easat-4161	54	11	𝑡𝑣𝑠(𝐺	𝑡𝑣𝑠(𝐺	NOUN
easat-4161	54	12	)	)	PUNCT
easat-4161	54	13	is	be	AUX
easat-4161	54	14	a	a	DET
easat-4161	54	15	minimum	minimum	ADJ
easat-4161	54	16	positive	positive	ADJ
easat-4161	54	17	integer	integer	NOUN
easat-4161	54	18	number	number	NOUN
easat-4161	54	19	𝑘	𝑘	ADP
easat-4161	54	20	such	such	ADJ
easat-4161	54	21	that	that	SCONJ
easat-4161	54	22	𝐺	𝐺	PROPN
easat-4161	54	23	have	have	VERB
easat-4161	54	24	a	a	DET
easat-4161	54	25	total	total	ADJ
easat-4161	54	26	irregular	irregular	ADJ
easat-4161	54	27	𝑘	𝑘	DET
easat-4161	54	28	−	−	PROPN
easat-4161	54	29	𝑙𝑎𝑏𝑒𝑙𝑙𝑖𝑛𝑔.	𝑙𝑎𝑏𝑒𝑙𝑙𝑖𝑛𝑔.	NOUN
easat-4161	54	30	theorem	theorem	VERB
easat-4161	54	31	1	1	NUM
easat-4161	54	32	.	.	X
easat-4161	55	1	nurdin	nurdin	VERB
easat-4161	55	2	[	[	X
easat-4161	55	3	4	4	NUM
easat-4161	55	4	]	]	PUNCT
easat-4161	55	5	let	let	VERB
easat-4161	55	6	𝐺(𝑉	𝐺(𝑉	NUM
easat-4161	55	7	,	,	PUNCT
easat-4161	55	8	𝐸	𝐸	PROPN
easat-4161	55	9	)	)	PUNCT
easat-4161	55	10	be	be	VERB
easat-4161	55	11	a	a	DET
easat-4161	55	12	connected	connected	ADJ
easat-4161	55	13	simple	simple	ADJ
easat-4161	55	14	graph	graph	NOUN
easat-4161	55	15	on	on	ADP
easat-4161	55	16	𝑛𝑖	𝑛𝑖	PROPN
easat-4161	55	17	vertices	vertex	NOUN
easat-4161	55	18	of	of	ADP
easat-4161	55	19	degree	degree	NOUN
easat-4161	55	20	𝑖	𝑖	X
easat-4161	55	21	(	(	PUNCT
easat-4161	55	22	𝑖	𝑖	NOUN
easat-4161	55	23	=	=	SYM
easat-4161	55	24	𝛿	𝛿	ADJ
easat-4161	55	25	,	,	PUNCT
easat-4161	55	26	𝛿	𝛿	ADJ
easat-4161	55	27	+	+	ADJ
easat-4161	55	28	1	1	NUM
easat-4161	55	29	,	,	PUNCT
easat-4161	55	30	𝛿	𝛿	ADJ
easat-4161	55	31	+	+	ADJ
easat-4161	55	32	2	2	NUM
easat-4161	55	33	,	,	PUNCT
easat-4161	55	34	…	…	PUNCT
easat-4161	55	35	,	,	PUNCT
easat-4161	55	36	∆	∆	PROPN
easat-4161	55	37	)	)	PUNCT
easat-4161	55	38	,	,	PUNCT
easat-4161	55	39	where	where	SCONJ
easat-4161	55	40	𝛿	𝛿	NOUN
easat-4161	55	41	and	and	CCONJ
easat-4161	55	42	∆	∆	PROPN
easat-4161	55	43	are	be	AUX
easat-4161	55	44	minimum	minimum	ADJ
easat-4161	55	45	and	and	CCONJ
easat-4161	55	46	maximum	maximum	ADJ
easat-4161	55	47	degree	degree	NOUN
easat-4161	55	48	on	on	ADP
easat-4161	55	49	𝐺	𝐺	PROPN
easat-4161	55	50	,	,	PUNCT
easat-4161	55	51	respectively	respectively	ADV
easat-4161	55	52	.	.	PUNCT
easat-4161	56	1	then	then	ADV
easat-4161	56	2	𝑡𝑣𝑠(𝐺	𝑡𝑣𝑠(𝐺	NUM
easat-4161	56	3	)	)	PUNCT
easat-4161	56	4	≥	≥	X
easat-4161	56	5	𝑚𝑎𝑥	𝑚𝑎𝑥	ADJ
easat-4161	56	6	{	{	PUNCT
easat-4161	56	7	⌈	⌈	X
easat-4161	56	8	𝛿	𝛿	ADJ
easat-4161	56	9	+	+	NOUN
easat-4161	56	10	𝑛𝛿	𝑛𝛿	NOUN
easat-4161	56	11	𝛿	𝛿	NOUN
easat-4161	56	12	+	+	NUM
easat-4161	56	13	1	1	NUM
easat-4161	56	14	⌉	⌉	NOUN
easat-4161	56	15	,	,	PUNCT
easat-4161	56	16	⌈	⌈	SYM
easat-4161	56	17	𝛿	𝛿	ADJ
easat-4161	56	18	+	+	NOUN
easat-4161	56	19	𝑛𝛿	𝑛𝛿	NOUN
easat-4161	56	20	+	+	NOUN
easat-4161	56	21	𝑛𝛿+1	𝑛𝛿+1	NOUN
easat-4161	56	22	𝛿	𝛿	ADJ
easat-4161	56	23	+	+	NUM
easat-4161	56	24	2	2	NUM
easat-4161	56	25	⌉	⌉	NOUN
easat-4161	56	26	,	,	PUNCT
easat-4161	56	27	…	…	PUNCT
easat-4161	56	28	,	,	PUNCT
easat-4161	56	29	⌈	⌈	ADP
easat-4161	56	30	𝛿	𝛿	ADJ
easat-4161	56	31	+	+	PROPN
easat-4161	56	32	∑	∑	PROPN
easat-4161	56	33	𝑛𝑖	𝑛𝑖	PROPN
easat-4161	56	34	∆	∆	X
easat-4161	56	35	𝑖=𝛿	𝑖=𝛿	NOUN
easat-4161	56	36	∆	∆	PROPN
easat-4161	56	37	+	+	CCONJ
easat-4161	56	38	1	1	NUM
easat-4161	56	39	⌉	⌉	NOUN
easat-4161	56	40	}	}	PUNCT
easat-4161	56	41	.	.	PUNCT
easat-4161	57	1	several	several	ADJ
easat-4161	57	2	studies	study	NOUN
easat-4161	57	3	have	have	AUX
easat-4161	57	4	been	be	AUX
easat-4161	57	5	carried	carry	VERB
easat-4161	57	6	out	out	ADP
easat-4161	57	7	using	use	VERB
easat-4161	57	8	total	total	ADJ
easat-4161	57	9	irregular	irregular	ADJ
easat-4161	57	10	labeling	labeling	NOUN
easat-4161	57	11	.	.	PUNCT
easat-4161	58	1	aarthi	aarthi	VERB
easat-4161	59	1	[	[	X
easat-4161	59	2	5	5	NUM
easat-4161	59	3	]	]	PUNCT
easat-4161	59	4	,	,	PUNCT
easat-4161	59	5	reminded	remind	VERB
easat-4161	59	6	the	the	DET
easat-4161	59	7	total	total	ADJ
easat-4161	59	8	vertex	vertex	NOUN
easat-4161	59	9	irregularity	irregularity	NOUN
easat-4161	59	10	strength	strength	NOUN
easat-4161	59	11	in	in	ADP
easat-4161	59	12	the	the	DET
easat-4161	59	13	helm	helm	NOUN
easat-4161	59	14	graph	graph	NOUN
easat-4161	59	15	aarthi	aarthi	VERB
easat-4161	60	1	[	[	X
easat-4161	60	2	5	5	NUM
easat-4161	60	3	]	]	PUNCT
easat-4161	60	4	.	.	PUNCT
easat-4161	61	1	ahmad	ahmad	PROPN
easat-4161	61	2	,	,	PUNCT
easat-4161	61	3	et	et	PROPN
easat-4161	61	4	al	al	PROPN
easat-4161	61	5	.	.	PUNCT
easat-4161	62	1	[	[	X
easat-4161	62	2	6	6	NUM
easat-4161	62	3	]	]	PUNCT
easat-4161	62	4	determined	determine	VERB
easat-4161	62	5	the	the	DET
easat-4161	62	6	total	total	ADJ
easat-4161	62	7	vertex	vertex	NOUN
easat-4161	62	8	irregularity	irregularity	NOUN
easat-4161	62	9	strength	strength	NOUN
easat-4161	62	10	in	in	ADP
easat-4161	62	11	the	the	DET
easat-4161	62	12	composite	composite	ADJ
easat-4161	62	13	isomorphic	isomorphic	ADJ
easat-4161	62	14	helm	helm	NOUN
easat-4161	62	15	graph	graph	NOUN
easat-4161	62	16	ahmad	ahmad	PROPN
easat-4161	62	17	,	,	PUNCT
easat-4161	62	18	et	et	PROPN
easat-4161	62	19	al	al	PROPN
easat-4161	62	20	.	.	PUNCT
easat-4161	63	1	[	[	X
easat-4161	63	2	6	6	NUM
easat-4161	63	3	]	]	PUNCT
easat-4161	63	4	.	.	PUNCT
easat-4161	64	1	indriati	indriati	PROPN
easat-4161	64	2	widodo	widodo	PROPN
easat-4161	64	3	,	,	PUNCT
easat-4161	64	4	et	et	PROPN
easat-4161	64	5	al	al	PROPN
easat-4161	64	6	.	.	PUNCT
easat-4161	65	1	[	[	X
easat-4161	65	2	7	7	NUM
easat-4161	65	3	]	]	X
easat-4161	65	4	determined	determine	VERB
easat-4161	65	5	generalized	generalized	ADJ
easat-4161	65	6	helm	helm	NOUN
easat-4161	65	7	graphs	graph	NOUN
easat-4161	65	8	'	'	PART
easat-4161	65	9	total	total	ADJ
easat-4161	65	10	vertex	vertex	NOUN
easat-4161	65	11	irregularity	irregularity	NOUN
easat-4161	65	12	strength	strength	NOUN
easat-4161	66	1	[	[	X
easat-4161	66	2	7	7	NUM
easat-4161	66	3	]	]	PUNCT
easat-4161	66	4	.	.	PUNCT
easat-4161	67	1	previously	previously	ADV
easat-4161	67	2	,	,	PUNCT
easat-4161	67	3	nurdin	nurdin	VERB
easat-4161	67	4	[	[	X
easat-4161	67	5	4	4	NUM
easat-4161	67	6	]	]	PUNCT
easat-4161	67	7	had	have	AUX
easat-4161	67	8	determined	determine	VERB
easat-4161	67	9	a	a	DET
easat-4161	67	10	caterpillar	caterpillar	ADJ
easat-4161	67	11	graph	graph	NOUN
easat-4161	67	12	’s	’s	PART
easat-4161	67	13	total	total	ADJ
easat-4161	67	14	vertex	vertex	NOUN
easat-4161	67	15	irregularity	irregularity	NOUN
easat-4161	67	16	strength	strength	NOUN
easat-4161	67	17	nurdin	nurdin	VERB
easat-4161	67	18	[	[	X
easat-4161	67	19	4	4	NUM
easat-4161	67	20	]	]	PUNCT
easat-4161	67	21	.	.	PUNCT
easat-4161	68	1	likewise	likewise	ADV
easat-4161	68	2	,	,	PUNCT
easat-4161	68	3	in	in	ADP
easat-4161	68	4	hinding	hinding	NOUN
easat-4161	68	5	,	,	PUNCT
easat-4161	68	6	et	et	PROPN
easat-4161	68	7	al	al	PROPN
easat-4161	68	8	.	.	PUNCT
easat-4161	69	1	[	[	X
easat-4161	69	2	8	8	NUM
easat-4161	69	3	]	]	PUNCT
easat-4161	69	4	determined	determine	VERB
easat-4161	69	5	the	the	DET
easat-4161	69	6	irregularity	irregularity	NOUN
easat-4161	69	7	strength	strength	NOUN
easat-4161	69	8	of	of	ADP
easat-4161	69	9	a	a	DET
easat-4161	69	10	diamond	diamond	NOUN
easat-4161	69	11	graph	graph	NOUN
easat-4161	69	12	[	[	X
easat-4161	69	13	8	8	NUM
easat-4161	69	14	]	]	PUNCT
easat-4161	69	15	.	.	PUNCT
easat-4161	70	1	in	in	ADP
easat-4161	70	2	this	this	DET
easat-4161	70	3	regard	regard	NOUN
easat-4161	70	4	,	,	PUNCT
easat-4161	70	5	siddiqui	siddiqui	NOUN
easat-4161	70	6	nurdin	nurdin	ADJ
easat-4161	70	7	and	and	CCONJ
easat-4161	70	8	baskoro	baskoro	PRON
easat-4161	71	1	[	[	X
easat-4161	71	2	9	9	NUM
easat-4161	71	3	]	]	PUNCT
easat-4161	71	4	examined	examine	VERB
easat-4161	71	5	the	the	DET
easat-4161	71	6	total	total	ADJ
easat-4161	71	7	edge	edge	NOUN
easat-4161	71	8	irregularity	irregularity	NOUN
easat-4161	71	9	strength	strength	NOUN
easat-4161	71	10	of	of	ADP
easat-4161	71	11	the	the	DET
easat-4161	71	12	disjoint	disjoint	PROPN
easat-4161	71	13	union	union	NOUN
easat-4161	71	14	of	of	ADP
easat-4161	71	15	the	the	DET
easat-4161	71	16	helm	helm	NOUN
easat-4161	71	17	graph	graph	NOUN
easat-4161	71	18	[	[	X
easat-4161	71	19	9	9	NUM
easat-4161	71	20	]	]	PUNCT
easat-4161	71	21	.	.	PUNCT
easat-4161	72	1	however	however	ADV
easat-4161	72	2	,	,	PUNCT
easat-4161	72	3	researchers	researcher	NOUN
easat-4161	72	4	have	have	VERB
easat-4161	72	5	yet	yet	ADV
easat-4161	72	6	to	to	PART
easat-4161	72	7	determine	determine	VERB
easat-4161	72	8	the	the	DET
easat-4161	72	9	total	total	ADJ
easat-4161	72	10	irregularity	irregularity	NOUN
easat-4161	72	11	strength	strength	NOUN
easat-4161	72	12	of	of	ADP
easat-4161	72	13	the	the	DET
easat-4161	72	14	modified	modify	VERB
easat-4161	72	15	helm	helm	NOUN
easat-4161	72	16	graph	graph	NOUN
easat-4161	72	17	vertices	vertex	NOUN
easat-4161	72	18	.	.	PUNCT
easat-4161	73	1	therefore	therefore	ADV
easat-4161	73	2	,	,	PUNCT
easat-4161	73	3	this	this	DET
easat-4161	73	4	study	study	NOUN
easat-4161	73	5	evaluates	evaluate	VERB
easat-4161	73	6	the	the	DET
easat-4161	73	7	total	total	ADJ
easat-4161	73	8	irregularity	irregularity	NOUN
easat-4161	73	9	strength	strength	NOUN
easat-4161	73	10	of	of	ADP
easat-4161	73	11	the	the	DET
easat-4161	73	12	modified	modify	VERB
easat-4161	73	13	helm	helm	NOUN
easat-4161	73	14	graph	graph	NOUN
easat-4161	73	15	.	.	PUNCT
easat-4161	74	1	3	3	X
easat-4161	74	2	.	.	X
easat-4161	74	3	results	result	VERB
easat-4161	74	4	the	the	DET
easat-4161	74	5	graph	graph	NOUN
easat-4161	74	6	for	for	ADP
easat-4161	74	7	which	which	PRON
easat-4161	74	8	the	the	DET
easat-4161	74	9	total	total	ADJ
easat-4161	74	10	vertex	vertex	NOUN
easat-4161	74	11	irregularity	irregularity	NOUN
easat-4161	74	12	strength	strength	NOUN
easat-4161	74	13	will	will	AUX
easat-4161	74	14	be	be	AUX
easat-4161	74	15	determined	determine	VERB
easat-4161	74	16	in	in	ADP
easat-4161	74	17	this	this	DET
easat-4161	74	18	paper	paper	NOUN
easat-4161	74	19	is	be	AUX
easat-4161	74	20	the	the	DET
easat-4161	74	21	helm	helm	NOUN
easat-4161	74	22	g	g	NOUN
easat-4161	74	23	,	,	PUNCT
easat-4161	74	24	which	which	PRON
easat-4161	74	25	is	be	AUX
easat-4161	74	26	modified	modify	VERB
easat-4161	74	27	so	so	SCONJ
easat-4161	74	28	that	that	SCONJ
easat-4161	74	29	the	the	DET
easat-4161	74	30	vertices	vertex	NOUN
easat-4161	74	31	are	be	AUX
easat-4161	74	32	only	only	ADV
easat-4161	74	33	degrees	degree	NOUN
easat-4161	74	34	3	3	NUM
easat-4161	74	35	or	or	CCONJ
easat-4161	74	36	5	5	NUM
easat-4161	74	37	.	.	PUNCT
easat-4161	75	1	formally	formally	ADV
easat-4161	75	2	,	,	PUNCT
easat-4161	75	3	the	the	DET
easat-4161	75	4	graph	graph	NOUN
easat-4161	75	5	in	in	ADP
easat-4161	75	6	question	question	NOUN
easat-4161	75	7	is	be	AUX
easat-4161	75	8	as	as	SCONJ
easat-4161	75	9	follows	follow	VERB
easat-4161	75	10	.	.	PUNCT
easat-4161	76	1	definition	definition	NOUN
easat-4161	76	2	4	4	NUM
easat-4161	76	3	.	.	PUNCT
easat-4161	76	4	let	let	VERB
easat-4161	76	5	𝐻𝑛	𝐻𝑛	PROPN
easat-4161	76	6	be	be	AUX
easat-4161	76	7	a	a	DET
easat-4161	76	8	helm	helm	NOUN
easat-4161	76	9	graph	graph	NOUN
easat-4161	76	10	.	.	PUNCT
easat-4161	77	1	the	the	DET
easat-4161	77	2	ℋ𝑛	ℋ𝑛	PROPN
easat-4161	77	3	is	be	AUX
easat-4161	77	4	a	a	DET
easat-4161	77	5	graph	graph	NOUN
easat-4161	77	6	constructed	construct	VERB
easat-4161	77	7	from	from	ADP
easat-4161	77	8	helm	helm	NOUN
easat-4161	77	9	graph	graph	NOUN
easat-4161	77	10	𝐻𝑛	𝐻𝑛	VERB
easat-4161	77	11	by	by	ADP
easat-4161	77	12	removing	remove	VERB
easat-4161	77	13	the	the	DET
easat-4161	77	14	central	central	ADJ
easat-4161	77	15	vertex	vertex	NOUN
easat-4161	77	16	and	and	CCONJ
easat-4161	77	17	adding	add	VERB
easat-4161	77	18	2𝑛	2𝑛	PROPN
easat-4161	77	19	vertices	vertex	NOUN
easat-4161	77	20	,	,	PUNCT
easat-4161	77	21	namely	namely	ADV
easat-4161	77	22	𝑤1	𝑤1	VERB
easat-4161	77	23	,	,	PUNCT
easat-4161	77	24	𝑣1	𝑣1	PROPN
easat-4161	77	25	,	,	PUNCT
easat-4161	77	26	𝑤2	𝑤2	NOUN
easat-4161	77	27	,	,	PUNCT
easat-4161	77	28	𝑣2	𝑣2	NOUN
easat-4161	77	29	,	,	PUNCT
easat-4161	77	30	…	…	PUNCT
easat-4161	77	31	,	,	PUNCT
easat-4161	77	32	𝑤𝑛	𝑤𝑛	NOUN
easat-4161	77	33	,	,	PUNCT
easat-4161	77	34	𝑣𝑛	𝑣𝑛	ADP
easat-4161	77	35	such	such	ADJ
easat-4161	77	36	that	that	DET
easat-4161	77	37	1	1	NUM
easat-4161	77	38	.	.	X
easat-4161	77	39	𝑥1𝑤𝑛	𝑥1𝑤𝑛	PROPN
easat-4161	77	40	,	,	PUNCT
easat-4161	77	41	𝑥𝑖+1𝑤𝑖	𝑥𝑖+1𝑤𝑖	VERB
easat-4161	77	42	for	for	ADP
easat-4161	77	43	𝑖	𝑖	NOUN
easat-4161	77	44	=	=	SYM
easat-4161	77	45	1	1	NUM
easat-4161	77	46	,	,	PUNCT
easat-4161	77	47	2	2	NUM
easat-4161	77	48	,	,	PUNCT
easat-4161	77	49	…	…	PUNCT
easat-4161	77	50	,	,	PUNCT
easat-4161	77	51	𝑛	𝑛	DET
easat-4161	77	52	−	−	PROPN
easat-4161	77	53	1	1	NUM
easat-4161	77	54	;	;	PUNCT
easat-4161	77	55	2	2	NUM
easat-4161	77	56	.	.	X
easat-4161	77	57	𝑥𝑛𝑣1	𝑥𝑛𝑣1	PROPN
easat-4161	77	58	,	,	PUNCT
easat-4161	77	59	𝑥𝑖−1𝑣𝑖	𝑥𝑖−1𝑣𝑖	NUM
easat-4161	77	60	for𝑖	for𝑖	NOUN
easat-4161	77	61	=	=	SYM
easat-4161	77	62	2	2	NUM
easat-4161	77	63	,	,	PUNCT
easat-4161	77	64	3	3	NUM
easat-4161	77	65	,	,	PUNCT
easat-4161	77	66	…	…	PUNCT
easat-4161	77	67	,	,	PUNCT
easat-4161	77	68	𝑛	𝑛	PROPN
easat-4161	77	69	;	;	PUNCT
easat-4161	77	70	483	483	NUM
easat-4161	77	71	edelweiss	edelweiss	PROPN
easat-4161	77	72	applied	apply	VERB
easat-4161	77	73	science	science	NOUN
easat-4161	77	74	and	and	CCONJ
easat-4161	77	75	technology	technology	NOUN
easat-4161	77	76	issn	issn	PROPN
easat-4161	77	77	:	:	PUNCT
easat-4161	77	78	2576	2576	NUM
easat-4161	77	79	-	-	SYM
easat-4161	77	80	8484	8484	NUM
easat-4161	77	81	vol	vol	NOUN
easat-4161	77	82	.	.	PROPN
easat-4161	78	1	9	9	NUM
easat-4161	78	2	,	,	PUNCT
easat-4161	78	3	no	no	INTJ
easat-4161	78	4	.	.	NOUN
easat-4161	78	5	1	1	NUM
easat-4161	78	6	:	:	PUNCT
easat-4161	78	7	481	481	NUM
easat-4161	78	8	-	-	SYM
easat-4161	78	9	492	492	NUM
easat-4161	78	10	,	,	PUNCT
easat-4161	78	11	2025	2025	NUM
easat-4161	78	12	doi	doi	NOUN
easat-4161	78	13	:	:	PUNCT
easat-4161	78	14	10.55214/25768484.v9i1.4161	10.55214/25768484.v9i1.4161	NUM
easat-4161	78	15	©	©	PROPN
easat-4161	78	16	2025	2025	NUM
easat-4161	78	17	by	by	ADP
easat-4161	78	18	the	the	DET
easat-4161	78	19	authors	author	NOUN
easat-4161	78	20	;	;	PUNCT
easat-4161	78	21	licensee	licensee	PROPN
easat-4161	78	22	learning	learning	NOUN
easat-4161	78	23	gate	gate	NOUN
easat-4161	78	24	3	3	NUM
easat-4161	78	25	.	.	NOUN
easat-4161	78	26	𝑦𝑖𝑤𝑖	𝑦𝑖𝑤𝑖	NOUN
easat-4161	78	27	,	,	PUNCT
easat-4161	78	28	𝑦𝑖𝑣𝑖	𝑦𝑖𝑣𝑖	NOUN
easat-4161	78	29	,	,	PUNCT
easat-4161	78	30	𝑤𝑖𝑣𝑖	𝑤𝑖𝑣𝑖	VERB
easat-4161	78	31	for	for	ADP
easat-4161	78	32	𝑖	𝑖	NOUN
easat-4161	78	33	=	=	SYM
easat-4161	78	34	2	2	NUM
easat-4161	78	35	,	,	PUNCT
easat-4161	78	36	3	3	NUM
easat-4161	78	37	,	,	PUNCT
easat-4161	78	38	…	…	PUNCT
easat-4161	78	39	,	,	PUNCT
easat-4161	78	40	𝑛	𝑛	DET
easat-4161	78	41	the	the	DET
easat-4161	78	42	set	set	NOUN
easat-4161	78	43	of	of	ADP
easat-4161	78	44	vertices	vertex	NOUN
easat-4161	78	45	and	and	CCONJ
easat-4161	78	46	set	set	NOUN
easat-4161	78	47	of	of	ADP
easat-4161	78	48	edges	edge	NOUN
easat-4161	78	49	of	of	ADP
easat-4161	78	50	the	the	DET
easat-4161	78	51	graph	graph	NOUN
easat-4161	79	1	𝐻𝑛	𝐻𝑛	PROPN
easat-4161	79	2	are	be	AUX
easat-4161	79	3	as	as	SCONJ
easat-4161	79	4	follows	follow	VERB
easat-4161	79	5	𝑉(ℋ𝑛	𝑉(ℋ𝑛	NOUN
easat-4161	79	6	)	)	PUNCT
easat-4161	80	1	=	=	PRON
easat-4161	80	2	{	{	PUNCT
easat-4161	80	3	𝑥𝑖	𝑥𝑖	PROPN
easat-4161	80	4	,	,	PUNCT
easat-4161	80	5	𝑦𝑖	𝑦𝑖	PROPN
easat-4161	80	6	,	,	PUNCT
easat-4161	80	7	𝑤𝑖	𝑤𝑖	ADP
easat-4161	80	8	,	,	PUNCT
easat-4161	80	9	𝑣𝑖|	𝑣𝑖|	VERB
easat-4161	80	10	𝑖	𝑖	NOUN
easat-4161	80	11	=	=	NOUN
easat-4161	80	12	1	1	NUM
easat-4161	80	13	,	,	PUNCT
easat-4161	80	14	2	2	NUM
easat-4161	80	15	,	,	PUNCT
easat-4161	80	16	…	…	PUNCT
easat-4161	80	17	,	,	PUNCT
easat-4161	80	18	𝑛	𝑛	NOUN
easat-4161	80	19	}	}	PUNCT
easat-4161	80	20	and	and	CCONJ
easat-4161	80	21	𝐸(ℋ𝑛	𝐸(ℋ𝑛	ADJ
easat-4161	80	22	)	)	PUNCT
easat-4161	80	23	=	=	PRON
easat-4161	80	24	{	{	PUNCT
easat-4161	80	25	𝑥1𝑤𝑛	𝑥1𝑤𝑛	NOUN
easat-4161	80	26	,	,	PUNCT
easat-4161	80	27	𝑥𝑛𝑣𝑖	𝑥𝑛𝑣𝑖	ADJ
easat-4161	80	28	}	}	PUNCT
easat-4161	80	29	∪	∪	NOUN
easat-4161	80	30	{	{	PUNCT
easat-4161	80	31	𝑥𝑖+1𝑤𝑖|	𝑥𝑖+1𝑤𝑖|	NOUN
easat-4161	80	32	𝑖	𝑖	NOUN
easat-4161	80	33	=	=	SYM
easat-4161	80	34	1	1	NUM
easat-4161	80	35	,	,	PUNCT
easat-4161	80	36	2	2	NUM
easat-4161	80	37	,	,	PUNCT
easat-4161	80	38	…	…	PUNCT
easat-4161	80	39	,	,	PUNCT
easat-4161	80	40	𝑛	𝑛	PRON
easat-4161	80	41	−	−	PROPN
easat-4161	80	42	1	1	NUM
easat-4161	80	43	}	}	PUNCT
easat-4161	80	44	∪	∪	ADJ
easat-4161	80	45	{	{	PUNCT
easat-4161	80	46	𝑥𝑖−1𝑣𝑖|	𝑥𝑖−1𝑣𝑖|	PROPN
easat-4161	80	47	𝑖	𝑖	NOUN
easat-4161	80	48	=	=	SYM
easat-4161	80	49	2	2	NUM
easat-4161	80	50	,	,	PUNCT
easat-4161	80	51	3	3	NUM
easat-4161	80	52	,	,	PUNCT
easat-4161	80	53	…	…	PUNCT
easat-4161	80	54	,	,	PUNCT
easat-4161	80	55	𝑛	𝑛	ADJ
easat-4161	80	56	}	}	PUNCT
easat-4161	80	57	∪	∪	ADJ
easat-4161	80	58	{	{	PUNCT
easat-4161	80	59	𝑥𝑖𝑦𝑖	𝑥𝑖𝑦𝑖	ADJ
easat-4161	80	60	,	,	PUNCT
easat-4161	80	61	𝑦𝑖𝑤𝑖	𝑦𝑖𝑤𝑖	NOUN
easat-4161	80	62	,	,	PUNCT
easat-4161	80	63	𝑦𝑖𝑣𝑖	𝑦𝑖𝑣𝑖	PROPN
easat-4161	80	64	,	,	PUNCT
easat-4161	80	65	𝑤𝑖𝑣𝑖|	𝑤𝑖𝑣𝑖|	NOUN
easat-4161	80	66	𝑖	𝑖	SYM
easat-4161	80	67	=	=	NOUN
easat-4161	80	68	1	1	NUM
easat-4161	80	69	,	,	PUNCT
easat-4161	80	70	2	2	NUM
easat-4161	80	71	,	,	PUNCT
easat-4161	80	72	…	…	PUNCT
easat-4161	80	73	,	,	PUNCT
easat-4161	80	74	𝑛	𝑛	ADJ
easat-4161	80	75	}	}	PUNCT
easat-4161	80	76	∪	∪	ADJ
easat-4161	80	77	{	{	PUNCT
easat-4161	80	78	𝑥1𝑥2	𝑥1𝑥2	NOUN
easat-4161	80	79	,	,	PUNCT
easat-4161	80	80	𝑥2𝑥3	𝑥2𝑥3	NOUN
easat-4161	80	81	,	,	PUNCT
easat-4161	80	82	…	…	PUNCT
easat-4161	80	83	,	,	PUNCT
easat-4161	80	84	𝑥𝑛−1𝑥𝑛	𝑥𝑛−1𝑥𝑛	NOUN
easat-4161	80	85	,	,	PUNCT
easat-4161	80	86	𝑥𝑛𝑥1	𝑥𝑛𝑥1	PROPN
easat-4161	80	87	}	}	PUNCT
easat-4161	80	88	.	.	PUNCT
easat-4161	81	1	in	in	ADP
easat-4161	81	2	determining	determine	VERB
easat-4161	81	3	the	the	DET
easat-4161	81	4	total	total	ADJ
easat-4161	81	5	vertex	vertex	NOUN
easat-4161	81	6	irregularity	irregularity	NOUN
easat-4161	81	7	strength	strength	NOUN
easat-4161	81	8	of	of	ADP
easat-4161	81	9	the	the	DET
easat-4161	81	10	modified	modify	VERB
easat-4161	81	11	helm	helm	NOUN
easat-4161	81	12	graph	graph	NOUN
easat-4161	81	13	,	,	PUNCT
easat-4161	81	14	the	the	DET
easat-4161	81	15	lower	low	ADJ
easat-4161	81	16	bound	bind	VERB
easat-4161	81	17	will	will	AUX
easat-4161	81	18	be	be	AUX
easat-4161	81	19	analyzed	analyze	VERB
easat-4161	81	20	first	first	ADV
easat-4161	81	21	based	base	VERB
easat-4161	81	22	on	on	ADP
easat-4161	81	23	the	the	DET
easat-4161	81	24	properties	property	NOUN
easat-4161	81	25	of	of	ADP
easat-4161	81	26	the	the	DET
easat-4161	81	27	graph	graph	NOUN
easat-4161	81	28	𝓗𝒏	𝓗𝒏	ADV
easat-4161	81	29	and	and	CCONJ
easat-4161	81	30	use	use	VERB
easat-4161	81	31	theorem	theorem	NOUN
easat-4161	81	32	1	1	NUM
easat-4161	81	33	.	.	PUNCT
easat-4161	82	1	meanwhile	meanwhile	ADV
easat-4161	82	2	,	,	PUNCT
easat-4161	82	3	to	to	PART
easat-4161	82	4	determine	determine	VERB
easat-4161	82	5	the	the	DET
easat-4161	82	6	upper	upper	ADJ
easat-4161	82	7	bound	bind	VERB
easat-4161	82	8	,	,	PUNCT
easat-4161	82	9	a	a	DET
easat-4161	82	10	total	total	ADJ
easat-4161	82	11	vertex	vertex	NOUN
easat-4161	82	12	irregular	irregular	ADJ
easat-4161	82	13	labeling	labeling	NOUN
easat-4161	82	14	will	will	AUX
easat-4161	82	15	be	be	AUX
easat-4161	82	16	constructed	construct	VERB
easat-4161	82	17	theorem	theorem	VERB
easat-4161	82	18	2	2	NUM
easat-4161	82	19	.	.	PUNCT
easat-4161	83	1	let	let	AUX
easat-4161	83	2	𝓗𝒏	𝓗𝒏	ADV
easat-4161	83	3	be	be	AUX
easat-4161	83	4	modified	modify	VERB
easat-4161	83	5	helm	helm	NOUN
easat-4161	83	6	graph	graph	NOUN
easat-4161	83	7	.	.	PUNCT
easat-4161	84	1	for	for	ADP
easat-4161	84	2	𝒏	𝒏	PROPN
easat-4161	84	3	≥	≥	X
easat-4161	84	4	𝟑	𝟑	NUM
easat-4161	84	5	and	and	CCONJ
easat-4161	84	6	𝒏	𝒏	PROPN
easat-4161	84	7	is	be	AUX
easat-4161	84	8	a	a	DET
easat-4161	84	9	positive	positive	ADJ
easat-4161	84	10	integer	integer	NOUN
easat-4161	84	11	number	number	NOUN
easat-4161	84	12	,	,	PUNCT
easat-4161	84	13	then	then	ADV
easat-4161	84	14	𝒕𝒗𝒔(𝓗𝒏	𝒕𝒗𝒔(𝓗𝒏	ADV
easat-4161	84	15	)	)	PUNCT
easat-4161	84	16	≥	≥	NOUN
easat-4161	85	1	⌈	⌈	NOUN
easat-4161	85	2	𝟑	𝟑	ADP
easat-4161	85	3	+	+	NUM
easat-4161	85	4	𝟑𝒏	𝟑𝒏	NOUN
easat-4161	85	5	𝟒	𝟒	VERB
easat-4161	85	6	⌉.	⌉.	ADV
easat-4161	85	7	next	next	ADV
easat-4161	85	8	,	,	PUNCT
easat-4161	85	9	to	to	PART
easat-4161	85	10	prove	prove	VERB
easat-4161	85	11	that	that	SCONJ
easat-4161	85	12	𝒕𝒗𝒔(𝓗𝒏	𝒕𝒗𝒔(𝓗𝒏	ADP
easat-4161	85	13	)	)	PUNCT
easat-4161	85	14	≤	≤	NOUN
easat-4161	85	15	⌈	⌈	SYM
easat-4161	85	16	𝟑+𝟑𝒏	𝟑+𝟑𝒏	NOUN
easat-4161	85	17	𝟒	𝟒	NUM
easat-4161	85	18	⌉	⌉	NOUN
easat-4161	85	19	,	,	PUNCT
easat-4161	85	20	a	a	DET
easat-4161	85	21	total	total	ADJ
easat-4161	85	22	vertex	vertex	NOUN
easat-4161	85	23	irregular	irregular	ADJ
easat-4161	85	24	labeling	labeling	NOUN
easat-4161	85	25	is	be	AUX
easat-4161	85	26	constructed	construct	VERB
easat-4161	85	27	as	as	SCONJ
easat-4161	85	28	follows	follow	VERB
easat-4161	85	29	.	.	PUNCT
easat-4161	86	1	there	there	PRON
easat-4161	86	2	are	be	VERB
easat-4161	86	3	four	four	NUM
easat-4161	86	4	cases	case	NOUN
easat-4161	86	5	in	in	ADP
easat-4161	86	6	the	the	DET
easat-4161	86	7	construction	construction	NOUN
easat-4161	86	8	of	of	ADP
easat-4161	86	9	a	a	DET
easat-4161	86	10	total	total	ADJ
easat-4161	86	11	vertex	vertex	NOUN
easat-4161	86	12	labeling	labeling	NOUN
easat-4161	86	13	on	on	ADP
easat-4161	86	14	𝓗𝒏.	𝓗𝒏.	PROPN
easat-4161	86	15	case	case	NOUN
easat-4161	86	16	1	1	NUM
easat-4161	86	17	.	.	X
easat-4161	87	1	for	for	ADP
easat-4161	87	2	𝑛	𝑛	NOUN
easat-4161	87	3	=	=	NOUN
easat-4161	87	4	4𝑡	4𝑡	NUM
easat-4161	87	5	−	−	PROPN
easat-4161	87	6	1	1	NUM
easat-4161	87	7	,	,	PUNCT
easat-4161	87	8	where	where	SCONJ
easat-4161	87	9	𝑡	𝑡	PROPN
easat-4161	87	10	is	be	AUX
easat-4161	87	11	some	some	DET
easat-4161	87	12	positive	positive	ADJ
easat-4161	87	13	integer	integer	NOUN
easat-4161	87	14	.	.	PUNCT
easat-4161	88	1	the	the	DET
easat-4161	88	2	total	total	ADJ
easat-4161	88	3	vertex	vertex	NOUN
easat-4161	88	4	labeling	labeling	NOUN
easat-4161	88	5	𝑓	𝑓	NOUN
easat-4161	88	6	is	be	AUX
easat-4161	88	7	𝑓(𝑥1	𝑓(𝑥1	ADV
easat-4161	88	8	)	)	PUNCT
easat-4161	88	9	=	=	SYM
easat-4161	88	10	1	1	X
easat-4161	88	11	.	.	X
easat-4161	88	12	𝑓(𝑥2	𝑓(𝑥2	NOUN
easat-4161	88	13	)	)	PUNCT
easat-4161	89	1	=	=	SYM
easat-4161	89	2	𝑠	𝑠	PROPN
easat-4161	89	3	+	+	NOUN
easat-4161	89	4	1	1	NUM
easat-4161	89	5	.	.	NUM
easat-4161	89	6	𝑓(𝑥𝑖	𝑓(𝑥𝑖	NUM
easat-4161	89	7	)	)	PUNCT
easat-4161	89	8	=	=	PRON
easat-4161	89	9	{	{	PUNCT
easat-4161	89	10	3𝑖+3	3𝑖+3	PROPN
easat-4161	89	11	4	4	NUM
easat-4161	90	1	+	+	CCONJ
easat-4161	90	2	𝑠	𝑠	PROPN
easat-4161	90	3	−	−	NOUN
easat-4161	90	4	𝑖	𝑖	PROPN
easat-4161	91	1	+	+	NOUN
easat-4161	91	2	1	1	NUM
easat-4161	91	3	,	,	PUNCT
easat-4161	91	4	𝑖	𝑖	PRON
easat-4161	91	5	≤	≤	NOUN
easat-4161	91	6	𝑠	𝑠	X
easat-4161	91	7	3𝑖+3	3𝑖+3	PROPN
easat-4161	91	8	4	4	NUM
easat-4161	91	9	,	,	PUNCT
easat-4161	92	1	𝑖	𝑖	PROPN
easat-4161	92	2	>	>	X
easat-4161	92	3	𝑠	𝑠	PROPN
easat-4161	92	4	,	,	PUNCT
easat-4161	92	5	𝑖	𝑖	PROPN
easat-4161	92	6	=	=	SYM
easat-4161	92	7	3	3	NUM
easat-4161	92	8	,	,	PUNCT
easat-4161	92	9	7	7	NUM
easat-4161	92	10	,	,	PUNCT
easat-4161	92	11	11	11	NUM
easat-4161	92	12	,	,	PUNCT
easat-4161	92	13	…	…	PUNCT
easat-4161	92	14	,	,	PUNCT
easat-4161	92	15	𝑛	𝑛	DET
easat-4161	92	16	−	−	PROPN
easat-4161	92	17	4	4	NUM
easat-4161	92	18	.	.	NUM
easat-4161	92	19	𝑓(𝑥𝑖	𝑓(𝑥𝑖	NUM
easat-4161	92	20	)	)	PUNCT
easat-4161	92	21	=	=	PRON
easat-4161	92	22	{	{	PUNCT
easat-4161	92	23	3𝑖+4	3𝑖+4	NUM
easat-4161	92	24	4	4	NUM
easat-4161	93	1	+	+	CCONJ
easat-4161	93	2	𝑠	𝑠	PROPN
easat-4161	93	3	−	−	NOUN
easat-4161	93	4	𝑖	𝑖	PROPN
easat-4161	94	1	+	+	NOUN
easat-4161	94	2	1	1	NUM
easat-4161	94	3	,	,	PUNCT
easat-4161	94	4	𝑖	𝑖	PRON
easat-4161	94	5	≤	≤	NUM
easat-4161	94	6	𝑠	𝑠	X
easat-4161	94	7	3𝑖+4	3𝑖+4	PROPN
easat-4161	94	8	4	4	NUM
easat-4161	94	9	,	,	PUNCT
easat-4161	95	1	𝑖	𝑖	PROPN
easat-4161	95	2	>	>	X
easat-4161	95	3	𝑠	𝑠	PROPN
easat-4161	95	4	,	,	PUNCT
easat-4161	95	5	𝑖	𝑖	X
easat-4161	95	6	=	=	NOUN
easat-4161	95	7	4	4	NUM
easat-4161	95	8	,	,	PUNCT
easat-4161	95	9	8	8	NUM
easat-4161	95	10	,	,	PUNCT
easat-4161	95	11	12	12	NUM
easat-4161	95	12	,	,	PUNCT
easat-4161	95	13	…	…	PUNCT
easat-4161	95	14	,	,	PUNCT
easat-4161	95	15	𝑛	𝑛	DET
easat-4161	95	16	−	−	PROPN
easat-4161	95	17	3	3	NUM
easat-4161	95	18	.	.	NUM
easat-4161	95	19	𝑓(𝑥𝑖	𝑓(𝑥𝑖	NUM
easat-4161	95	20	)	)	PUNCT
easat-4161	95	21	=	=	PRON
easat-4161	95	22	{	{	PUNCT
easat-4161	95	23	3𝑖+5	3𝑖+5	PROPN
easat-4161	95	24	4	4	NUM
easat-4161	96	1	+	+	NUM
easat-4161	96	2	𝑠	𝑠	PROPN
easat-4161	96	3	−	−	NOUN
easat-4161	96	4	𝑖	𝑖	PROPN
easat-4161	97	1	+	+	NOUN
easat-4161	97	2	1	1	NUM
easat-4161	97	3	,	,	PUNCT
easat-4161	97	4	𝑖	𝑖	PRON
easat-4161	97	5	≤	≤	NOUN
easat-4161	97	6	𝑠	𝑠	X
easat-4161	97	7	3𝑖+5	3𝑖+5	PROPN
easat-4161	97	8	4	4	NUM
easat-4161	97	9	,	,	PUNCT
easat-4161	97	10	𝑖	𝑖	PROPN
easat-4161	97	11	>	>	X
easat-4161	97	12	𝑠	𝑠	PROPN
easat-4161	97	13	,	,	PUNCT
easat-4161	97	14	𝑖	𝑖	PROPN
easat-4161	97	15	=	=	SYM
easat-4161	97	16	5	5	NUM
easat-4161	97	17	,	,	PUNCT
easat-4161	97	18	9	9	NUM
easat-4161	97	19	,	,	PUNCT
easat-4161	97	20	13	13	NUM
easat-4161	97	21	,	,	PUNCT
easat-4161	97	22	…	…	PUNCT
easat-4161	97	23	,	,	PUNCT
easat-4161	97	24	𝑛	𝑛	DET
easat-4161	97	25	−	−	PROPN
easat-4161	97	26	2	2	NUM
easat-4161	97	27	.	.	NUM
easat-4161	97	28	𝑓(𝑥𝑖	𝑓(𝑥𝑖	NUM
easat-4161	97	29	)	)	PUNCT
easat-4161	97	30	=	=	PRON
easat-4161	97	31	{	{	PUNCT
easat-4161	98	1	3𝑖+6	3𝑖+6	PROPN
easat-4161	98	2	4	4	NUM
easat-4161	99	1	+	+	CCONJ
easat-4161	99	2	𝑠	𝑠	PROPN
easat-4161	99	3	−	−	NOUN
easat-4161	99	4	𝑖	𝑖	PROPN
easat-4161	100	1	+	+	NOUN
easat-4161	100	2	1	1	NUM
easat-4161	100	3	,	,	PUNCT
easat-4161	100	4	𝑖	𝑖	DET
easat-4161	100	5	≤	≤	NUM
easat-4161	100	6	𝑠	𝑠	X
easat-4161	101	1	3𝑖+6	3𝑖+6	PROPN
easat-4161	101	2	4	4	NUM
easat-4161	101	3	,	,	PUNCT
easat-4161	101	4	𝑖	𝑖	PROPN
easat-4161	101	5	>	>	X
easat-4161	101	6	𝑠	𝑠	PROPN
easat-4161	101	7	,	,	PUNCT
easat-4161	101	8	𝑖	𝑖	PROPN
easat-4161	101	9	=	=	SYM
easat-4161	101	10	6	6	NUM
easat-4161	101	11	,	,	PUNCT
easat-4161	101	12	10	10	NUM
easat-4161	101	13	,	,	PUNCT
easat-4161	101	14	14	14	NUM
easat-4161	101	15	,	,	PUNCT
easat-4161	101	16	…	…	PUNCT
easat-4161	101	17	,	,	PUNCT
easat-4161	101	18	𝑛	𝑛	DET
easat-4161	101	19	−	−	PROPN
easat-4161	101	20	1	1	NUM
easat-4161	101	21	.	.	X
easat-4161	102	1	𝑓(𝑥𝑛	𝑓(𝑥𝑛	NOUN
easat-4161	102	2	)	)	PUNCT
easat-4161	102	3	=	=	SYM
easat-4161	103	1	3𝑛+3	3𝑛+3	PROPN
easat-4161	103	2	4	4	NUM
easat-4161	103	3	.	.	PUNCT
easat-4161	104	1	𝑓(𝑦𝑖	𝑓(𝑦𝑖	ADV
easat-4161	104	2	)	)	PUNCT
easat-4161	105	1	=	=	SYM
easat-4161	105	2	1	1	X
easat-4161	105	3	,	,	PUNCT
easat-4161	105	4	𝑖	𝑖	NOUN
easat-4161	105	5	=	=	SYM
easat-4161	105	6	1	1	NUM
easat-4161	105	7	,	,	PUNCT
easat-4161	105	8	2	2	NUM
easat-4161	105	9	,	,	PUNCT
easat-4161	105	10	…	…	PUNCT
easat-4161	105	11	,	,	PUNCT
easat-4161	105	12	𝑛.	𝑛.	NOUN
easat-4161	105	13	𝑓(𝑤1	𝑓(𝑤1	NOUN
easat-4161	105	14	)	)	PUNCT
easat-4161	105	15	=	=	SYM
easat-4161	105	16	1	1	X
easat-4161	105	17	.	.	X
easat-4161	105	18	𝑓(𝑤2	𝑓(𝑤2	NOUN
easat-4161	105	19	)	)	PUNCT
easat-4161	105	20	=	=	NOUN
easat-4161	105	21	{	{	PUNCT
easat-4161	105	22	2	2	NUM
easat-4161	105	23	,	,	PUNCT
easat-4161	105	24	𝑠	𝑠	PROPN
easat-4161	105	25	=	=	SYM
easat-4161	105	26	1	1	NUM
easat-4161	105	27	1	1	NUM
easat-4161	105	28	,	,	PUNCT
easat-4161	105	29	𝑠	𝑠	PROPN
easat-4161	105	30	=	=	SYM
easat-4161	105	31	2	2	NUM
easat-4161	105	32	,	,	PUNCT
easat-4161	105	33	3	3	NUM
easat-4161	105	34	,	,	PUNCT
easat-4161	105	35	…	…	PUNCT
easat-4161	105	36	𝑓(𝑤𝑖	𝑓(𝑤𝑖	X
easat-4161	105	37	)	)	PUNCT
easat-4161	105	38	=	=	SYM
easat-4161	105	39	{	{	PUNCT
easat-4161	105	40	1	1	NUM
easat-4161	105	41	,	,	PUNCT
easat-4161	105	42	𝑖	𝑖	PROPN
easat-4161	105	43	≤	≤	NOUN
easat-4161	106	1	𝑠	𝑠	X
easat-4161	106	2	3𝑖+3	3𝑖+3	PROPN
easat-4161	106	3	4	4	NUM
easat-4161	106	4	−	−	NOUN
easat-4161	106	5	𝑠	𝑠	PROPN
easat-4161	106	6	+	+	NOUN
easat-4161	106	7	1	1	NUM
easat-4161	106	8	,	,	PUNCT
easat-4161	106	9	𝑖	𝑖	PROPN
easat-4161	106	10	>	>	X
easat-4161	106	11	𝑠	𝑠	PROPN
easat-4161	106	12	,	,	PUNCT
easat-4161	106	13	𝑖	𝑖	PROPN
easat-4161	106	14	=	=	SYM
easat-4161	106	15	3	3	NUM
easat-4161	106	16	,	,	PUNCT
easat-4161	106	17	7	7	NUM
easat-4161	106	18	,	,	PUNCT
easat-4161	106	19	11	11	NUM
easat-4161	106	20	,	,	PUNCT
easat-4161	106	21	…	…	PUNCT
easat-4161	106	22	,	,	PUNCT
easat-4161	106	23	𝑛	𝑛	DET
easat-4161	106	24	−	−	PROPN
easat-4161	106	25	4	4	NUM
easat-4161	106	26	.	.	X
easat-4161	106	27	484	484	NUM
easat-4161	106	28	edelweiss	edelweiss	PROPN
easat-4161	106	29	applied	apply	VERB
easat-4161	106	30	science	science	NOUN
easat-4161	106	31	and	and	CCONJ
easat-4161	106	32	technology	technology	NOUN
easat-4161	106	33	issn	issn	PROPN
easat-4161	106	34	:	:	PUNCT
easat-4161	106	35	2576	2576	NUM
easat-4161	106	36	-	-	SYM
easat-4161	106	37	8484	8484	NUM
easat-4161	106	38	vol	vol	NOUN
easat-4161	106	39	.	.	PROPN
easat-4161	106	40	9	9	NUM
easat-4161	106	41	,	,	PUNCT
easat-4161	106	42	no	no	INTJ
easat-4161	106	43	.	.	NOUN
easat-4161	106	44	1	1	NUM
easat-4161	106	45	:	:	PUNCT
easat-4161	106	46	481	481	NUM
easat-4161	106	47	-	-	SYM
easat-4161	106	48	492	492	NUM
easat-4161	106	49	,	,	PUNCT
easat-4161	106	50	2025	2025	NUM
easat-4161	106	51	doi	doi	NOUN
easat-4161	106	52	:	:	PUNCT
easat-4161	106	53	10.55214/25768484.v9i1.4161	10.55214/25768484.v9i1.4161	NUM
easat-4161	106	54	©	©	PROPN
easat-4161	106	55	2025	2025	NUM
easat-4161	106	56	by	by	ADP
easat-4161	106	57	the	the	DET
easat-4161	106	58	authors	author	NOUN
easat-4161	106	59	;	;	PUNCT
easat-4161	106	60	licensee	licensee	PROPN
easat-4161	106	61	learning	learning	NOUN
easat-4161	106	62	gate	gate	NOUN
easat-4161	106	63	𝑓(𝑤𝑖	𝑓(𝑤𝑖	PROPN
easat-4161	106	64	)	)	PUNCT
easat-4161	106	65	=	=	SYM
easat-4161	106	66	{	{	PUNCT
easat-4161	106	67	1	1	NUM
easat-4161	106	68	,	,	PUNCT
easat-4161	106	69	𝑖	𝑖	DET
easat-4161	106	70	≤	≤	NUM
easat-4161	106	71	𝑠	𝑠	X
easat-4161	106	72	3𝑖+4	3𝑖+4	PROPN
easat-4161	106	73	4	4	NUM
easat-4161	106	74	−	−	NOUN
easat-4161	106	75	𝑠	𝑠	PROPN
easat-4161	106	76	+	+	NOUN
easat-4161	106	77	1	1	NUM
easat-4161	106	78	,	,	PUNCT
easat-4161	106	79	𝑖	𝑖	PROPN
easat-4161	106	80	>	>	X
easat-4161	106	81	𝑠	𝑠	PROPN
easat-4161	106	82	,	,	PUNCT
easat-4161	106	83	𝑖	𝑖	X
easat-4161	106	84	=	=	NOUN
easat-4161	106	85	4	4	NUM
easat-4161	106	86	,	,	PUNCT
easat-4161	106	87	8	8	NUM
easat-4161	106	88	,	,	PUNCT
easat-4161	106	89	12	12	NUM
easat-4161	106	90	,	,	PUNCT
easat-4161	106	91	…	…	PUNCT
easat-4161	106	92	,	,	PUNCT
easat-4161	106	93	𝑛	𝑛	DET
easat-4161	106	94	−	−	NOUN
easat-4161	106	95	3	3	NUM
easat-4161	106	96	.	.	PUNCT
easat-4161	106	97	𝑓(𝑤𝑖	𝑓(𝑤𝑖	VERB
easat-4161	106	98	)	)	PUNCT
easat-4161	106	99	=	=	PRON
easat-4161	106	100	{	{	PUNCT
easat-4161	106	101	1	1	NUM
easat-4161	106	102	,	,	PUNCT
easat-4161	106	103	𝑖	𝑖	PRON
easat-4161	106	104	≤	≤	NOUN
easat-4161	106	105	𝑠	𝑠	X
easat-4161	107	1	3𝑖+5	3𝑖+5	PROPN
easat-4161	107	2	4	4	NUM
easat-4161	107	3	−	−	NOUN
easat-4161	107	4	𝑠	𝑠	PROPN
easat-4161	107	5	+	+	NOUN
easat-4161	107	6	1	1	NUM
easat-4161	107	7	,	,	PUNCT
easat-4161	107	8	𝑖	𝑖	PROPN
easat-4161	107	9	>	>	X
easat-4161	107	10	𝑠	𝑠	PROPN
easat-4161	107	11	,	,	PUNCT
easat-4161	107	12	𝑖	𝑖	PROPN
easat-4161	107	13	=	=	SYM
easat-4161	107	14	5	5	NUM
easat-4161	107	15	,	,	PUNCT
easat-4161	107	16	9	9	NUM
easat-4161	107	17	,	,	PUNCT
easat-4161	107	18	13	13	NUM
easat-4161	107	19	,	,	PUNCT
easat-4161	107	20	…	…	PUNCT
easat-4161	107	21	,	,	PUNCT
easat-4161	107	22	𝑛	𝑛	DET
easat-4161	107	23	−	−	PROPN
easat-4161	107	24	2	2	NUM
easat-4161	107	25	.	.	PUNCT
easat-4161	107	26	𝑓(𝑤𝑖	𝑓(𝑤𝑖	X
easat-4161	107	27	)	)	PUNCT
easat-4161	107	28	=	=	SYM
easat-4161	107	29	{	{	PUNCT
easat-4161	107	30	1	1	NUM
easat-4161	107	31	,	,	PUNCT
easat-4161	107	32	𝑖	𝑖	PROPN
easat-4161	107	33	≤	≤	NUM
easat-4161	107	34	𝑠	𝑠	X
easat-4161	107	35	3𝑖+6	3𝑖+6	PROPN
easat-4161	107	36	4	4	NUM
easat-4161	107	37	−	−	NOUN
easat-4161	107	38	𝑠	𝑠	PROPN
easat-4161	107	39	+	+	NOUN
easat-4161	107	40	1	1	NUM
easat-4161	107	41	,	,	PUNCT
easat-4161	107	42	𝑖	𝑖	PROPN
easat-4161	107	43	>	>	X
easat-4161	107	44	𝑠	𝑠	PROPN
easat-4161	107	45	,	,	PUNCT
easat-4161	107	46	𝑖	𝑖	PROPN
easat-4161	107	47	=	=	SYM
easat-4161	107	48	6	6	NUM
easat-4161	107	49	,	,	PUNCT
easat-4161	107	50	10	10	NUM
easat-4161	107	51	,	,	PUNCT
easat-4161	107	52	14	14	NUM
easat-4161	107	53	,	,	PUNCT
easat-4161	107	54	…	…	PUNCT
easat-4161	107	55	,	,	PUNCT
easat-4161	107	56	𝑛	𝑛	DET
easat-4161	107	57	−	−	PROPN
easat-4161	107	58	1	1	NUM
easat-4161	107	59	.	.	PUNCT
easat-4161	107	60	𝑓(𝑤𝑛	𝑓(𝑤𝑛	NOUN
easat-4161	107	61	)	)	PUNCT
easat-4161	107	62	=	=	NOUN
easat-4161	107	63	2𝑠	2𝑠	NOUN
easat-4161	107	64	+	+	CCONJ
easat-4161	107	65	1	1	X
easat-4161	107	66	.	.	X
easat-4161	107	67	𝑓(𝑣𝑖	𝑓(𝑣𝑖	NOUN
easat-4161	107	68	)	)	PUNCT
easat-4161	107	69	=	=	NOUN
easat-4161	108	1	3𝑠	3𝑠	NOUN
easat-4161	108	2	,	,	PUNCT
easat-4161	108	3	𝑖	𝑖	SYM
easat-4161	108	4	=	=	SYM
easat-4161	108	5	1	1	NUM
easat-4161	108	6	,	,	PUNCT
easat-4161	108	7	2	2	NUM
easat-4161	108	8	,	,	PUNCT
easat-4161	108	9	…	…	PUNCT
easat-4161	108	10	,	,	PUNCT
easat-4161	108	11	𝑛.	𝑛.	NOUN
easat-4161	108	12	𝑓(𝑥1𝑥2	𝑓(𝑥1𝑥2	NOUN
easat-4161	108	13	)	)	PUNCT
easat-4161	108	14	=	=	SYM
easat-4161	108	15	𝑓(𝑥2𝑥3	𝑓(𝑥2𝑥3	PROPN
easat-4161	108	16	)	)	PUNCT
easat-4161	108	17	=	=	SYM
easat-4161	108	18	𝑓(𝑥𝑖−1𝑥𝑖	𝑓(𝑥𝑖−1𝑥𝑖	ADJ
easat-4161	108	19	)	)	PUNCT
easat-4161	108	20	=	=	SYM
easat-4161	108	21	𝑓(𝑥𝑖𝑥𝑖+1	𝑓(𝑥𝑖𝑥𝑖+1	PROPN
easat-4161	108	22	)	)	PUNCT
easat-4161	108	23	=	=	SYM
easat-4161	108	24	𝑓(𝑥𝑛−1𝑥𝑛	𝑓(𝑥𝑛−1𝑥𝑛	NOUN
easat-4161	108	25	)	)	PUNCT
easat-4161	108	26	=	=	SYM
easat-4161	108	27	𝑓(𝑥𝑛𝑥1	𝑓(𝑥𝑛𝑥1	X
easat-4161	108	28	)	)	PUNCT
easat-4161	108	29	=	=	SYM
easat-4161	108	30	3𝑠.	3𝑠.	NUM
easat-4161	108	31	𝑓(𝑥1𝑦1	𝑓(𝑥1𝑦1	NOUN
easat-4161	108	32	)	)	PUNCT
easat-4161	108	33	=	=	SYM
easat-4161	108	34	𝑓(𝑥2𝑦2	𝑓(𝑥2𝑦2	NOUN
easat-4161	108	35	)	)	PUNCT
easat-4161	108	36	=	=	SYM
easat-4161	109	1	1	1	X
easat-4161	109	2	.	.	X
easat-4161	109	3	𝑓(𝑥𝑖𝑦𝑖	𝑓(𝑥𝑖𝑦𝑖	NOUN
easat-4161	109	4	)	)	PUNCT
easat-4161	110	1	=	=	PRON
easat-4161	110	2	{	{	PUNCT
easat-4161	110	3	𝑖+1	𝑖+1	NUM
easat-4161	110	4	4	4	NUM
easat-4161	110	5	,	,	PUNCT
easat-4161	110	6	𝑖	𝑖	NOUN
easat-4161	110	7	=	=	SYM
easat-4161	110	8	3	3	NUM
easat-4161	110	9	,	,	PUNCT
easat-4161	110	10	7	7	NUM
easat-4161	110	11	,	,	PUNCT
easat-4161	110	12	11	11	NUM
easat-4161	110	13	,	,	PUNCT
easat-4161	110	14	…	…	PUNCT
easat-4161	110	15	,	,	PUNCT
easat-4161	110	16	𝑛	𝑛	DET
easat-4161	110	17	−	−	NOUN
easat-4161	110	18	4	4	NUM
easat-4161	110	19	.	.	PUNCT
easat-4161	110	20	𝑖	𝑖	ADP
easat-4161	110	21	4	4	NUM
easat-4161	110	22	,	,	PUNCT
easat-4161	110	23	𝑖	𝑖	NOUN
easat-4161	110	24	=	=	SYM
easat-4161	110	25	4	4	NUM
easat-4161	110	26	,	,	PUNCT
easat-4161	110	27	8	8	NUM
easat-4161	110	28	,	,	PUNCT
easat-4161	110	29	12	12	NUM
easat-4161	110	30	,	,	PUNCT
easat-4161	110	31	…	…	PUNCT
easat-4161	110	32	,	,	PUNCT
easat-4161	110	33	𝑛	𝑛	DET
easat-4161	110	34	−	−	NOUN
easat-4161	110	35	3	3	X
easat-4161	110	36	.	.	PUNCT
easat-4161	111	1	𝑖−1	𝑖−1	ADP
easat-4161	111	2	4	4	NUM
easat-4161	111	3	,	,	PUNCT
easat-4161	111	4	𝑖	𝑖	NOUN
easat-4161	111	5	=	=	SYM
easat-4161	111	6	5	5	NUM
easat-4161	111	7	,	,	PUNCT
easat-4161	111	8	9	9	NUM
easat-4161	111	9	,	,	PUNCT
easat-4161	111	10	13	13	NUM
easat-4161	111	11	,	,	PUNCT
easat-4161	111	12	…	…	PUNCT
easat-4161	111	13	,	,	PUNCT
easat-4161	111	14	𝑛	𝑛	DET
easat-4161	111	15	−	−	PROPN
easat-4161	111	16	2	2	NUM
easat-4161	111	17	.	.	PUNCT
easat-4161	112	1	𝑖−2	𝑖−2	PROPN
easat-4161	112	2	4	4	NUM
easat-4161	112	3	,	,	PUNCT
easat-4161	112	4	𝑖	𝑖	NOUN
easat-4161	112	5	=	=	SYM
easat-4161	112	6	6	6	NUM
easat-4161	112	7	,	,	PUNCT
easat-4161	112	8	10	10	NUM
easat-4161	112	9	,	,	PUNCT
easat-4161	112	10	14	14	NUM
easat-4161	112	11	,	,	PUNCT
easat-4161	112	12	…	…	PUNCT
easat-4161	112	13	,	,	PUNCT
easat-4161	112	14	𝑛	𝑛	DET
easat-4161	112	15	−	−	PROPN
easat-4161	112	16	1	1	NUM
easat-4161	112	17	.	.	PUNCT
easat-4161	112	18	𝑓(𝑥𝑛𝑦𝑛	𝑓(𝑥𝑛𝑦𝑛	ADJ
easat-4161	112	19	)	)	PUNCT
easat-4161	113	1	=	=	SYM
easat-4161	113	2	𝑛+1	𝑛+1	PROPN
easat-4161	113	3	4	4	NUM
easat-4161	113	4	.	.	PUNCT
easat-4161	114	1	𝑓(𝑥2𝑤1	𝑓(𝑥2𝑤1	ADJ
easat-4161	114	2	)	)	PUNCT
easat-4161	115	1	=	=	NOUN
easat-4161	115	2	2𝑠.	2𝑠.	NUM
easat-4161	115	3	𝑓(𝑥3𝑤2	𝑓(𝑥3𝑤2	PROPN
easat-4161	115	4	)	)	PUNCT
easat-4161	116	1	=	=	PRON
easat-4161	116	2	{	{	PUNCT
easat-4161	116	3	3𝑠	3𝑠	NUM
easat-4161	116	4	−	−	PROPN
easat-4161	116	5	1	1	NUM
easat-4161	116	6	,	,	PUNCT
easat-4161	116	7	𝑠	𝑠	PROPN
easat-4161	116	8	=	=	SYM
easat-4161	116	9	1	1	NUM
easat-4161	116	10	2𝑠	2𝑠	NOUN
easat-4161	116	11	+	+	CCONJ
easat-4161	116	12	1	1	NUM
easat-4161	116	13	,	,	PUNCT
easat-4161	116	14	𝑠	𝑠	NOUN
easat-4161	116	15	=	=	SYM
easat-4161	116	16	2	2	NUM
easat-4161	116	17	,	,	PUNCT
easat-4161	116	18	3	3	NUM
easat-4161	116	19	,	,	PUNCT
easat-4161	116	20	…	…	PUNCT
easat-4161	116	21	𝑓(𝑥𝑖+1𝑤𝑖	𝑓(𝑥𝑖+1𝑤𝑖	NOUN
easat-4161	116	22	)	)	PUNCT
easat-4161	116	23	=	=	NOUN
easat-4161	116	24	{	{	PUNCT
easat-4161	116	25	2𝑠	2𝑠	NOUN
easat-4161	117	1	+	+	CCONJ
easat-4161	117	2	3𝑖+3	3𝑖+3	PROPN
easat-4161	117	3	4	4	NUM
easat-4161	117	4	−	−	NOUN
easat-4161	117	5	1	1	NUM
easat-4161	117	6	,	,	PUNCT
easat-4161	117	7	𝑖	𝑖	PRON
easat-4161	117	8	≤	≤	NOUN
easat-4161	117	9	𝑠	𝑠	NUM
easat-4161	117	10	3𝑠	3𝑠	NUM
easat-4161	117	11	−	−	PROPN
easat-4161	117	12	1	1	NUM
easat-4161	117	13	,	,	PUNCT
easat-4161	117	14	𝑖	𝑖	PROPN
easat-4161	117	15	>	>	X
easat-4161	117	16	𝑠	𝑠	PROPN
easat-4161	117	17	,	,	PUNCT
easat-4161	117	18	𝑖	𝑖	PROPN
easat-4161	117	19	=	=	SYM
easat-4161	117	20	3	3	NUM
easat-4161	117	21	,	,	PUNCT
easat-4161	117	22	7	7	NUM
easat-4161	117	23	,	,	PUNCT
easat-4161	117	24	11	11	NUM
easat-4161	117	25	,	,	PUNCT
easat-4161	117	26	…	…	PUNCT
easat-4161	117	27	,	,	PUNCT
easat-4161	117	28	𝑛	𝑛	DET
easat-4161	117	29	−	−	PROPN
easat-4161	117	30	4	4	NUM
easat-4161	117	31	.	.	PUNCT
easat-4161	117	32	𝑓(𝑥𝑖+1𝑤𝑖	𝑓(𝑥𝑖+1𝑤𝑖	NOUN
easat-4161	117	33	)	)	PUNCT
easat-4161	117	34	=	=	PRON
easat-4161	117	35	{	{	PUNCT
easat-4161	117	36	2𝑠	2𝑠	NOUN
easat-4161	118	1	+	+	CCONJ
easat-4161	118	2	3𝑖+4	3𝑖+4	NUM
easat-4161	118	3	4	4	NUM
easat-4161	118	4	−	−	NOUN
easat-4161	118	5	1	1	NUM
easat-4161	118	6	,	,	PUNCT
easat-4161	118	7	𝑖	𝑖	PRON
easat-4161	118	8	≤	≤	NOUN
easat-4161	118	9	𝑠	𝑠	NUM
easat-4161	118	10	3𝑠	3𝑠	NUM
easat-4161	118	11	−	−	PROPN
easat-4161	118	12	1	1	NUM
easat-4161	118	13	,	,	PUNCT
easat-4161	118	14	𝑖	𝑖	PROPN
easat-4161	118	15	>	>	X
easat-4161	118	16	𝑠	𝑠	PROPN
easat-4161	118	17	,	,	PUNCT
easat-4161	118	18	𝑖	𝑖	X
easat-4161	118	19	=	=	NOUN
easat-4161	118	20	4	4	NUM
easat-4161	118	21	,	,	PUNCT
easat-4161	118	22	8	8	NUM
easat-4161	118	23	,	,	PUNCT
easat-4161	118	24	12,	12,	NUM
easat-4161	118	25	…	…	SYM
easat-4161	118	26	𝑛	𝑛	PRON
easat-4161	118	27	−	−	PROPN
easat-4161	118	28	3	3	NUM
easat-4161	118	29	.	.	PUNCT
easat-4161	118	30	𝑓(𝑥𝑖+1𝑤𝑖	𝑓(𝑥𝑖+1𝑤𝑖	NOUN
easat-4161	118	31	)	)	PUNCT
easat-4161	119	1	=	=	PRON
easat-4161	119	2	{	{	PUNCT
easat-4161	119	3	2𝑠	2𝑠	NOUN
easat-4161	120	1	+	+	CCONJ
easat-4161	120	2	3𝑖+5	3𝑖+5	PROPN
easat-4161	120	3	4	4	NUM
easat-4161	120	4	−	−	NUM
easat-4161	120	5	1	1	NUM
easat-4161	120	6	,	,	PUNCT
easat-4161	120	7	𝑖	𝑖	PRON
easat-4161	120	8	≤	≤	NOUN
easat-4161	120	9	𝑠	𝑠	NUM
easat-4161	120	10	3𝑠	3𝑠	NUM
easat-4161	120	11	−	−	PROPN
easat-4161	120	12	1	1	NUM
easat-4161	120	13	,	,	PUNCT
easat-4161	120	14	𝑖	𝑖	PROPN
easat-4161	120	15	>	>	X
easat-4161	120	16	𝑠	𝑠	PROPN
easat-4161	120	17	,	,	PUNCT
easat-4161	120	18	𝑖	𝑖	PROPN
easat-4161	120	19	=	=	SYM
easat-4161	120	20	5	5	NUM
easat-4161	120	21	,	,	PUNCT
easat-4161	120	22	9	9	NUM
easat-4161	120	23	,	,	PUNCT
easat-4161	120	24	13	13	NUM
easat-4161	120	25	,	,	PUNCT
easat-4161	120	26	…	…	PUNCT
easat-4161	120	27	,	,	PUNCT
easat-4161	120	28	𝑛	𝑛	DET
easat-4161	120	29	−	−	PROPN
easat-4161	120	30	2	2	NUM
easat-4161	120	31	.	.	X
easat-4161	120	32	𝑓(𝑥𝑖+1𝑤𝑖	𝑓(𝑥𝑖+1𝑤𝑖	NOUN
easat-4161	120	33	)	)	PUNCT
easat-4161	121	1	=	=	PRON
easat-4161	121	2	{	{	PUNCT
easat-4161	121	3	2𝑠	2𝑠	NOUN
easat-4161	122	1	+	+	CCONJ
easat-4161	122	2	3𝑖+6	3𝑖+6	NUM
easat-4161	122	3	4	4	NUM
easat-4161	122	4	−	−	NOUN
easat-4161	122	5	1	1	NUM
easat-4161	122	6	,	,	PUNCT
easat-4161	122	7	𝑖	𝑖	PRON
easat-4161	122	8	≤	≤	NOUN
easat-4161	122	9	𝑠	𝑠	NUM
easat-4161	122	10	3𝑠	3𝑠	NUM
easat-4161	122	11	−	−	PROPN
easat-4161	122	12	1	1	NUM
easat-4161	122	13	,	,	PUNCT
easat-4161	122	14	𝑖	𝑖	PROPN
easat-4161	122	15	>	>	X
easat-4161	122	16	𝑠	𝑠	PROPN
easat-4161	122	17	,	,	PUNCT
easat-4161	122	18	𝑖	𝑖	PROPN
easat-4161	122	19	=	=	SYM
easat-4161	122	20	6	6	NUM
easat-4161	122	21	,	,	PUNCT
easat-4161	122	22	10	10	NUM
easat-4161	122	23	,	,	PUNCT
easat-4161	122	24	14	14	NUM
easat-4161	122	25	,	,	PUNCT
easat-4161	122	26	…	…	PUNCT
easat-4161	122	27	,	,	PUNCT
easat-4161	122	28	𝑛	𝑛	DET
easat-4161	122	29	−	−	PROPN
easat-4161	122	30	1	1	NUM
easat-4161	122	31	.	.	PUNCT
easat-4161	122	32	𝑓(𝑥1𝑤𝑛	𝑓(𝑥1𝑤𝑛	NOUN
easat-4161	122	33	)	)	PUNCT
easat-4161	123	1	=	=	SYM
easat-4161	123	2	𝑓(𝑥𝑛𝑤𝑛−1	𝑓(𝑥𝑛𝑤𝑛−1	PROPN
easat-4161	123	3	)	)	PUNCT
easat-4161	123	4	=	=	SYM
easat-4161	124	1	3𝑛+3	3𝑛+3	NOUN
easat-4161	124	2	4	4	NUM
easat-4161	124	3	−	−	NOUN
easat-4161	124	4	1	1	NUM
easat-4161	124	5	=	=	SYM
easat-4161	124	6	3𝑠	3𝑠	NUM
easat-4161	124	7	−	−	ADP
easat-4161	124	8	1	1	X
easat-4161	124	9	.	.	PUNCT
easat-4161	125	1	𝑓(𝑥𝑖𝑤𝑖−1	𝑓(𝑥𝑖𝑤𝑖−1	PROPN
easat-4161	125	2	)	)	PUNCT
easat-4161	125	3	=	=	PRON
easat-4161	125	4	{	{	PUNCT
easat-4161	125	5	2𝑠	2𝑠	NOUN
easat-4161	126	1	+	+	CCONJ
easat-4161	126	2	𝑖	𝑖	SYM
easat-4161	126	3	−	−	NOUN
easat-4161	126	4	2	2	NUM
easat-4161	126	5	,	,	PUNCT
easat-4161	126	6	𝑖	𝑖	PRON
easat-4161	126	7	≤	≤	NOUN
easat-4161	126	8	𝑠	𝑠	NUM
easat-4161	126	9	3𝑠	3𝑠	NUM
easat-4161	126	10	−	−	PROPN
easat-4161	126	11	1	1	NUM
easat-4161	126	12	,	,	PUNCT
easat-4161	126	13	𝑖	𝑖	PROPN
easat-4161	126	14	>	>	X
easat-4161	126	15	𝑠	𝑠	X
easat-4161	126	16	𝑓(𝑥1𝑣2	𝑓(𝑥1𝑣2	PROPN
easat-4161	126	17	)	)	PUNCT
easat-4161	126	18	=	=	SYM
easat-4161	126	19	𝑓(𝑥𝑖𝑣𝑖+1	𝑓(𝑥𝑖𝑣𝑖+1	PROPN
easat-4161	126	20	)	)	PUNCT
easat-4161	126	21	=	=	SYM
easat-4161	126	22	𝑓(𝑥𝑛−1𝑣𝑛	𝑓(𝑥𝑛−1𝑣𝑛	NOUN
easat-4161	126	23	)	)	PUNCT
easat-4161	127	1	=	=	SYM
easat-4161	127	2	𝑓(𝑥𝑛𝑣1	𝑓(𝑥𝑛𝑣1	NOUN
easat-4161	127	3	)	)	PUNCT
easat-4161	127	4	=	=	SYM
easat-4161	127	5	3𝑠.	3𝑠.	NUM
easat-4161	127	6	𝑓(𝑦𝑖𝑤𝑖	𝑓(𝑦𝑖𝑤𝑖	NOUN
easat-4161	127	7	)	)	PUNCT
easat-4161	127	8	=	=	SYM
easat-4161	127	9	1	1	NUM
easat-4161	127	10	,	,	PUNCT
easat-4161	127	11	𝑖	𝑖	NOUN
easat-4161	127	12	=	=	SYM
easat-4161	127	13	1	1	NUM
easat-4161	127	14	,	,	PUNCT
easat-4161	127	15	2	2	NUM
easat-4161	127	16	,	,	PUNCT
easat-4161	127	17	…	…	PUNCT
easat-4161	127	18	,	,	PUNCT
easat-4161	127	19	𝑛.	𝑛.	NOUN
easat-4161	127	20	𝑓(𝑦1𝑣1	𝑓(𝑦1𝑣1	NOUN
easat-4161	127	21	)	)	PUNCT
easat-4161	127	22	=	=	SYM
easat-4161	127	23	1	1	X
easat-4161	127	24	.	.	X
easat-4161	127	25	𝑓(𝑦2𝑣2	𝑓(𝑦2𝑣2	NOUN
easat-4161	127	26	)	)	PUNCT
easat-4161	127	27	=	=	SYM
easat-4161	128	1	2	2	NUM
easat-4161	128	2	.	.	X
easat-4161	128	3	485	485	NUM
easat-4161	128	4	edelweiss	edelweiss	PROPN
easat-4161	128	5	applied	apply	VERB
easat-4161	128	6	science	science	NOUN
easat-4161	128	7	and	and	CCONJ
easat-4161	128	8	technology	technology	NOUN
easat-4161	128	9	issn	issn	PROPN
easat-4161	128	10	:	:	PUNCT
easat-4161	128	11	2576	2576	NUM
easat-4161	128	12	-	-	SYM
easat-4161	128	13	8484	8484	NUM
easat-4161	128	14	vol	vol	NOUN
easat-4161	128	15	.	.	PROPN
easat-4161	129	1	9	9	NUM
easat-4161	129	2	,	,	PUNCT
easat-4161	129	3	no	no	INTJ
easat-4161	129	4	.	.	NOUN
easat-4161	129	5	1	1	NUM
easat-4161	129	6	:	:	PUNCT
easat-4161	129	7	481	481	NUM
easat-4161	129	8	-	-	SYM
easat-4161	129	9	492	492	NUM
easat-4161	129	10	,	,	PUNCT
easat-4161	129	11	2025	2025	NUM
easat-4161	129	12	doi	doi	NOUN
easat-4161	129	13	:	:	PUNCT
easat-4161	129	14	10.55214/25768484.v9i1.4161	10.55214/25768484.v9i1.4161	NUM
easat-4161	129	15	©	©	PROPN
easat-4161	129	16	2025	2025	NUM
easat-4161	129	17	by	by	ADP
easat-4161	129	18	the	the	DET
easat-4161	129	19	authors	author	NOUN
easat-4161	129	20	;	;	PUNCT
easat-4161	129	21	licensee	licensee	PROPN
easat-4161	129	22	learning	learn	VERB
easat-4161	129	23	gate	gate	PROPN
easat-4161	129	24	𝑓(𝑦𝑖𝑣𝑖	𝑓(𝑦𝑖𝑣𝑖	PROPN
easat-4161	129	25	)	)	PUNCT
easat-4161	130	1	=	=	PRON
easat-4161	130	2	{	{	PUNCT
easat-4161	130	3	3𝑖+3	3𝑖+3	PROPN
easat-4161	130	4	4	4	NUM
easat-4161	130	5	,	,	PUNCT
easat-4161	130	6	𝑖	𝑖	PROPN
easat-4161	130	7	=	=	SYM
easat-4161	130	8	3	3	NUM
easat-4161	130	9	,	,	PUNCT
easat-4161	130	10	7	7	NUM
easat-4161	130	11	,	,	PUNCT
easat-4161	130	12	11	11	NUM
easat-4161	130	13	,	,	PUNCT
easat-4161	130	14	…	…	PUNCT
easat-4161	130	15	,	,	PUNCT
easat-4161	130	16	𝑛	𝑛	DET
easat-4161	130	17	−	−	PROPN
easat-4161	130	18	4	4	NUM
easat-4161	130	19	,	,	PUNCT
easat-4161	130	20	3𝑖+4	3𝑖+4	NUM
easat-4161	130	21	4	4	NUM
easat-4161	130	22	,	,	PUNCT
easat-4161	130	23	𝑖	𝑖	NOUN
easat-4161	130	24	=	=	SYM
easat-4161	130	25	4	4	NUM
easat-4161	130	26	,	,	PUNCT
easat-4161	130	27	8	8	NUM
easat-4161	130	28	,	,	PUNCT
easat-4161	130	29	12	12	NUM
easat-4161	130	30	,	,	PUNCT
easat-4161	130	31	…	…	PUNCT
easat-4161	130	32	,	,	PUNCT
easat-4161	130	33	𝑛	𝑛	DET
easat-4161	130	34	−	−	PROPN
easat-4161	130	35	3	3	NUM
easat-4161	130	36	,	,	PUNCT
easat-4161	130	37	3𝑖+5	3𝑖+5	PROPN
easat-4161	130	38	4	4	NUM
easat-4161	130	39	,	,	PUNCT
easat-4161	130	40	𝑖	𝑖	NOUN
easat-4161	130	41	=	=	SYM
easat-4161	130	42	5	5	NUM
easat-4161	130	43	,	,	PUNCT
easat-4161	130	44	9	9	NUM
easat-4161	130	45	,	,	PUNCT
easat-4161	130	46	13	13	NUM
easat-4161	130	47	,	,	PUNCT
easat-4161	130	48	…	…	PUNCT
easat-4161	130	49	,	,	PUNCT
easat-4161	130	50	𝑛	𝑛	DET
easat-4161	130	51	−	−	PROPN
easat-4161	130	52	2	2	NUM
easat-4161	130	53	,	,	PUNCT
easat-4161	130	54	3𝑖+6	3𝑖+6	NOUN
easat-4161	130	55	4	4	NUM
easat-4161	130	56	,	,	PUNCT
easat-4161	130	57	𝑖	𝑖	NOUN
easat-4161	130	58	=	=	SYM
easat-4161	130	59	6	6	NUM
easat-4161	130	60	,	,	PUNCT
easat-4161	130	61	10	10	NUM
easat-4161	130	62	,	,	PUNCT
easat-4161	130	63	14	14	NUM
easat-4161	130	64	,	,	PUNCT
easat-4161	130	65	…	…	PUNCT
easat-4161	130	66	,	,	PUNCT
easat-4161	130	67	𝑛	𝑛	DET
easat-4161	130	68	−	−	PROPN
easat-4161	130	69	1	1	NUM
easat-4161	130	70	,	,	PUNCT
easat-4161	130	71	𝑓(𝑦𝑛𝑣𝑛	𝑓(𝑦𝑛𝑣𝑛	X
easat-4161	130	72	)	)	PUNCT
easat-4161	130	73	=	=	PUNCT
easat-4161	131	1	3𝑛+3	3𝑛+3	NOUN
easat-4161	131	2	4	4	NUM
easat-4161	131	3	.	.	PUNCT
easat-4161	132	1	𝑓(𝑤1𝑣1	𝑓(𝑤1𝑣1	NOUN
easat-4161	132	2	)	)	PUNCT
easat-4161	132	3	=	=	SYM
easat-4161	132	4	𝑓(𝑤2𝑣2	𝑓(𝑤2𝑣2	NOUN
easat-4161	132	5	)	)	PUNCT
easat-4161	132	6	=	=	NOUN
easat-4161	132	7	2𝑠	2𝑠	NOUN
easat-4161	132	8	+	+	CCONJ
easat-4161	132	9	1	1	X
easat-4161	132	10	.	.	NUM
easat-4161	132	11	𝑓(𝑤𝑖𝑣𝑖	𝑓(𝑤𝑖𝑣𝑖	NOUN
easat-4161	132	12	)	)	PUNCT
easat-4161	133	1	=	=	PRON
easat-4161	133	2	{	{	PUNCT
easat-4161	133	3	𝑖+1	𝑖+1	PUNCT
easat-4161	133	4	4	4	NUM
easat-4161	133	5	+	+	CCONJ
easat-4161	133	6	2𝑠	2𝑠	NOUN
easat-4161	133	7	,	,	PUNCT
easat-4161	133	8	𝑖	𝑖	NOUN
easat-4161	133	9	=	=	SYM
easat-4161	133	10	3	3	NUM
easat-4161	133	11	,	,	PUNCT
easat-4161	133	12	7	7	NUM
easat-4161	133	13	,	,	PUNCT
easat-4161	133	14	11	11	NUM
easat-4161	133	15	,	,	PUNCT
easat-4161	133	16	…	…	PUNCT
easat-4161	133	17	,	,	PUNCT
easat-4161	133	18	𝑛	𝑛	DET
easat-4161	133	19	−	−	PROPN
easat-4161	133	20	4	4	NUM
easat-4161	133	21	,	,	PUNCT
easat-4161	133	22	𝑖	𝑖	PRON
easat-4161	133	23	4	4	NUM
easat-4161	133	24	+	+	CCONJ
easat-4161	133	25	2𝑠	2𝑠	NOUN
easat-4161	133	26	,	,	PUNCT
easat-4161	133	27	𝑖	𝑖	NOUN
easat-4161	133	28	=	=	SYM
easat-4161	133	29	4	4	NUM
easat-4161	133	30	,	,	PUNCT
easat-4161	133	31	8	8	NUM
easat-4161	133	32	,	,	PUNCT
easat-4161	133	33	12	12	NUM
easat-4161	133	34	,	,	PUNCT
easat-4161	133	35	…	…	PUNCT
easat-4161	133	36	,	,	PUNCT
easat-4161	133	37	𝑛	𝑛	DET
easat-4161	133	38	−	−	NOUN
easat-4161	133	39	3	3	NUM
easat-4161	133	40	,	,	PUNCT
easat-4161	133	41	𝑖−1	𝑖−1	PROPN
easat-4161	133	42	4	4	NUM
easat-4161	133	43	+	+	NOUN
easat-4161	133	44	2𝑠	2𝑠	NOUN
easat-4161	133	45	,	,	PUNCT
easat-4161	133	46	𝑖	𝑖	X
easat-4161	133	47	=	=	SYM
easat-4161	133	48	5	5	NUM
easat-4161	133	49	,	,	PUNCT
easat-4161	133	50	9	9	NUM
easat-4161	133	51	,	,	PUNCT
easat-4161	133	52	13	13	NUM
easat-4161	133	53	,	,	PUNCT
easat-4161	133	54	…	…	PUNCT
easat-4161	133	55	,	,	PUNCT
easat-4161	133	56	𝑛	𝑛	DET
easat-4161	133	57	−	−	PROPN
easat-4161	133	58	2	2	NUM
easat-4161	133	59	,	,	PUNCT
easat-4161	133	60	𝑖−2	𝑖−2	PROPN
easat-4161	133	61	4	4	NUM
easat-4161	133	62	+	+	NOUN
easat-4161	133	63	2𝑠	2𝑠	NOUN
easat-4161	133	64	,	,	PUNCT
easat-4161	133	65	𝑖	𝑖	NOUN
easat-4161	133	66	=	=	SYM
easat-4161	133	67	6	6	NUM
easat-4161	133	68	,	,	PUNCT
easat-4161	133	69	10	10	NUM
easat-4161	133	70	,	,	PUNCT
easat-4161	133	71	14	14	NUM
easat-4161	133	72	,	,	PUNCT
easat-4161	133	73	…	…	PUNCT
easat-4161	133	74	,	,	PUNCT
easat-4161	133	75	𝑛	𝑛	DET
easat-4161	133	76	−	−	PROPN
easat-4161	133	77	1	1	NUM
easat-4161	133	78	,	,	PUNCT
easat-4161	133	79	𝑓(𝑤𝑛𝑣𝑛	𝑓(𝑤𝑛𝑣𝑛	NOUN
easat-4161	133	80	)	)	PUNCT
easat-4161	133	81	=	=	SYM
easat-4161	134	1	𝑛	𝑛	PROPN
easat-4161	134	2	+	+	NOUN
easat-4161	134	3	1	1	NUM
easat-4161	134	4	4	4	NUM
easat-4161	134	5	+	+	SYM
easat-4161	134	6	2𝑠.	2𝑠.	NUM
easat-4161	134	7	based	base	VERB
easat-4161	134	8	on	on	ADP
easat-4161	134	9	this	this	DET
easat-4161	134	10	function	function	NOUN
easat-4161	134	11	,	,	PUNCT
easat-4161	134	12	it	it	PRON
easat-4161	134	13	can	can	AUX
easat-4161	134	14	be	be	AUX
easat-4161	134	15	shown	show	VERB
easat-4161	134	16	that	that	SCONJ
easat-4161	134	17	all	all	DET
easat-4161	134	18	vertices	vertice	VERB
easat-4161	134	19	weights	weight	NOUN
easat-4161	134	20	are	be	AUX
easat-4161	134	21	different	different	ADJ
easat-4161	134	22	and	and	CCONJ
easat-4161	134	23	the	the	DET
easat-4161	134	24	maximum	maximum	ADJ
easat-4161	134	25	value	value	NOUN
easat-4161	134	26	of	of	ADP
easat-4161	134	27	the	the	DET
easat-4161	134	28	function	function	NOUN
easat-4161	134	29	is	be	AUX
easat-4161	134	30	⌈	⌈	SYM
easat-4161	134	31	𝟑+𝟑𝒏	𝟑+𝟑𝒏	NOUN
easat-4161	134	32	𝟒	𝟒	X
easat-4161	134	33	⌉.	⌉.	ADV
easat-4161	134	34	this	this	PRON
easat-4161	134	35	shows	show	VERB
easat-4161	134	36	that	that	SCONJ
easat-4161	134	37	𝑓	𝑓	X
easat-4161	134	38	:	:	PUNCT
easat-4161	134	39	𝑉	𝑉	PROPN
easat-4161	134	40	∪	∪	NOUN
easat-4161	134	41	𝐸	𝐸	PROPN
easat-4161	134	42	→	→	SYM
easat-4161	134	43	{	{	PUNCT
easat-4161	134	44	1	1	NUM
easat-4161	134	45	,	,	PUNCT
easat-4161	134	46	2	2	NUM
easat-4161	134	47	,	,	PUNCT
easat-4161	134	48	3,⋯	3,⋯	NUM
easat-4161	134	49	,	,	PUNCT
easat-4161	134	50	⌈	⌈	X
easat-4161	134	51	𝟑+𝟑𝒏	𝟑+𝟑𝒏	X
easat-4161	134	52	𝟒	𝟒	NUM
easat-4161	134	53	⌉	⌉	NOUN
easat-4161	134	54	}	}	PUNCT
easat-4161	134	55	is	be	AUX
easat-4161	134	56	a	a	DET
easat-4161	134	57	function	function	NOUN
easat-4161	134	58	a	a	DET
easat-4161	134	59	total	total	ADJ
easat-4161	134	60	vertex	vertex	NOUN
easat-4161	134	61	irregular	irregular	ADJ
easat-4161	134	62	𝑘	𝑘	DET
easat-4161	134	63	−	−	NOUN
easat-4161	134	64	𝑙𝑎𝑏𝑒𝑙𝑙𝑖𝑛𝑔	𝑙𝑎𝑏𝑒𝑙𝑙𝑖𝑛𝑔	NOUN
easat-4161	134	65	where	where	SCONJ
easat-4161	134	66	𝑘	𝑘	NOUN
easat-4161	134	67	=	=	PUNCT
easat-4161	134	68	⌈	⌈	NOUN
easat-4161	134	69	𝟑+𝟑𝒏	𝟑+𝟑𝒏	NOUN
easat-4161	134	70	𝟒	𝟒	X
easat-4161	134	71	⌉.	⌉.	ADV
easat-4161	134	72	thus	thus	ADV
easat-4161	134	73	it	it	PRON
easat-4161	134	74	is	be	AUX
easat-4161	134	75	obtained	obtain	VERB
easat-4161	134	76	that	that	SCONJ
easat-4161	134	77	𝒕𝒗𝒔(𝓗𝒏	𝒕𝒗𝒔(𝓗𝒏	NOUN
easat-4161	134	78	)	)	PUNCT
easat-4161	134	79	≤	≤	NOUN
easat-4161	135	1	⌈	⌈	SYM
easat-4161	135	2	𝟑+𝟑𝒏	𝟑+𝟑𝒏	NOUN
easat-4161	135	3	𝟒	𝟒	NUM
easat-4161	135	4	⌉	⌉	X
easat-4161	135	5	for	for	ADP
easat-4161	135	6	𝑛	𝑛	PRON
easat-4161	135	7	=	=	NOUN
easat-4161	135	8	4𝑡	4𝑡	NUM
easat-4161	135	9	−	−	PROPN
easat-4161	135	10	1	1	NUM
easat-4161	135	11	,	,	PUNCT
easat-4161	135	12	where	where	SCONJ
easat-4161	135	13	𝑡	𝑡	PROPN
easat-4161	135	14	is	be	AUX
easat-4161	135	15	some	some	DET
easat-4161	135	16	positive	positive	ADJ
easat-4161	135	17	integer	integer	NOUN
easat-4161	135	18	.	.	PUNCT
easat-4161	136	1	case	case	NOUN
easat-4161	136	2	2	2	NUM
easat-4161	136	3	.	.	X
easat-4161	137	1	for	for	ADP
easat-4161	137	2	𝑛	𝑛	NOUN
easat-4161	137	3	=	=	SYM
easat-4161	137	4	4𝑡	4𝑡	NOUN
easat-4161	137	5	,	,	PUNCT
easat-4161	137	6	where	where	SCONJ
easat-4161	137	7	𝑡	𝑡	PROPN
easat-4161	137	8	is	be	AUX
easat-4161	137	9	some	some	DET
easat-4161	137	10	positive	positive	ADJ
easat-4161	137	11	integer	integer	NOUN
easat-4161	137	12	.	.	PUNCT
easat-4161	138	1	the	the	DET
easat-4161	138	2	total	total	ADJ
easat-4161	138	3	vertex	vertex	NOUN
easat-4161	138	4	labeling	labeling	NOUN
easat-4161	138	5	𝑔	𝑔	PROPN
easat-4161	138	6	is	be	AUX
easat-4161	138	7	𝑔(𝑥1	𝑔(𝑥1	ADJ
easat-4161	138	8	)	)	PUNCT
easat-4161	139	1	=	=	SYM
easat-4161	139	2	1	1	X
easat-4161	139	3	.	.	X
easat-4161	139	4	𝑔(𝑥2	𝑔(𝑥2	NOUN
easat-4161	139	5	)	)	PUNCT
easat-4161	140	1	=	=	SYM
easat-4161	140	2	𝑠	𝑠	PROPN
easat-4161	140	3	+	+	NOUN
easat-4161	140	4	1	1	X
easat-4161	140	5	.	.	X
easat-4161	140	6	𝑔(𝑥𝑖	𝑔(𝑥𝑖	NUM
easat-4161	140	7	)	)	PUNCT
easat-4161	140	8	=	=	PRON
easat-4161	140	9	{	{	PUNCT
easat-4161	140	10	3𝑖+3	3𝑖+3	PROPN
easat-4161	140	11	4	4	NUM
easat-4161	141	1	+	+	CCONJ
easat-4161	141	2	𝑠	𝑠	PROPN
easat-4161	141	3	−	−	NOUN
easat-4161	141	4	𝑖	𝑖	PROPN
easat-4161	142	1	+	+	NOUN
easat-4161	142	2	1	1	NUM
easat-4161	142	3	,	,	PUNCT
easat-4161	142	4	𝑖	𝑖	PRON
easat-4161	142	5	≤	≤	NOUN
easat-4161	142	6	𝑠	𝑠	X
easat-4161	142	7	3𝑖+3	3𝑖+3	PROPN
easat-4161	142	8	4	4	NUM
easat-4161	142	9	,	,	PUNCT
easat-4161	143	1	𝑖	𝑖	PROPN
easat-4161	143	2	>	>	X
easat-4161	143	3	𝑠	𝑠	PROPN
easat-4161	143	4	,	,	PUNCT
easat-4161	143	5	𝑖	𝑖	PROPN
easat-4161	143	6	=	=	SYM
easat-4161	143	7	3	3	NUM
easat-4161	143	8	,	,	PUNCT
easat-4161	143	9	7	7	NUM
easat-4161	143	10	,	,	PUNCT
easat-4161	143	11	11	11	NUM
easat-4161	143	12	,	,	PUNCT
easat-4161	143	13	…	…	PUNCT
easat-4161	143	14	,	,	PUNCT
easat-4161	143	15	𝑛	𝑛	DET
easat-4161	143	16	−	−	PROPN
easat-4161	143	17	1	1	NUM
easat-4161	143	18	.	.	PUNCT
easat-4161	143	19	𝑔(𝑥𝑖	𝑔(𝑥𝑖	NUM
easat-4161	143	20	)	)	PUNCT
easat-4161	143	21	=	=	PRON
easat-4161	143	22	{	{	PUNCT
easat-4161	143	23	3𝑖+4	3𝑖+4	NUM
easat-4161	143	24	4	4	NUM
easat-4161	144	1	+	+	CCONJ
easat-4161	144	2	𝑠	𝑠	PROPN
easat-4161	144	3	−	−	NOUN
easat-4161	144	4	𝑖	𝑖	PROPN
easat-4161	145	1	+	+	NOUN
easat-4161	145	2	1	1	NUM
easat-4161	145	3	,	,	PUNCT
easat-4161	145	4	𝑖	𝑖	PRON
easat-4161	145	5	≤	≤	NUM
easat-4161	145	6	𝑠	𝑠	X
easat-4161	145	7	3𝑖+4	3𝑖+4	PROPN
easat-4161	145	8	4	4	NUM
easat-4161	145	9	,	,	PUNCT
easat-4161	146	1	𝑖	𝑖	PROPN
easat-4161	146	2	>	>	X
easat-4161	146	3	𝑠	𝑠	PROPN
easat-4161	146	4	,	,	PUNCT
easat-4161	146	5	𝑖	𝑖	X
easat-4161	146	6	=	=	NOUN
easat-4161	146	7	4	4	NUM
easat-4161	146	8	,	,	PUNCT
easat-4161	146	9	8	8	NUM
easat-4161	146	10	,	,	PUNCT
easat-4161	146	11	12	12	NUM
easat-4161	146	12	,	,	PUNCT
easat-4161	146	13	…	…	PUNCT
easat-4161	146	14	,	,	PUNCT
easat-4161	146	15	𝑛	𝑛	DET
easat-4161	146	16	−	−	PROPN
easat-4161	146	17	4	4	NUM
easat-4161	146	18	.	.	PUNCT
easat-4161	146	19	𝑔(𝑥𝑖	𝑔(𝑥𝑖	NUM
easat-4161	146	20	)	)	PUNCT
easat-4161	146	21	=	=	PRON
easat-4161	146	22	{	{	PUNCT
easat-4161	146	23	3𝑖+5	3𝑖+5	PROPN
easat-4161	146	24	4	4	NUM
easat-4161	147	1	+	+	NUM
easat-4161	147	2	𝑠	𝑠	PROPN
easat-4161	147	3	−	−	NOUN
easat-4161	147	4	𝑖	𝑖	PROPN
easat-4161	148	1	+	+	NOUN
easat-4161	148	2	1	1	NUM
easat-4161	148	3	,	,	PUNCT
easat-4161	148	4	𝑖	𝑖	PRON
easat-4161	148	5	≤	≤	NOUN
easat-4161	148	6	𝑠	𝑠	X
easat-4161	148	7	3𝑖+5	3𝑖+5	PROPN
easat-4161	148	8	4	4	NUM
easat-4161	148	9	,	,	PUNCT
easat-4161	148	10	𝑖	𝑖	PROPN
easat-4161	148	11	>	>	X
easat-4161	148	12	𝑠	𝑠	PROPN
easat-4161	148	13	,	,	PUNCT
easat-4161	148	14	𝑖	𝑖	PROPN
easat-4161	148	15	=	=	SYM
easat-4161	148	16	5	5	NUM
easat-4161	148	17	,	,	PUNCT
easat-4161	148	18	9	9	NUM
easat-4161	148	19	,	,	PUNCT
easat-4161	148	20	13	13	NUM
easat-4161	148	21	,	,	PUNCT
easat-4161	148	22	…	…	PUNCT
easat-4161	148	23	,	,	PUNCT
easat-4161	148	24	𝑛	𝑛	DET
easat-4161	148	25	−	−	PROPN
easat-4161	148	26	3	3	NUM
easat-4161	148	27	.	.	PUNCT
easat-4161	148	28	𝑔(𝑥𝑖	𝑔(𝑥𝑖	PROPN
easat-4161	148	29	)	)	PUNCT
easat-4161	148	30	=	=	PRON
easat-4161	148	31	{	{	PUNCT
easat-4161	148	32	3𝑖+6	3𝑖+6	PROPN
easat-4161	148	33	4	4	NUM
easat-4161	149	1	+	+	CCONJ
easat-4161	149	2	𝑠	𝑠	PROPN
easat-4161	149	3	−	−	NOUN
easat-4161	149	4	𝑖	𝑖	PROPN
easat-4161	150	1	+	+	NOUN
easat-4161	150	2	1	1	NUM
easat-4161	150	3	,	,	PUNCT
easat-4161	150	4	𝑖	𝑖	DET
easat-4161	150	5	≤	≤	NUM
easat-4161	150	6	𝑠	𝑠	X
easat-4161	151	1	3𝑖+6	3𝑖+6	PROPN
easat-4161	151	2	4	4	NUM
easat-4161	151	3	,	,	PUNCT
easat-4161	151	4	𝑖	𝑖	PROPN
easat-4161	151	5	>	>	X
easat-4161	151	6	𝑠	𝑠	PROPN
easat-4161	151	7	,	,	PUNCT
easat-4161	151	8	𝑖	𝑖	PROPN
easat-4161	151	9	=	=	SYM
easat-4161	151	10	6	6	NUM
easat-4161	151	11	,	,	PUNCT
easat-4161	151	12	10	10	NUM
easat-4161	151	13	,	,	PUNCT
easat-4161	151	14	14	14	NUM
easat-4161	151	15	,	,	PUNCT
easat-4161	151	16	…	…	PUNCT
easat-4161	151	17	,	,	PUNCT
easat-4161	151	18	𝑛	𝑛	DET
easat-4161	151	19	−	−	PROPN
easat-4161	151	20	2	2	NUM
easat-4161	151	21	.	.	PUNCT
easat-4161	152	1	𝑔(𝑥𝑛	𝑔(𝑥𝑛	NUM
easat-4161	152	2	)	)	PUNCT
easat-4161	152	3	=	=	SYM
easat-4161	152	4	3𝑛+4	3𝑛+4	PROPN
easat-4161	152	5	4	4	NUM
easat-4161	152	6	.	.	PUNCT
easat-4161	153	1	𝑔(𝑦𝑖	𝑔(𝑦𝑖	ADV
easat-4161	153	2	)	)	PUNCT
easat-4161	154	1	=	=	SYM
easat-4161	154	2	1	1	X
easat-4161	154	3	,	,	PUNCT
easat-4161	154	4	𝑖	𝑖	NOUN
easat-4161	154	5	=	=	SYM
easat-4161	154	6	1	1	NUM
easat-4161	154	7	,	,	PUNCT
easat-4161	154	8	2	2	NUM
easat-4161	154	9	,	,	PUNCT
easat-4161	154	10	…	…	PUNCT
easat-4161	154	11	,	,	PUNCT
easat-4161	154	12	𝑛.	𝑛.	NOUN
easat-4161	154	13	𝑔(𝑤1	𝑔(𝑤1	NOUN
easat-4161	154	14	)	)	PUNCT
easat-4161	154	15	=	=	SYM
easat-4161	155	1	1	1	X
easat-4161	155	2	.	.	X
easat-4161	155	3	𝑔(𝑤2	𝑔(𝑤2	NOUN
easat-4161	155	4	)	)	PUNCT
easat-4161	156	1	=	=	PRON
easat-4161	156	2	{	{	PUNCT
easat-4161	156	3	2	2	NUM
easat-4161	156	4	,	,	PUNCT
easat-4161	156	5	𝑠	𝑠	PROPN
easat-4161	156	6	=	=	SYM
easat-4161	156	7	1	1	NUM
easat-4161	156	8	1	1	NUM
easat-4161	156	9	,	,	PUNCT
easat-4161	156	10	𝑠	𝑠	PROPN
easat-4161	156	11	=	=	SYM
easat-4161	156	12	2	2	NUM
easat-4161	156	13	,	,	PUNCT
easat-4161	156	14	3	3	NUM
easat-4161	156	15	,	,	PUNCT
easat-4161	156	16	…	…	PUNCT
easat-4161	156	17	486	486	NUM
easat-4161	156	18	edelweiss	edelweiss	PROPN
easat-4161	156	19	applied	apply	VERB
easat-4161	156	20	science	science	NOUN
easat-4161	156	21	and	and	CCONJ
easat-4161	156	22	technology	technology	NOUN
easat-4161	156	23	issn	issn	PROPN
easat-4161	156	24	:	:	PUNCT
easat-4161	156	25	2576	2576	NUM
easat-4161	156	26	-	-	SYM
easat-4161	156	27	8484	8484	NUM
easat-4161	156	28	vol	vol	NOUN
easat-4161	156	29	.	.	PROPN
easat-4161	157	1	9	9	NUM
easat-4161	157	2	,	,	PUNCT
easat-4161	157	3	no	no	INTJ
easat-4161	157	4	.	.	NOUN
easat-4161	157	5	1	1	NUM
easat-4161	157	6	:	:	PUNCT
easat-4161	157	7	481	481	NUM
easat-4161	157	8	-	-	SYM
easat-4161	157	9	492	492	NUM
easat-4161	157	10	,	,	PUNCT
easat-4161	157	11	2025	2025	NUM
easat-4161	157	12	doi	doi	NOUN
easat-4161	157	13	:	:	PUNCT
easat-4161	157	14	10.55214/25768484.v9i1.4161	10.55214/25768484.v9i1.4161	NUM
easat-4161	157	15	©	©	PROPN
easat-4161	157	16	2025	2025	NUM
easat-4161	157	17	by	by	ADP
easat-4161	157	18	the	the	DET
easat-4161	157	19	authors	author	NOUN
easat-4161	157	20	;	;	PUNCT
easat-4161	158	1	licensee	licensee	PROPN
easat-4161	158	2	learning	learning	NOUN
easat-4161	158	3	gate	gate	NOUN
easat-4161	158	4	𝑔(𝑤𝑖	𝑔(𝑤𝑖	PROPN
easat-4161	158	5	)	)	PUNCT
easat-4161	158	6	=	=	PRON
easat-4161	158	7	{	{	PUNCT
easat-4161	158	8	1	1	NUM
easat-4161	158	9	,	,	PUNCT
easat-4161	158	10	𝑖	𝑖	PROPN
easat-4161	158	11	≤	≤	NOUN
easat-4161	158	12	𝑠	𝑠	X
easat-4161	158	13	3𝑖+3	3𝑖+3	PROPN
easat-4161	158	14	4	4	NUM
easat-4161	158	15	−	−	NOUN
easat-4161	158	16	𝑠	𝑠	PROPN
easat-4161	158	17	+	+	NOUN
easat-4161	158	18	1	1	NUM
easat-4161	158	19	,	,	PUNCT
easat-4161	158	20	𝑖	𝑖	PROPN
easat-4161	158	21	>	>	X
easat-4161	158	22	𝑠	𝑠	PROPN
easat-4161	158	23	,	,	PUNCT
easat-4161	158	24	𝑖	𝑖	PROPN
easat-4161	158	25	=	=	SYM
easat-4161	158	26	3	3	NUM
easat-4161	158	27	,	,	PUNCT
easat-4161	158	28	7	7	NUM
easat-4161	158	29	,	,	PUNCT
easat-4161	158	30	11	11	NUM
easat-4161	158	31	,	,	PUNCT
easat-4161	158	32	…	…	PUNCT
easat-4161	158	33	,	,	PUNCT
easat-4161	158	34	𝑛	𝑛	PRON
easat-4161	158	35	−	−	PROPN
easat-4161	158	36	1	1	NUM
easat-4161	158	37	.	.	PUNCT
easat-4161	158	38	𝑔(𝑤𝑖	𝑔(𝑤𝑖	PROPN
easat-4161	158	39	)	)	PUNCT
easat-4161	158	40	=	=	PRON
easat-4161	158	41	{	{	PUNCT
easat-4161	158	42	1	1	NUM
easat-4161	158	43	,	,	PUNCT
easat-4161	158	44	𝑖	𝑖	DET
easat-4161	158	45	≤	≤	NUM
easat-4161	159	1	𝑠	𝑠	X
easat-4161	159	2	3𝑖+4	3𝑖+4	PROPN
easat-4161	159	3	4	4	NUM
easat-4161	159	4	−	−	NOUN
easat-4161	159	5	𝑠	𝑠	PROPN
easat-4161	159	6	+	+	NOUN
easat-4161	159	7	1	1	NUM
easat-4161	159	8	,	,	PUNCT
easat-4161	159	9	𝑖	𝑖	PROPN
easat-4161	159	10	>	>	X
easat-4161	159	11	𝑠	𝑠	PROPN
easat-4161	159	12	,	,	PUNCT
easat-4161	159	13	𝑖	𝑖	X
easat-4161	159	14	=	=	NOUN
easat-4161	159	15	4	4	NUM
easat-4161	159	16	,	,	PUNCT
easat-4161	159	17	8	8	NUM
easat-4161	159	18	,	,	PUNCT
easat-4161	159	19	12	12	NUM
easat-4161	159	20	,	,	PUNCT
easat-4161	159	21	…	…	PUNCT
easat-4161	159	22	,	,	PUNCT
easat-4161	159	23	𝑛	𝑛	DET
easat-4161	159	24	−	−	PROPN
easat-4161	159	25	4	4	NUM
easat-4161	159	26	.	.	PUNCT
easat-4161	159	27	𝑔(𝑤𝑖	𝑔(𝑤𝑖	PROPN
easat-4161	159	28	)	)	PUNCT
easat-4161	159	29	=	=	PRON
easat-4161	159	30	{	{	PUNCT
easat-4161	159	31	1	1	NUM
easat-4161	159	32	,	,	PUNCT
easat-4161	159	33	𝑖	𝑖	PRON
easat-4161	159	34	≤	≤	NOUN
easat-4161	159	35	𝑠	𝑠	X
easat-4161	160	1	3𝑖+5	3𝑖+5	PROPN
easat-4161	160	2	4	4	NUM
easat-4161	160	3	−	−	NOUN
easat-4161	160	4	𝑠	𝑠	PROPN
easat-4161	160	5	+	+	NOUN
easat-4161	160	6	1	1	NUM
easat-4161	160	7	,	,	PUNCT
easat-4161	160	8	𝑖	𝑖	PROPN
easat-4161	160	9	>	>	X
easat-4161	160	10	𝑠	𝑠	PROPN
easat-4161	160	11	,	,	PUNCT
easat-4161	160	12	𝑖	𝑖	PROPN
easat-4161	160	13	=	=	SYM
easat-4161	160	14	5	5	NUM
easat-4161	160	15	,	,	PUNCT
easat-4161	160	16	9	9	NUM
easat-4161	160	17	,	,	PUNCT
easat-4161	160	18	13	13	NUM
easat-4161	160	19	,	,	PUNCT
easat-4161	160	20	…	…	PUNCT
easat-4161	160	21	,	,	PUNCT
easat-4161	160	22	𝑛	𝑛	DET
easat-4161	160	23	−	−	NOUN
easat-4161	160	24	3	3	NUM
easat-4161	160	25	.	.	PUNCT
easat-4161	160	26	𝑔(𝑤𝑖	𝑔(𝑤𝑖	PROPN
easat-4161	160	27	)	)	PUNCT
easat-4161	160	28	=	=	PRON
easat-4161	160	29	{	{	PUNCT
easat-4161	160	30	1	1	NUM
easat-4161	160	31	,	,	PUNCT
easat-4161	160	32	𝑖	𝑖	PROPN
easat-4161	160	33	≤	≤	NUM
easat-4161	160	34	𝑠	𝑠	X
easat-4161	160	35	3𝑖+6	3𝑖+6	PROPN
easat-4161	160	36	4	4	NUM
easat-4161	160	37	−	−	NOUN
easat-4161	160	38	𝑠	𝑠	PROPN
easat-4161	160	39	+	+	NOUN
easat-4161	160	40	1	1	NUM
easat-4161	160	41	,	,	PUNCT
easat-4161	160	42	𝑖	𝑖	PROPN
easat-4161	160	43	>	>	X
easat-4161	160	44	𝑠	𝑠	PROPN
easat-4161	160	45	,	,	PUNCT
easat-4161	160	46	𝑖	𝑖	PROPN
easat-4161	160	47	=	=	SYM
easat-4161	160	48	6	6	NUM
easat-4161	160	49	,	,	PUNCT
easat-4161	160	50	10	10	NUM
easat-4161	160	51	,	,	PUNCT
easat-4161	160	52	14	14	NUM
easat-4161	160	53	,	,	PUNCT
easat-4161	160	54	…	…	PUNCT
easat-4161	160	55	,	,	PUNCT
easat-4161	160	56	𝑛	𝑛	DET
easat-4161	160	57	−	−	PROPN
easat-4161	160	58	2	2	NUM
easat-4161	160	59	.	.	NUM
easat-4161	160	60	𝑔(𝑤𝑛	𝑔(𝑤𝑛	PROPN
easat-4161	160	61	)	)	PUNCT
easat-4161	160	62	=	=	SYM
easat-4161	160	63	2𝑠	2𝑠	NOUN
easat-4161	160	64	+	+	CCONJ
easat-4161	160	65	2	2	X
easat-4161	160	66	.	.	NUM
easat-4161	160	67	𝑔(𝑣𝑖	𝑔(𝑣𝑖	NUM
easat-4161	160	68	)	)	PUNCT
easat-4161	160	69	=	=	SYM
easat-4161	161	1	3𝑠	3𝑠	NUM
easat-4161	161	2	+	+	CCONJ
easat-4161	161	3	1	1	NUM
easat-4161	161	4	,	,	PUNCT
easat-4161	161	5	𝑖	𝑖	NOUN
easat-4161	161	6	=	=	SYM
easat-4161	161	7	1	1	NUM
easat-4161	161	8	,	,	PUNCT
easat-4161	161	9	2	2	NUM
easat-4161	161	10	,	,	PUNCT
easat-4161	161	11	…	…	PUNCT
easat-4161	161	12	,	,	PUNCT
easat-4161	161	13	𝑛.	𝑛.	NOUN
easat-4161	161	14	𝑔(𝑥1𝑥2	𝑔(𝑥1𝑥2	NOUN
easat-4161	161	15	)	)	PUNCT
easat-4161	161	16	=	=	SYM
easat-4161	161	17	𝑔(𝑥𝑛−1𝑥𝑛	𝑔(𝑥𝑛−1𝑥𝑛	NOUN
easat-4161	161	18	)	)	PUNCT
easat-4161	161	19	=	=	SYM
easat-4161	161	20	3𝑠.	3𝑠.	NUM
easat-4161	161	21	𝑔(𝑥2𝑥3	𝑔(𝑥2𝑥3	NOUN
easat-4161	161	22	)	)	PUNCT
easat-4161	161	23	=	=	SYM
easat-4161	161	24	𝑔(𝑥𝑛𝑥1	𝑔(𝑥𝑛𝑥1	NOUN
easat-4161	161	25	)	)	PUNCT
easat-4161	161	26	=	=	SYM
easat-4161	161	27	3𝑠	3𝑠	NUM
easat-4161	161	28	+	+	CCONJ
easat-4161	161	29	1	1	X
easat-4161	161	30	.	.	X
easat-4161	162	1	𝑔(𝑥𝑖𝑥𝑖+1	𝑔(𝑥𝑖𝑥𝑖+1	PROPN
easat-4161	162	2	)	)	PUNCT
easat-4161	163	1	=	=	NOUN
easat-4161	163	2	{	{	PUNCT
easat-4161	163	3	3𝑠	3𝑠	NUM
easat-4161	163	4	,	,	PUNCT
easat-4161	163	5	{	{	PUNCT
easat-4161	163	6	𝑖	𝑖	SYM
easat-4161	163	7	=	=	SYM
easat-4161	163	8	3	3	NUM
easat-4161	163	9	,	,	PUNCT
easat-4161	163	10	7	7	NUM
easat-4161	163	11	,	,	PUNCT
easat-4161	163	12	11	11	NUM
easat-4161	163	13	,	,	PUNCT
easat-4161	163	14	…	…	PUNCT
easat-4161	163	15	,	,	PUNCT
easat-4161	163	16	𝑛	𝑛	DET
easat-4161	163	17	−	−	NOUN
easat-4161	164	1	1	1	NUM
easat-4161	164	2	.	.	PUNCT
easat-4161	164	3	𝑖	𝑖	NOUN
easat-4161	164	4	=	=	SYM
easat-4161	164	5	5	5	NUM
easat-4161	164	6	,	,	PUNCT
easat-4161	164	7	9	9	NUM
easat-4161	164	8	,	,	PUNCT
easat-4161	164	9	13,	13,	NUM
easat-4161	164	10	…	…	SYM
easat-4161	164	11	𝑛	𝑛	PRON
easat-4161	164	12	−	−	PROPN
easat-4161	164	13	3	3	NUM
easat-4161	164	14	.	.	X
easat-4161	164	15	3𝑠	3𝑠	NUM
easat-4161	164	16	+	+	CCONJ
easat-4161	164	17	1	1	NUM
easat-4161	164	18	,	,	PUNCT
easat-4161	164	19	{	{	PUNCT
easat-4161	165	1	𝑖	𝑖	NOUN
easat-4161	165	2	=	=	NOUN
easat-4161	165	3	4	4	NUM
easat-4161	165	4	,	,	PUNCT
easat-4161	165	5	8	8	NUM
easat-4161	165	6	,	,	PUNCT
easat-4161	165	7	12	12	NUM
easat-4161	165	8	,	,	PUNCT
easat-4161	165	9	…	…	PUNCT
easat-4161	165	10	,	,	PUNCT
easat-4161	165	11	𝑛	𝑛	DET
easat-4161	165	12	−	−	NOUN
easat-4161	165	13	4	4	NUM
easat-4161	165	14	.	.	PUNCT
easat-4161	165	15	𝑖	𝑖	SYM
easat-4161	166	1	=	=	NOUN
easat-4161	166	2	6	6	NUM
easat-4161	166	3	,	,	PUNCT
easat-4161	166	4	10	10	NUM
easat-4161	166	5	,	,	PUNCT
easat-4161	166	6	14	14	NUM
easat-4161	166	7	,	,	PUNCT
easat-4161	166	8	…	…	PUNCT
easat-4161	166	9	,	,	PUNCT
easat-4161	166	10	𝑛	𝑛	DET
easat-4161	166	11	−	−	PROPN
easat-4161	166	12	2	2	NUM
easat-4161	166	13	.	.	PUNCT
easat-4161	166	14	𝑔(𝑥𝑖−1𝑥𝑖	𝑔(𝑥𝑖−1𝑥𝑖	ADJ
easat-4161	166	15	)	)	PUNCT
easat-4161	166	16	=	=	NOUN
easat-4161	166	17	{	{	PUNCT
easat-4161	166	18	3𝑠	3𝑠	NUM
easat-4161	166	19	+	+	CCONJ
easat-4161	166	20	1	1	NUM
easat-4161	166	21	,	,	PUNCT
easat-4161	166	22	{	{	PUNCT
easat-4161	167	1	𝑖	𝑖	PUNCT
easat-4161	167	2	=	=	SYM
easat-4161	167	3	3	3	NUM
easat-4161	167	4	,	,	PUNCT
easat-4161	167	5	7	7	NUM
easat-4161	167	6	,	,	PUNCT
easat-4161	167	7	11	11	NUM
easat-4161	167	8	,	,	PUNCT
easat-4161	167	9	…	…	PUNCT
easat-4161	167	10	,	,	PUNCT
easat-4161	167	11	𝑛	𝑛	DET
easat-4161	167	12	−	−	NOUN
easat-4161	168	1	1	1	NUM
easat-4161	168	2	.	.	PUNCT
easat-4161	168	3	𝑖	𝑖	NOUN
easat-4161	168	4	=	=	SYM
easat-4161	168	5	5	5	NUM
easat-4161	168	6	,	,	PUNCT
easat-4161	168	7	9	9	NUM
easat-4161	168	8	,	,	PUNCT
easat-4161	168	9	13,	13,	NUM
easat-4161	168	10	…	…	SYM
easat-4161	168	11	𝑛	𝑛	PRON
easat-4161	168	12	−	−	PROPN
easat-4161	168	13	3	3	NUM
easat-4161	168	14	.	.	PUNCT
easat-4161	169	1	3𝑠	3𝑠	NOUN
easat-4161	169	2	,	,	PUNCT
easat-4161	169	3	{	{	PUNCT
easat-4161	169	4	𝑖	𝑖	NOUN
easat-4161	169	5	=	=	SYM
easat-4161	169	6	4	4	NUM
easat-4161	169	7	,	,	PUNCT
easat-4161	169	8	8	8	NUM
easat-4161	169	9	,	,	PUNCT
easat-4161	169	10	12	12	NUM
easat-4161	169	11	,	,	PUNCT
easat-4161	169	12	…	…	PUNCT
easat-4161	169	13	,	,	PUNCT
easat-4161	169	14	𝑛	𝑛	PRON
easat-4161	169	15	−	−	NOUN
easat-4161	169	16	4	4	NUM
easat-4161	169	17	.	.	PUNCT
easat-4161	169	18	𝑖	𝑖	SYM
easat-4161	170	1	=	=	NOUN
easat-4161	170	2	6	6	NUM
easat-4161	170	3	,	,	PUNCT
easat-4161	170	4	10	10	NUM
easat-4161	170	5	,	,	PUNCT
easat-4161	170	6	14	14	NUM
easat-4161	170	7	,	,	PUNCT
easat-4161	170	8	…	…	PUNCT
easat-4161	170	9	,	,	PUNCT
easat-4161	170	10	𝑛	𝑛	PRON
easat-4161	170	11	−	−	PROPN
easat-4161	170	12	2	2	NUM
easat-4161	170	13	.	.	X
easat-4161	170	14	𝑔(𝑥1𝑦1	𝑔(𝑥1𝑦1	NOUN
easat-4161	170	15	)	)	PUNCT
easat-4161	170	16	=	=	SYM
easat-4161	170	17	𝑓(𝑥2𝑦2	𝑓(𝑥2𝑦2	NOUN
easat-4161	170	18	)	)	PUNCT
easat-4161	170	19	=	=	SYM
easat-4161	170	20	1	1	NUM
easat-4161	170	21	.	.	X
easat-4161	170	22	𝑔(𝑥𝑖𝑦𝑖	𝑔(𝑥𝑖𝑦𝑖	ADJ
easat-4161	170	23	)	)	PUNCT
easat-4161	171	1	=	=	PRON
easat-4161	171	2	{	{	PUNCT
easat-4161	171	3	𝑖+1	𝑖+1	NUM
easat-4161	171	4	4	4	NUM
easat-4161	171	5	,	,	PUNCT
easat-4161	171	6	𝑖	𝑖	NOUN
easat-4161	171	7	=	=	SYM
easat-4161	171	8	3	3	NUM
easat-4161	171	9	,	,	PUNCT
easat-4161	171	10	7	7	NUM
easat-4161	171	11	,	,	PUNCT
easat-4161	171	12	11	11	NUM
easat-4161	171	13	,	,	PUNCT
easat-4161	171	14	…	…	PUNCT
easat-4161	171	15	,	,	PUNCT
easat-4161	171	16	𝑛	𝑛	PRON
easat-4161	171	17	−	−	NOUN
easat-4161	172	1	1	1	NUM
easat-4161	172	2	.	.	PUNCT
easat-4161	172	3	𝑖	𝑖	ADP
easat-4161	172	4	4	4	NUM
easat-4161	172	5	,	,	PUNCT
easat-4161	172	6	𝑖	𝑖	NOUN
easat-4161	172	7	=	=	SYM
easat-4161	172	8	4	4	NUM
easat-4161	172	9	,	,	PUNCT
easat-4161	172	10	8	8	NUM
easat-4161	172	11	,	,	PUNCT
easat-4161	172	12	12	12	NUM
easat-4161	172	13	,	,	PUNCT
easat-4161	172	14	…	…	PUNCT
easat-4161	172	15	,	,	PUNCT
easat-4161	172	16	𝑛	𝑛	DET
easat-4161	172	17	−	−	NOUN
easat-4161	172	18	4	4	NUM
easat-4161	172	19	.	.	PUNCT
easat-4161	173	1	𝑖−1	𝑖−1	ADP
easat-4161	173	2	4	4	NUM
easat-4161	173	3	,	,	PUNCT
easat-4161	173	4	𝑖	𝑖	NOUN
easat-4161	173	5	=	=	SYM
easat-4161	173	6	5	5	NUM
easat-4161	173	7	,	,	PUNCT
easat-4161	173	8	9	9	NUM
easat-4161	173	9	,	,	PUNCT
easat-4161	173	10	13	13	NUM
easat-4161	173	11	,	,	PUNCT
easat-4161	173	12	…	…	PUNCT
easat-4161	173	13	,	,	PUNCT
easat-4161	173	14	𝑛	𝑛	DET
easat-4161	173	15	−	−	NOUN
easat-4161	173	16	3	3	X
easat-4161	173	17	.	.	PUNCT
easat-4161	174	1	𝑖−2	𝑖−2	PROPN
easat-4161	174	2	4	4	NUM
easat-4161	174	3	,	,	PUNCT
easat-4161	174	4	𝑖	𝑖	NOUN
easat-4161	174	5	=	=	SYM
easat-4161	174	6	6	6	NUM
easat-4161	174	7	,	,	PUNCT
easat-4161	174	8	10	10	NUM
easat-4161	174	9	,	,	PUNCT
easat-4161	174	10	14	14	NUM
easat-4161	174	11	,	,	PUNCT
easat-4161	174	12	…	…	PUNCT
easat-4161	174	13	,	,	PUNCT
easat-4161	174	14	𝑛	𝑛	DET
easat-4161	174	15	−	−	PROPN
easat-4161	174	16	2	2	NUM
easat-4161	174	17	.	.	PUNCT
easat-4161	174	18	𝑔(𝑥𝑛𝑦𝑛	𝑔(𝑥𝑛𝑦𝑛	VERB
easat-4161	174	19	)	)	PUNCT
easat-4161	175	1	=	=	SYM
easat-4161	175	2	𝑛	𝑛	DET
easat-4161	175	3	4	4	NUM
easat-4161	175	4	.	.	PUNCT
easat-4161	176	1	𝑔(𝑥2𝑤1	𝑔(𝑥2𝑤1	NOUN
easat-4161	176	2	)	)	PUNCT
easat-4161	176	3	=	=	NOUN
easat-4161	177	1	2𝑠	2𝑠	NOUN
easat-4161	177	2	+	+	CCONJ
easat-4161	177	3	1	1	X
easat-4161	177	4	.	.	PUNCT
easat-4161	177	5	𝑔(𝑥3𝑤2	𝑔(𝑥3𝑤2	NOUN
easat-4161	177	6	)	)	PUNCT
easat-4161	178	1	=	=	NOUN
easat-4161	178	2	{	{	PUNCT
easat-4161	178	3	3𝑠	3𝑠	NUM
easat-4161	178	4	,	,	PUNCT
easat-4161	178	5	𝑠	𝑠	X
easat-4161	178	6	=	=	SYM
easat-4161	178	7	1	1	NUM
easat-4161	178	8	2𝑠	2𝑠	NOUN
easat-4161	178	9	+	+	CCONJ
easat-4161	178	10	2	2	NUM
easat-4161	178	11	,	,	PUNCT
easat-4161	178	12	𝑠	𝑠	NOUN
easat-4161	178	13	=	=	SYM
easat-4161	178	14	2	2	NUM
easat-4161	178	15	,	,	PUNCT
easat-4161	178	16	3	3	NUM
easat-4161	178	17	,	,	PUNCT
easat-4161	178	18	…	…	PUNCT
easat-4161	178	19	𝑔(𝑥𝑖+1𝑤𝑖	𝑔(𝑥𝑖+1𝑤𝑖	NOUN
easat-4161	178	20	)	)	PUNCT
easat-4161	178	21	=	=	SYM
easat-4161	178	22	{	{	PUNCT
easat-4161	178	23	2𝑠	2𝑠	NOUN
easat-4161	179	1	+	+	CCONJ
easat-4161	179	2	3𝑖+3	3𝑖+3	PROPN
easat-4161	179	3	4	4	NUM
easat-4161	179	4	,	,	PUNCT
easat-4161	179	5	𝑖	𝑖	PROPN
easat-4161	179	6	≤	≤	NOUN
easat-4161	179	7	𝑠	𝑠	NUM
easat-4161	179	8	3𝑠	3𝑠	NUM
easat-4161	179	9	,	,	PUNCT
easat-4161	179	10	𝑖	𝑖	PROPN
easat-4161	179	11	>	>	X
easat-4161	179	12	𝑠	𝑠	PROPN
easat-4161	179	13	,	,	PUNCT
easat-4161	179	14	𝑖	𝑖	PROPN
easat-4161	179	15	=	=	SYM
easat-4161	179	16	3	3	NUM
easat-4161	179	17	,	,	PUNCT
easat-4161	179	18	7	7	NUM
easat-4161	179	19	,	,	PUNCT
easat-4161	179	20	11	11	NUM
easat-4161	179	21	,	,	PUNCT
easat-4161	179	22	…	…	PUNCT
easat-4161	179	23	,	,	PUNCT
easat-4161	179	24	𝑛	𝑛	DET
easat-4161	179	25	−	−	NOUN
easat-4161	179	26	1	1	NUM
easat-4161	179	27	.	.	PUNCT
easat-4161	180	1	𝑔(𝑥𝑖+1𝑤𝑖	𝑔(𝑥𝑖+1𝑤𝑖	NOUN
easat-4161	180	2	)	)	PUNCT
easat-4161	181	1	=	=	PRON
easat-4161	181	2	{	{	PUNCT
easat-4161	181	3	2𝑠	2𝑠	NOUN
easat-4161	182	1	+	+	CCONJ
easat-4161	182	2	3𝑖+4	3𝑖+4	NUM
easat-4161	182	3	4	4	NUM
easat-4161	182	4	,	,	PUNCT
easat-4161	182	5	𝑖	𝑖	NOUN
easat-4161	182	6	≤	≤	NOUN
easat-4161	182	7	𝑠	𝑠	NUM
easat-4161	182	8	3𝑠	3𝑠	NUM
easat-4161	182	9	,	,	PUNCT
easat-4161	182	10	𝑖	𝑖	PROPN
easat-4161	182	11	>	>	X
easat-4161	182	12	𝑠	𝑠	PROPN
easat-4161	182	13	,	,	PUNCT
easat-4161	182	14	𝑖	𝑖	X
easat-4161	182	15	=	=	NOUN
easat-4161	182	16	4	4	NUM
easat-4161	182	17	,	,	PUNCT
easat-4161	182	18	8	8	NUM
easat-4161	182	19	,	,	PUNCT
easat-4161	182	20	12	12	NUM
easat-4161	182	21	,	,	PUNCT
easat-4161	182	22	…	…	PUNCT
easat-4161	182	23	,	,	PUNCT
easat-4161	182	24	𝑛	𝑛	DET
easat-4161	182	25	−	−	NOUN
easat-4161	182	26	4	4	NUM
easat-4161	182	27	.	.	PUNCT
easat-4161	183	1	𝑔(𝑥𝑖+1𝑤𝑖	𝑔(𝑥𝑖+1𝑤𝑖	NOUN
easat-4161	183	2	)	)	PUNCT
easat-4161	184	1	=	=	PRON
easat-4161	184	2	{	{	PUNCT
easat-4161	184	3	2𝑠	2𝑠	NOUN
easat-4161	185	1	+	+	CCONJ
easat-4161	185	2	3𝑖+5	3𝑖+5	PROPN
easat-4161	185	3	4	4	NUM
easat-4161	185	4	,	,	PUNCT
easat-4161	185	5	𝑖	𝑖	PROPN
easat-4161	185	6	≤	≤	NOUN
easat-4161	185	7	𝑠	𝑠	NUM
easat-4161	185	8	3𝑠	3𝑠	NUM
easat-4161	185	9	,	,	PUNCT
easat-4161	185	10	𝑖	𝑖	PROPN
easat-4161	185	11	>	>	X
easat-4161	186	1	𝑠	𝑠	PROPN
easat-4161	186	2	,	,	PUNCT
easat-4161	186	3	𝑖	𝑖	PROPN
easat-4161	186	4	=	=	SYM
easat-4161	186	5	5	5	NUM
easat-4161	186	6	,	,	PUNCT
easat-4161	186	7	9	9	NUM
easat-4161	186	8	,	,	PUNCT
easat-4161	186	9	13	13	NUM
easat-4161	186	10	,	,	PUNCT
easat-4161	186	11	…	…	PUNCT
easat-4161	186	12	,	,	PUNCT
easat-4161	186	13	𝑛	𝑛	PRON
easat-4161	186	14	−	−	NOUN
easat-4161	186	15	3	3	X
easat-4161	186	16	.	.	PUNCT
easat-4161	186	17	𝑔(𝑥𝑖+1𝑤𝑖	𝑔(𝑥𝑖+1𝑤𝑖	NOUN
easat-4161	186	18	)	)	PUNCT
easat-4161	187	1	=	=	PRON
easat-4161	187	2	{	{	PUNCT
easat-4161	187	3	2𝑠	2𝑠	NOUN
easat-4161	188	1	+	+	CCONJ
easat-4161	188	2	3𝑖+6	3𝑖+6	PROPN
easat-4161	188	3	4	4	NUM
easat-4161	188	4	,	,	PUNCT
easat-4161	188	5	𝑖	𝑖	PROPN
easat-4161	188	6	≤	≤	NOUN
easat-4161	188	7	𝑠	𝑠	NUM
easat-4161	188	8	3𝑠	3𝑠	NUM
easat-4161	188	9	,	,	PUNCT
easat-4161	188	10	𝑖	𝑖	PROPN
easat-4161	188	11	>	>	X
easat-4161	188	12	𝑠	𝑠	PROPN
easat-4161	188	13	,	,	PUNCT
easat-4161	188	14	𝑖	𝑖	PROPN
easat-4161	188	15	=	=	SYM
easat-4161	188	16	6	6	NUM
easat-4161	188	17	,	,	PUNCT
easat-4161	188	18	10	10	NUM
easat-4161	188	19	,	,	PUNCT
easat-4161	188	20	14	14	NUM
easat-4161	188	21	,	,	PUNCT
easat-4161	188	22	…	…	PUNCT
easat-4161	188	23	,	,	PUNCT
easat-4161	188	24	𝑛	𝑛	PRON
easat-4161	188	25	−	−	PROPN
easat-4161	188	26	2	2	NUM
easat-4161	188	27	.	.	NUM
easat-4161	188	28	𝑔(𝑥1𝑤𝑛	𝑔(𝑥1𝑤𝑛	NOUN
easat-4161	188	29	)	)	PUNCT
easat-4161	189	1	=	=	SYM
easat-4161	189	2	𝑔(𝑥𝑛𝑤𝑛−1	𝑔(𝑥𝑛𝑤𝑛−1	NOUN
easat-4161	189	3	)	)	PUNCT
easat-4161	189	4	=	=	SYM
easat-4161	190	1	3𝑛+4	3𝑛+4	NUM
easat-4161	190	2	4	4	NUM
easat-4161	190	3	−	−	NOUN
easat-4161	190	4	1	1	NUM
easat-4161	190	5	=	=	SYM
easat-4161	190	6	3𝑠.	3𝑠.	NUM
easat-4161	190	7	487	487	NUM
easat-4161	190	8	edelweiss	edelweiss	PROPN
easat-4161	190	9	applied	apply	VERB
easat-4161	190	10	science	science	NOUN
easat-4161	190	11	and	and	CCONJ
easat-4161	190	12	technology	technology	NOUN
easat-4161	190	13	issn	issn	PROPN
easat-4161	190	14	:	:	PUNCT
easat-4161	190	15	2576	2576	NUM
easat-4161	190	16	-	-	SYM
easat-4161	190	17	8484	8484	NUM
easat-4161	190	18	vol	vol	NOUN
easat-4161	190	19	.	.	PROPN
easat-4161	191	1	9	9	NUM
easat-4161	191	2	,	,	PUNCT
easat-4161	191	3	no	no	INTJ
easat-4161	191	4	.	.	NOUN
easat-4161	191	5	1	1	NUM
easat-4161	191	6	:	:	PUNCT
easat-4161	191	7	481	481	NUM
easat-4161	191	8	-	-	SYM
easat-4161	191	9	492	492	NUM
easat-4161	191	10	,	,	PUNCT
easat-4161	191	11	2025	2025	NUM
easat-4161	191	12	doi	doi	NOUN
easat-4161	191	13	:	:	PUNCT
easat-4161	191	14	10.55214/25768484.v9i1.4161	10.55214/25768484.v9i1.4161	NUM
easat-4161	191	15	©	©	PROPN
easat-4161	191	16	2025	2025	NUM
easat-4161	191	17	by	by	ADP
easat-4161	191	18	the	the	DET
easat-4161	191	19	authors	author	NOUN
easat-4161	191	20	;	;	PUNCT
easat-4161	191	21	licensee	licensee	PROPN
easat-4161	191	22	learning	learn	VERB
easat-4161	191	23	gate	gate	NOUN
easat-4161	191	24	𝑔(𝑥𝑖𝑤𝑖−1	𝑔(𝑥𝑖𝑤𝑖−1	PROPN
easat-4161	191	25	)	)	PUNCT
easat-4161	191	26	=	=	PRON
easat-4161	191	27	{	{	PUNCT
easat-4161	191	28	2𝑠	2𝑠	NOUN
easat-4161	192	1	+	+	CCONJ
easat-4161	192	2	𝑖	𝑖	SYM
easat-4161	192	3	−	−	NOUN
easat-4161	192	4	1	1	NUM
easat-4161	192	5	,	,	PUNCT
easat-4161	192	6	𝑖	𝑖	PROPN
easat-4161	192	7	≤	≤	NOUN
easat-4161	192	8	𝑠	𝑠	NUM
easat-4161	192	9	3𝑠	3𝑠	NUM
easat-4161	192	10	,	,	PUNCT
easat-4161	192	11	𝑖	𝑖	PROPN
easat-4161	192	12	>	>	X
easat-4161	192	13	𝑠	𝑠	PRON
easat-4161	192	14	𝑔(𝑥1𝑣2	𝑔(𝑥1𝑣2	PROPN
easat-4161	192	15	)	)	PUNCT
easat-4161	192	16	=	=	PUNCT
easat-4161	192	17	𝑔(𝑥𝑖𝑣𝑖+1	𝑔(𝑥𝑖𝑣𝑖+1	NOUN
easat-4161	192	18	)	)	PUNCT
easat-4161	192	19	=	=	SYM
easat-4161	192	20	𝑔(𝑥𝑛−1𝑣𝑛	𝑔(𝑥𝑛−1𝑣𝑛	NOUN
easat-4161	192	21	)	)	PUNCT
easat-4161	192	22	=	=	SYM
easat-4161	192	23	𝑔(𝑥𝑛𝑣1	𝑔(𝑥𝑛𝑣1	NUM
easat-4161	192	24	)	)	PUNCT
easat-4161	193	1	=	=	NOUN
easat-4161	193	2	3𝑠	3𝑠	NUM
easat-4161	193	3	+	+	CCONJ
easat-4161	193	4	1	1	NUM
easat-4161	193	5	𝑔(𝑦𝑖𝑤𝑖	𝑔(𝑦𝑖𝑤𝑖	NOUN
easat-4161	193	6	)	)	PUNCT
easat-4161	193	7	=	=	SYM
easat-4161	193	8	1	1	NUM
easat-4161	193	9	,	,	PUNCT
easat-4161	193	10	𝑖	𝑖	NOUN
easat-4161	193	11	=	=	SYM
easat-4161	193	12	1	1	NUM
easat-4161	193	13	,	,	PUNCT
easat-4161	193	14	2	2	NUM
easat-4161	193	15	,	,	PUNCT
easat-4161	193	16	…	…	PUNCT
easat-4161	193	17	,	,	PUNCT
easat-4161	193	18	𝑛.	𝑛.	NOUN
easat-4161	193	19	𝑔(𝑦1𝑣1	𝑔(𝑦1𝑣1	NOUN
easat-4161	193	20	)	)	PUNCT
easat-4161	193	21	=	=	SYM
easat-4161	193	22	1	1	X
easat-4161	193	23	.	.	X
easat-4161	193	24	𝑔(𝑦2𝑣2	𝑔(𝑦2𝑣2	NOUN
easat-4161	193	25	)	)	PUNCT
easat-4161	193	26	=	=	SYM
easat-4161	193	27	2	2	X
easat-4161	193	28	.	.	PUNCT
easat-4161	193	29	𝑔(𝑦𝑖𝑣𝑖	𝑔(𝑦𝑖𝑣𝑖	NUM
easat-4161	193	30	)	)	PUNCT
easat-4161	194	1	=	=	PRON
easat-4161	194	2	{	{	PUNCT
easat-4161	194	3	3𝑖+3	3𝑖+3	PROPN
easat-4161	194	4	4	4	NUM
easat-4161	194	5	,	,	PUNCT
easat-4161	194	6	𝑖	𝑖	PROPN
easat-4161	194	7	=	=	SYM
easat-4161	194	8	3	3	NUM
easat-4161	194	9	,	,	PUNCT
easat-4161	194	10	7	7	NUM
easat-4161	194	11	,	,	PUNCT
easat-4161	194	12	11	11	NUM
easat-4161	194	13	,	,	PUNCT
easat-4161	194	14	…	…	PUNCT
easat-4161	194	15	,	,	PUNCT
easat-4161	194	16	𝑛	𝑛	DET
easat-4161	194	17	−	−	PROPN
easat-4161	194	18	1	1	NUM
easat-4161	194	19	,	,	PUNCT
easat-4161	194	20	3𝑖+4	3𝑖+4	NUM
easat-4161	194	21	4	4	NUM
easat-4161	194	22	,	,	PUNCT
easat-4161	194	23	𝑖	𝑖	NOUN
easat-4161	194	24	=	=	SYM
easat-4161	194	25	4	4	NUM
easat-4161	194	26	,	,	PUNCT
easat-4161	194	27	8	8	NUM
easat-4161	194	28	,	,	PUNCT
easat-4161	194	29	12	12	NUM
easat-4161	194	30	,	,	PUNCT
easat-4161	194	31	…	…	PUNCT
easat-4161	194	32	,	,	PUNCT
easat-4161	194	33	𝑛	𝑛	DET
easat-4161	194	34	−	−	PROPN
easat-4161	194	35	4	4	NUM
easat-4161	194	36	,	,	PUNCT
easat-4161	194	37	3𝑖+5	3𝑖+5	PROPN
easat-4161	194	38	4	4	NUM
easat-4161	194	39	,	,	PUNCT
easat-4161	194	40	𝑖	𝑖	NOUN
easat-4161	194	41	=	=	SYM
easat-4161	194	42	5	5	NUM
easat-4161	194	43	,	,	PUNCT
easat-4161	194	44	9	9	NUM
easat-4161	194	45	,	,	PUNCT
easat-4161	194	46	13	13	NUM
easat-4161	194	47	,	,	PUNCT
easat-4161	194	48	…	…	PUNCT
easat-4161	194	49	,	,	PUNCT
easat-4161	194	50	𝑛	𝑛	DET
easat-4161	194	51	−	−	PROPN
easat-4161	194	52	3	3	NUM
easat-4161	194	53	,	,	PUNCT
easat-4161	194	54	3𝑖+6	3𝑖+6	PROPN
easat-4161	194	55	4	4	NUM
easat-4161	194	56	,	,	PUNCT
easat-4161	194	57	𝑖	𝑖	NOUN
easat-4161	194	58	=	=	SYM
easat-4161	194	59	6	6	NUM
easat-4161	194	60	,	,	PUNCT
easat-4161	194	61	10	10	NUM
easat-4161	194	62	,	,	PUNCT
easat-4161	194	63	14	14	NUM
easat-4161	194	64	,	,	PUNCT
easat-4161	194	65	…	…	PUNCT
easat-4161	194	66	,	,	PUNCT
easat-4161	194	67	𝑛	𝑛	DET
easat-4161	194	68	−	−	PROPN
easat-4161	194	69	2	2	NUM
easat-4161	194	70	,	,	PUNCT
easat-4161	194	71	𝑔(𝑦𝑛𝑣𝑛	𝑔(𝑦𝑛𝑣𝑛	NOUN
easat-4161	194	72	)	)	PUNCT
easat-4161	194	73	=	=	SYM
easat-4161	195	1	3𝑛+4	3𝑛+4	NUM
easat-4161	195	2	4	4	NUM
easat-4161	195	3	.	.	PUNCT
easat-4161	196	1	𝑔(𝑤1𝑣1	𝑔(𝑤1𝑣1	ADJ
easat-4161	196	2	)	)	PUNCT
easat-4161	196	3	=	=	SYM
easat-4161	196	4	𝑔(𝑤2𝑣2	𝑔(𝑤2𝑣2	NOUN
easat-4161	196	5	)	)	PUNCT
easat-4161	196	6	=	=	SYM
easat-4161	196	7	2𝑠	2𝑠	NOUN
easat-4161	196	8	+	+	CCONJ
easat-4161	196	9	1	1	X
easat-4161	196	10	.	.	X
easat-4161	196	11	𝑔(𝑤𝑖𝑣𝑖	𝑔(𝑤𝑖𝑣𝑖	NOUN
easat-4161	196	12	)	)	PUNCT
easat-4161	196	13	=	=	PRON
easat-4161	196	14	{	{	PUNCT
easat-4161	196	15	𝑖+1	𝑖+1	PUNCT
easat-4161	196	16	4	4	NUM
easat-4161	196	17	+	+	CCONJ
easat-4161	196	18	2𝑠	2𝑠	NOUN
easat-4161	196	19	,	,	PUNCT
easat-4161	196	20	𝑖	𝑖	NOUN
easat-4161	196	21	=	=	SYM
easat-4161	196	22	3	3	NUM
easat-4161	196	23	,	,	PUNCT
easat-4161	196	24	7	7	NUM
easat-4161	196	25	,	,	PUNCT
easat-4161	196	26	11	11	NUM
easat-4161	196	27	,	,	PUNCT
easat-4161	196	28	…	…	PUNCT
easat-4161	196	29	,	,	PUNCT
easat-4161	196	30	𝑛	𝑛	DET
easat-4161	196	31	−	−	PROPN
easat-4161	196	32	1	1	NUM
easat-4161	196	33	,	,	PUNCT
easat-4161	196	34	𝑖	𝑖	PRON
easat-4161	196	35	4	4	NUM
easat-4161	196	36	+	+	CCONJ
easat-4161	196	37	2𝑠	2𝑠	NOUN
easat-4161	196	38	,	,	PUNCT
easat-4161	196	39	𝑖	𝑖	NOUN
easat-4161	196	40	=	=	SYM
easat-4161	196	41	4	4	NUM
easat-4161	196	42	,	,	PUNCT
easat-4161	196	43	8	8	NUM
easat-4161	196	44	,	,	PUNCT
easat-4161	196	45	12	12	NUM
easat-4161	196	46	,	,	PUNCT
easat-4161	196	47	…	…	PUNCT
easat-4161	196	48	,	,	PUNCT
easat-4161	196	49	𝑛	𝑛	DET
easat-4161	196	50	−	−	PROPN
easat-4161	196	51	4	4	NUM
easat-4161	196	52	,	,	PUNCT
easat-4161	196	53	𝑖−1	𝑖−1	PROPN
easat-4161	196	54	4	4	NUM
easat-4161	196	55	+	+	NOUN
easat-4161	196	56	2𝑠	2𝑠	NOUN
easat-4161	196	57	,	,	PUNCT
easat-4161	196	58	𝑖	𝑖	X
easat-4161	196	59	=	=	SYM
easat-4161	196	60	5	5	NUM
easat-4161	196	61	,	,	PUNCT
easat-4161	196	62	9	9	NUM
easat-4161	196	63	,	,	PUNCT
easat-4161	196	64	13	13	NUM
easat-4161	196	65	,	,	PUNCT
easat-4161	196	66	…	…	PUNCT
easat-4161	196	67	,	,	PUNCT
easat-4161	196	68	𝑛	𝑛	DET
easat-4161	196	69	−	−	PROPN
easat-4161	196	70	3	3	NUM
easat-4161	196	71	,	,	PUNCT
easat-4161	196	72	𝑖−2	𝑖−2	PROPN
easat-4161	196	73	4	4	NUM
easat-4161	196	74	+	+	NOUN
easat-4161	196	75	2𝑠	2𝑠	NOUN
easat-4161	196	76	,	,	PUNCT
easat-4161	196	77	𝑖	𝑖	NOUN
easat-4161	196	78	=	=	SYM
easat-4161	196	79	6	6	NUM
easat-4161	196	80	,	,	PUNCT
easat-4161	196	81	10	10	NUM
easat-4161	196	82	,	,	PUNCT
easat-4161	196	83	14	14	NUM
easat-4161	196	84	,	,	PUNCT
easat-4161	196	85	…	…	PUNCT
easat-4161	196	86	,	,	PUNCT
easat-4161	196	87	𝑛	𝑛	DET
easat-4161	196	88	−	−	PROPN
easat-4161	196	89	2	2	NUM
easat-4161	196	90	,	,	PUNCT
easat-4161	196	91	𝑔(𝑤𝑛𝑣𝑛	𝑔(𝑤𝑛𝑣𝑛	X
easat-4161	196	92	)	)	PUNCT
easat-4161	196	93	=	=	SYM
easat-4161	196	94	𝑛	𝑛	DET
easat-4161	196	95	4	4	NUM
easat-4161	196	96	+	+	SYM
easat-4161	196	97	2𝑠.	2𝑠.	NUM
easat-4161	196	98	based	base	VERB
easat-4161	196	99	on	on	ADP
easat-4161	196	100	this	this	DET
easat-4161	196	101	function	function	NOUN
easat-4161	196	102	,	,	PUNCT
easat-4161	196	103	it	it	PRON
easat-4161	196	104	can	can	AUX
easat-4161	196	105	be	be	AUX
easat-4161	196	106	shown	show	VERB
easat-4161	196	107	that	that	SCONJ
easat-4161	196	108	all	all	DET
easat-4161	196	109	vertices	vertice	VERB
easat-4161	196	110	weights	weight	NOUN
easat-4161	196	111	are	be	AUX
easat-4161	196	112	different	different	ADJ
easat-4161	196	113	and	and	CCONJ
easat-4161	196	114	the	the	DET
easat-4161	196	115	maximum	maximum	ADJ
easat-4161	196	116	value	value	NOUN
easat-4161	196	117	of	of	ADP
easat-4161	196	118	the	the	DET
easat-4161	196	119	function	function	NOUN
easat-4161	196	120	is	be	AUX
easat-4161	196	121	⌈	⌈	SYM
easat-4161	196	122	𝟑+𝟑𝒏	𝟑+𝟑𝒏	NOUN
easat-4161	196	123	𝟒	𝟒	X
easat-4161	196	124	⌉.	⌉.	ADV
easat-4161	196	125	this	this	PRON
easat-4161	196	126	shows	show	VERB
easat-4161	196	127	that	that	SCONJ
easat-4161	196	128	𝑔	𝑔	NOUN
easat-4161	196	129	:	:	PUNCT
easat-4161	196	130	𝑉	𝑉	PROPN
easat-4161	196	131	∪	∪	NOUN
easat-4161	196	132	𝐸	𝐸	PROPN
easat-4161	196	133	→	→	SYM
easat-4161	196	134	{	{	PUNCT
easat-4161	196	135	1	1	NUM
easat-4161	196	136	,	,	PUNCT
easat-4161	196	137	2	2	NUM
easat-4161	196	138	,	,	PUNCT
easat-4161	196	139	3,⋯	3,⋯	NUM
easat-4161	196	140	,	,	PUNCT
easat-4161	196	141	⌈	⌈	X
easat-4161	196	142	𝟑+𝟑𝒏	𝟑+𝟑𝒏	X
easat-4161	196	143	𝟒	𝟒	NUM
easat-4161	196	144	⌉	⌉	NOUN
easat-4161	196	145	}	}	PUNCT
easat-4161	196	146	is	be	AUX
easat-4161	196	147	a	a	DET
easat-4161	196	148	function	function	NOUN
easat-4161	196	149	a	a	DET
easat-4161	196	150	total	total	ADJ
easat-4161	196	151	vertex	vertex	NOUN
easat-4161	196	152	irregular	irregular	ADJ
easat-4161	196	153	𝑘	𝑘	DET
easat-4161	196	154	−	−	NOUN
easat-4161	196	155	𝑙𝑎𝑏𝑒𝑙𝑙𝑖𝑛𝑔	𝑙𝑎𝑏𝑒𝑙𝑙𝑖𝑛𝑔	NOUN
easat-4161	196	156	where	where	SCONJ
easat-4161	196	157	𝑘	𝑘	NOUN
easat-4161	196	158	=	=	PUNCT
easat-4161	196	159	⌈	⌈	NOUN
easat-4161	196	160	𝟑+𝟑𝒏	𝟑+𝟑𝒏	NOUN
easat-4161	196	161	𝟒	𝟒	X
easat-4161	196	162	⌉.	⌉.	ADV
easat-4161	196	163	thus	thus	ADV
easat-4161	196	164	it	it	PRON
easat-4161	196	165	is	be	AUX
easat-4161	196	166	obtained	obtain	VERB
easat-4161	196	167	that	that	SCONJ
easat-4161	196	168	𝒕𝒗𝒔(𝓗𝒏	𝒕𝒗𝒔(𝓗𝒏	NOUN
easat-4161	196	169	)	)	PUNCT
easat-4161	196	170	≤	≤	NOUN
easat-4161	197	1	⌈	⌈	SYM
easat-4161	197	2	𝟑+𝟑𝒏	𝟑+𝟑𝒏	NOUN
easat-4161	197	3	𝟒	𝟒	NUM
easat-4161	197	4	⌉	⌉	X
easat-4161	197	5	for	for	ADP
easat-4161	197	6	𝒏	𝒏	PROPN
easat-4161	197	7	=	=	SYM
easat-4161	197	8	𝟒𝒕	𝟒𝒕	NOUN
easat-4161	197	9	,	,	PUNCT
easat-4161	197	10	where	where	SCONJ
easat-4161	197	11	𝒕	𝒕	NOUN
easat-4161	197	12	is	be	AUX
easat-4161	197	13	some	some	DET
easat-4161	197	14	positive	positive	ADJ
easat-4161	197	15	integer	integer	NOUN
easat-4161	197	16	.	.	PUNCT
easat-4161	198	1	case	case	NOUN
easat-4161	198	2	3	3	NUM
easat-4161	198	3	.	.	X
easat-4161	199	1	for	for	ADP
easat-4161	199	2	𝑛	𝑛	NOUN
easat-4161	199	3	=	=	SYM
easat-4161	199	4	4𝑡	4𝑡	NOUN
easat-4161	199	5	+	+	CCONJ
easat-4161	199	6	1	1	NUM
easat-4161	199	7	,	,	PUNCT
easat-4161	199	8	where	where	SCONJ
easat-4161	199	9	𝑡	𝑡	PROPN
easat-4161	199	10	is	be	AUX
easat-4161	199	11	some	some	DET
easat-4161	199	12	positive	positive	ADJ
easat-4161	199	13	integer	integer	NOUN
easat-4161	199	14	.	.	PUNCT
easat-4161	200	1	the	the	DET
easat-4161	200	2	total	total	ADJ
easat-4161	200	3	vertex	vertex	NOUN
easat-4161	200	4	labeling	labeling	NOUN
easat-4161	200	5	ℎ	ℎ	NOUN
easat-4161	200	6	is	be	AUX
easat-4161	200	7	ℎ(𝑥1	ℎ(𝑥1	ADJ
easat-4161	200	8	)	)	PUNCT
easat-4161	200	9	=	=	SYM
easat-4161	200	10	1	1	X
easat-4161	200	11	.	.	X
easat-4161	200	12	ℎ(𝑥2	ℎ(𝑥2	NOUN
easat-4161	200	13	)	)	PUNCT
easat-4161	201	1	=	=	SYM
easat-4161	201	2	𝑠	𝑠	PROPN
easat-4161	201	3	+	+	NOUN
easat-4161	201	4	1	1	NUM
easat-4161	201	5	.	.	X
easat-4161	201	6	ℎ(𝑥𝑖	ℎ(𝑥𝑖	X
easat-4161	201	7	)	)	PUNCT
easat-4161	201	8	=	=	PRON
easat-4161	201	9	{	{	PUNCT
easat-4161	201	10	3𝑖+3	3𝑖+3	PROPN
easat-4161	201	11	4	4	NUM
easat-4161	202	1	+	+	CCONJ
easat-4161	202	2	𝑠	𝑠	PROPN
easat-4161	202	3	−	−	NOUN
easat-4161	202	4	𝑖	𝑖	PROPN
easat-4161	203	1	+	+	NOUN
easat-4161	203	2	1	1	NUM
easat-4161	203	3	,	,	PUNCT
easat-4161	203	4	𝑖	𝑖	PRON
easat-4161	203	5	≤	≤	NOUN
easat-4161	203	6	𝑠	𝑠	X
easat-4161	203	7	3𝑖+3	3𝑖+3	PROPN
easat-4161	203	8	4	4	NUM
easat-4161	203	9	,	,	PUNCT
easat-4161	204	1	𝑖	𝑖	PROPN
easat-4161	204	2	>	>	X
easat-4161	204	3	𝑠	𝑠	PROPN
easat-4161	204	4	,	,	PUNCT
easat-4161	204	5	𝑖	𝑖	PROPN
easat-4161	204	6	=	=	SYM
easat-4161	204	7	3	3	NUM
easat-4161	204	8	,	,	PUNCT
easat-4161	204	9	7	7	NUM
easat-4161	204	10	,	,	PUNCT
easat-4161	204	11	11	11	NUM
easat-4161	204	12	,	,	PUNCT
easat-4161	204	13	…	…	PUNCT
easat-4161	204	14	,	,	PUNCT
easat-4161	205	1	𝑛	𝑛	DET
easat-4161	205	2	−	−	PROPN
easat-4161	205	3	2	2	NUM
easat-4161	205	4	.	.	PUNCT
easat-4161	205	5	ℎ(𝑥𝑖	ℎ(𝑥𝑖	X
easat-4161	205	6	)	)	PUNCT
easat-4161	205	7	=	=	PRON
easat-4161	205	8	{	{	PUNCT
easat-4161	205	9	3𝑖+4	3𝑖+4	NUM
easat-4161	205	10	4	4	NUM
easat-4161	205	11	+	+	CCONJ
easat-4161	205	12	𝑠	𝑠	PROPN
easat-4161	205	13	−	−	NOUN
easat-4161	205	14	𝑖	𝑖	PROPN
easat-4161	206	1	+	+	NOUN
easat-4161	206	2	1	1	NUM
easat-4161	206	3	,	,	PUNCT
easat-4161	206	4	𝑖	𝑖	PRON
easat-4161	206	5	≤	≤	NUM
easat-4161	206	6	𝑠	𝑠	X
easat-4161	206	7	3𝑖+4	3𝑖+4	PROPN
easat-4161	206	8	4	4	NUM
easat-4161	206	9	,	,	PUNCT
easat-4161	207	1	𝑖	𝑖	PROPN
easat-4161	207	2	>	>	X
easat-4161	207	3	𝑠	𝑠	PROPN
easat-4161	207	4	,	,	PUNCT
easat-4161	207	5	𝑖	𝑖	X
easat-4161	207	6	=	=	NOUN
easat-4161	207	7	4	4	NUM
easat-4161	207	8	,	,	PUNCT
easat-4161	207	9	8	8	NUM
easat-4161	207	10	,	,	PUNCT
easat-4161	207	11	12	12	NUM
easat-4161	207	12	,	,	PUNCT
easat-4161	207	13	…	…	PUNCT
easat-4161	207	14	,	,	PUNCT
easat-4161	207	15	𝑛	𝑛	DET
easat-4161	207	16	−	−	NOUN
easat-4161	207	17	1	1	NUM
easat-4161	207	18	.	.	PUNCT
easat-4161	208	1	ℎ(𝑥𝑖	ℎ(𝑥𝑖	X
easat-4161	208	2	)	)	PUNCT
easat-4161	208	3	=	=	PRON
easat-4161	208	4	{	{	PUNCT
easat-4161	209	1	3𝑖+5	3𝑖+5	PROPN
easat-4161	209	2	4	4	NUM
easat-4161	209	3	+	+	NUM
easat-4161	209	4	𝑠	𝑠	PROPN
easat-4161	209	5	−	−	NOUN
easat-4161	209	6	𝑖	𝑖	PROPN
easat-4161	210	1	+	+	NOUN
easat-4161	210	2	1	1	NUM
easat-4161	210	3	,	,	PUNCT
easat-4161	210	4	𝑖	𝑖	PRON
easat-4161	210	5	≤	≤	NOUN
easat-4161	210	6	𝑠	𝑠	X
easat-4161	210	7	3𝑖+5	3𝑖+5	PROPN
easat-4161	210	8	4	4	NUM
easat-4161	210	9	,	,	PUNCT
easat-4161	210	10	𝑖	𝑖	PROPN
easat-4161	210	11	>	>	X
easat-4161	210	12	𝑠	𝑠	PROPN
easat-4161	210	13	,	,	PUNCT
easat-4161	210	14	𝑖	𝑖	PROPN
easat-4161	210	15	=	=	SYM
easat-4161	210	16	5	5	NUM
easat-4161	210	17	,	,	PUNCT
easat-4161	210	18	9	9	NUM
easat-4161	210	19	,	,	PUNCT
easat-4161	210	20	13	13	NUM
easat-4161	210	21	,	,	PUNCT
easat-4161	210	22	…	…	PUNCT
easat-4161	210	23	,	,	PUNCT
easat-4161	210	24	𝑛	𝑛	DET
easat-4161	210	25	−	−	NOUN
easat-4161	210	26	4	4	NUM
easat-4161	210	27	.	.	PUNCT
easat-4161	211	1	ℎ(𝑥𝑖	ℎ(𝑥𝑖	X
easat-4161	211	2	)	)	PUNCT
easat-4161	211	3	=	=	PRON
easat-4161	211	4	{	{	PUNCT
easat-4161	211	5	3𝑖+6	3𝑖+6	PROPN
easat-4161	211	6	4	4	NUM
easat-4161	212	1	+	+	CCONJ
easat-4161	212	2	𝑠	𝑠	PROPN
easat-4161	212	3	−	−	NOUN
easat-4161	212	4	𝑖	𝑖	PROPN
easat-4161	213	1	+	+	NOUN
easat-4161	213	2	1	1	NUM
easat-4161	213	3	,	,	PUNCT
easat-4161	213	4	𝑖	𝑖	DET
easat-4161	213	5	≤	≤	NUM
easat-4161	213	6	𝑠	𝑠	X
easat-4161	214	1	3𝑖+6	3𝑖+6	PROPN
easat-4161	214	2	4	4	NUM
easat-4161	214	3	,	,	PUNCT
easat-4161	214	4	𝑖	𝑖	PROPN
easat-4161	214	5	>	>	X
easat-4161	214	6	𝑠	𝑠	PROPN
easat-4161	214	7	,	,	PUNCT
easat-4161	214	8	𝑖	𝑖	PROPN
easat-4161	214	9	=	=	SYM
easat-4161	214	10	6	6	NUM
easat-4161	214	11	,	,	PUNCT
easat-4161	214	12	10	10	NUM
easat-4161	214	13	,	,	PUNCT
easat-4161	214	14	14	14	NUM
easat-4161	214	15	,	,	PUNCT
easat-4161	214	16	…	…	PUNCT
easat-4161	214	17	,	,	PUNCT
easat-4161	214	18	𝑛	𝑛	DET
easat-4161	214	19	−	−	NOUN
easat-4161	214	20	3	3	NUM
easat-4161	214	21	.	.	PUNCT
easat-4161	215	1	ℎ(𝑥𝑛	ℎ(𝑥𝑛	ADJ
easat-4161	215	2	)	)	PUNCT
easat-4161	216	1	=	=	SYM
easat-4161	216	2	3𝑛+5	3𝑛+5	PROPN
easat-4161	216	3	4	4	NUM
easat-4161	216	4	.	.	PUNCT
easat-4161	217	1	488	488	NUM
easat-4161	217	2	edelweiss	edelweiss	PROPN
easat-4161	217	3	applied	apply	VERB
easat-4161	217	4	science	science	NOUN
easat-4161	217	5	and	and	CCONJ
easat-4161	217	6	technology	technology	NOUN
easat-4161	217	7	issn	issn	PROPN
easat-4161	217	8	:	:	PUNCT
easat-4161	217	9	2576	2576	NUM
easat-4161	217	10	-	-	SYM
easat-4161	217	11	8484	8484	NUM
easat-4161	217	12	vol	vol	NOUN
easat-4161	217	13	.	.	PROPN
easat-4161	218	1	9	9	NUM
easat-4161	218	2	,	,	PUNCT
easat-4161	218	3	no	no	INTJ
easat-4161	218	4	.	.	NOUN
easat-4161	218	5	1	1	NUM
easat-4161	218	6	:	:	PUNCT
easat-4161	218	7	481	481	NUM
easat-4161	218	8	-	-	SYM
easat-4161	218	9	492	492	NUM
easat-4161	218	10	,	,	PUNCT
easat-4161	218	11	2025	2025	NUM
easat-4161	218	12	doi	doi	NOUN
easat-4161	218	13	:	:	PUNCT
easat-4161	218	14	10.55214/25768484.v9i1.4161	10.55214/25768484.v9i1.4161	NUM
easat-4161	218	15	©	©	PROPN
easat-4161	218	16	2025	2025	NUM
easat-4161	218	17	by	by	ADP
easat-4161	218	18	the	the	DET
easat-4161	218	19	authors	author	NOUN
easat-4161	218	20	;	;	PUNCT
easat-4161	218	21	licensee	licensee	PROPN
easat-4161	218	22	learning	learning	NOUN
easat-4161	218	23	gate	gate	NOUN
easat-4161	218	24	ℎ(𝑦𝑖	ℎ(𝑦𝑖	ADV
easat-4161	218	25	)	)	PUNCT
easat-4161	218	26	=	=	SYM
easat-4161	218	27	1	1	NUM
easat-4161	218	28	,	,	PUNCT
easat-4161	218	29	𝑖	𝑖	NOUN
easat-4161	218	30	=	=	SYM
easat-4161	218	31	1	1	NUM
easat-4161	218	32	,	,	PUNCT
easat-4161	218	33	2	2	NUM
easat-4161	218	34	,	,	PUNCT
easat-4161	218	35	…	…	PUNCT
easat-4161	218	36	,	,	PUNCT
easat-4161	218	37	𝑛.	𝑛.	NOUN
easat-4161	218	38	ℎ(𝑤1	ℎ(𝑤1	NOUN
easat-4161	218	39	)	)	PUNCT
easat-4161	218	40	=	=	SYM
easat-4161	218	41	1	1	X
easat-4161	218	42	.	.	PUNCT
easat-4161	218	43	ℎ(𝑤2	ℎ(𝑤2	NOUN
easat-4161	218	44	)	)	PUNCT
easat-4161	219	1	=	=	PRON
easat-4161	219	2	{	{	PUNCT
easat-4161	219	3	2	2	NUM
easat-4161	219	4	,	,	PUNCT
easat-4161	219	5	𝑠	𝑠	PROPN
easat-4161	219	6	=	=	SYM
easat-4161	219	7	1	1	NUM
easat-4161	219	8	1	1	NUM
easat-4161	219	9	,	,	PUNCT
easat-4161	219	10	𝑠	𝑠	PROPN
easat-4161	219	11	=	=	SYM
easat-4161	219	12	2	2	NUM
easat-4161	219	13	,	,	PUNCT
easat-4161	219	14	3	3	NUM
easat-4161	219	15	,	,	PUNCT
easat-4161	219	16	…	…	PUNCT
easat-4161	219	17	ℎ(𝑤𝑖	ℎ(𝑤𝑖	PROPN
easat-4161	219	18	)	)	PUNCT
easat-4161	219	19	=	=	SYM
easat-4161	219	20	{	{	PUNCT
easat-4161	219	21	1	1	NUM
easat-4161	219	22	,	,	PUNCT
easat-4161	219	23	𝑖	𝑖	PROPN
easat-4161	219	24	≤	≤	NOUN
easat-4161	220	1	𝑠	𝑠	X
easat-4161	220	2	3𝑖+3	3𝑖+3	PROPN
easat-4161	220	3	4	4	NUM
easat-4161	220	4	−	−	NOUN
easat-4161	220	5	𝑠	𝑠	PROPN
easat-4161	220	6	+	+	NOUN
easat-4161	220	7	1	1	NUM
easat-4161	220	8	,	,	PUNCT
easat-4161	220	9	𝑖	𝑖	PROPN
easat-4161	220	10	>	>	X
easat-4161	220	11	𝑠	𝑠	PROPN
easat-4161	220	12	,	,	PUNCT
easat-4161	220	13	𝑖	𝑖	PROPN
easat-4161	220	14	=	=	SYM
easat-4161	220	15	3	3	NUM
easat-4161	220	16	,	,	PUNCT
easat-4161	220	17	7	7	NUM
easat-4161	220	18	,	,	PUNCT
easat-4161	220	19	11	11	NUM
easat-4161	220	20	,	,	PUNCT
easat-4161	220	21	…	…	PUNCT
easat-4161	220	22	,	,	PUNCT
easat-4161	220	23	𝑛	𝑛	PRON
easat-4161	220	24	−	−	PROPN
easat-4161	220	25	2	2	NUM
easat-4161	220	26	.	.	PUNCT
easat-4161	220	27	ℎ(𝑤𝑖	ℎ(𝑤𝑖	PART
easat-4161	220	28	)	)	PUNCT
easat-4161	220	29	=	=	PRON
easat-4161	220	30	{	{	PUNCT
easat-4161	220	31	1	1	NUM
easat-4161	220	32	,	,	PUNCT
easat-4161	220	33	𝑖	𝑖	DET
easat-4161	220	34	≤	≤	NUM
easat-4161	221	1	𝑠	𝑠	X
easat-4161	221	2	3𝑖+4	3𝑖+4	PROPN
easat-4161	221	3	4	4	NUM
easat-4161	221	4	−	−	NOUN
easat-4161	221	5	𝑠	𝑠	PROPN
easat-4161	221	6	+	+	NOUN
easat-4161	221	7	1	1	NUM
easat-4161	221	8	,	,	PUNCT
easat-4161	221	9	𝑖	𝑖	PROPN
easat-4161	221	10	>	>	X
easat-4161	221	11	𝑠	𝑠	PROPN
easat-4161	221	12	,	,	PUNCT
easat-4161	221	13	𝑖	𝑖	X
easat-4161	221	14	=	=	NOUN
easat-4161	221	15	4	4	NUM
easat-4161	221	16	,	,	PUNCT
easat-4161	221	17	8	8	NUM
easat-4161	221	18	,	,	PUNCT
easat-4161	221	19	12	12	NUM
easat-4161	221	20	,	,	PUNCT
easat-4161	221	21	…	…	PUNCT
easat-4161	221	22	,	,	PUNCT
easat-4161	221	23	𝑛	𝑛	DET
easat-4161	221	24	−	−	PROPN
easat-4161	221	25	1	1	NUM
easat-4161	221	26	.	.	PUNCT
easat-4161	221	27	ℎ(𝑤𝑖	ℎ(𝑤𝑖	PART
easat-4161	221	28	)	)	PUNCT
easat-4161	221	29	=	=	PRON
easat-4161	221	30	{	{	PUNCT
easat-4161	221	31	1	1	NUM
easat-4161	221	32	,	,	PUNCT
easat-4161	221	33	𝑖	𝑖	PRON
easat-4161	221	34	≤	≤	NOUN
easat-4161	221	35	𝑠	𝑠	X
easat-4161	222	1	3𝑖+5	3𝑖+5	PROPN
easat-4161	222	2	4	4	NUM
easat-4161	222	3	−	−	NOUN
easat-4161	222	4	𝑠	𝑠	PROPN
easat-4161	222	5	+	+	NOUN
easat-4161	222	6	1	1	NUM
easat-4161	222	7	,	,	PUNCT
easat-4161	222	8	𝑖	𝑖	PROPN
easat-4161	222	9	>	>	X
easat-4161	222	10	𝑠	𝑠	PROPN
easat-4161	222	11	,	,	PUNCT
easat-4161	222	12	𝑖	𝑖	PROPN
easat-4161	222	13	=	=	SYM
easat-4161	222	14	5	5	NUM
easat-4161	222	15	,	,	PUNCT
easat-4161	222	16	9	9	NUM
easat-4161	222	17	,	,	PUNCT
easat-4161	222	18	13	13	NUM
easat-4161	222	19	,	,	PUNCT
easat-4161	222	20	…	…	PUNCT
easat-4161	222	21	,	,	PUNCT
easat-4161	222	22	𝑛	𝑛	DET
easat-4161	222	23	−	−	PROPN
easat-4161	222	24	4	4	NUM
easat-4161	222	25	.	.	PUNCT
easat-4161	222	26	ℎ(𝑤𝑖	ℎ(𝑤𝑖	PART
easat-4161	222	27	)	)	PUNCT
easat-4161	222	28	=	=	PRON
easat-4161	222	29	{	{	PUNCT
easat-4161	222	30	1	1	NUM
easat-4161	222	31	,	,	PUNCT
easat-4161	222	32	𝑖	𝑖	PROPN
easat-4161	222	33	≤	≤	NUM
easat-4161	222	34	𝑠	𝑠	X
easat-4161	222	35	3𝑖+6	3𝑖+6	PROPN
easat-4161	222	36	4	4	NUM
easat-4161	222	37	−	−	NOUN
easat-4161	222	38	𝑠	𝑠	PROPN
easat-4161	222	39	+	+	NOUN
easat-4161	222	40	1	1	NUM
easat-4161	222	41	,	,	PUNCT
easat-4161	222	42	𝑖	𝑖	PROPN
easat-4161	222	43	>	>	X
easat-4161	222	44	𝑠	𝑠	PROPN
easat-4161	222	45	,	,	PUNCT
easat-4161	222	46	𝑖	𝑖	PROPN
easat-4161	222	47	=	=	SYM
easat-4161	222	48	6	6	NUM
easat-4161	222	49	,	,	PUNCT
easat-4161	222	50	10	10	NUM
easat-4161	222	51	,	,	PUNCT
easat-4161	222	52	14	14	NUM
easat-4161	222	53	,	,	PUNCT
easat-4161	222	54	…	…	PUNCT
easat-4161	222	55	,	,	PUNCT
easat-4161	222	56	𝑛	𝑛	PRON
easat-4161	222	57	−	−	NOUN
easat-4161	222	58	3	3	NUM
easat-4161	222	59	.	.	X
easat-4161	222	60	ℎ(𝑤𝑛	ℎ(𝑤𝑛	PROPN
easat-4161	222	61	)	)	PUNCT
easat-4161	222	62	=	=	PUNCT
easat-4161	222	63	2𝑠	2𝑠	NOUN
easat-4161	222	64	+	+	CCONJ
easat-4161	222	65	3	3	X
easat-4161	222	66	.	.	X
easat-4161	222	67	ℎ(𝑣𝑖	ℎ(𝑣𝑖	VERB
easat-4161	222	68	)	)	PUNCT
easat-4161	222	69	=	=	PUNCT
easat-4161	223	1	3𝑠	3𝑠	NUM
easat-4161	223	2	+	+	CCONJ
easat-4161	223	3	2	2	NUM
easat-4161	223	4	,	,	PUNCT
easat-4161	223	5	𝑖	𝑖	NOUN
easat-4161	223	6	=	=	SYM
easat-4161	223	7	1	1	NUM
easat-4161	223	8	,	,	PUNCT
easat-4161	223	9	2	2	NUM
easat-4161	223	10	,	,	PUNCT
easat-4161	223	11	…	…	PUNCT
easat-4161	223	12	,	,	PUNCT
easat-4161	223	13	𝑛.	𝑛.	NOUN
easat-4161	223	14	ℎ(𝑥1𝑥2	ℎ(𝑥1𝑥2	NOUN
easat-4161	223	15	)	)	PUNCT
easat-4161	223	16	=	=	SYM
easat-4161	223	17	ℎ(𝑥2𝑥3	ℎ(𝑥2𝑥3	PROPN
easat-4161	223	18	)	)	PUNCT
easat-4161	223	19	=	=	PUNCT
easat-4161	223	20	ℎ(𝑥𝑖−1𝑥𝑖	ℎ(𝑥𝑖−1𝑥𝑖	ADJ
easat-4161	223	21	)	)	PUNCT
easat-4161	223	22	=	=	SYM
easat-4161	223	23	ℎ(𝑥𝑖𝑥𝑖+1	ℎ(𝑥𝑖𝑥𝑖+1	PROPN
easat-4161	223	24	)	)	PUNCT
easat-4161	223	25	=	=	SYM
easat-4161	223	26	ℎ(𝑥𝑛−1𝑥𝑛	ℎ(𝑥𝑛−1𝑥𝑛	NOUN
easat-4161	223	27	)	)	PUNCT
easat-4161	223	28	=	=	SYM
easat-4161	223	29	ℎ(𝑥𝑛𝑥1	ℎ(𝑥𝑛𝑥1	X
easat-4161	223	30	)	)	PUNCT
easat-4161	223	31	=	=	SYM
easat-4161	223	32	3𝑠	3𝑠	NUM
easat-4161	223	33	+	+	CCONJ
easat-4161	223	34	1	1	X
easat-4161	223	35	.	.	X
easat-4161	223	36	ℎ(𝑥1𝑦1	ℎ(𝑥1𝑦1	NOUN
easat-4161	223	37	)	)	PUNCT
easat-4161	223	38	=	=	SYM
easat-4161	223	39	ℎ(𝑥2𝑦2	ℎ(𝑥2𝑦2	PROPN
easat-4161	223	40	)	)	PUNCT
easat-4161	223	41	=	=	SYM
easat-4161	224	1	1	1	X
easat-4161	224	2	.	.	X
easat-4161	224	3	ℎ(𝑥𝑖𝑦𝑖	ℎ(𝑥𝑖𝑦𝑖	NUM
easat-4161	224	4	)	)	PUNCT
easat-4161	225	1	=	=	PRON
easat-4161	225	2	{	{	PUNCT
easat-4161	225	3	𝑖+1	𝑖+1	NUM
easat-4161	225	4	4	4	NUM
easat-4161	225	5	,	,	PUNCT
easat-4161	225	6	𝑖	𝑖	NOUN
easat-4161	225	7	=	=	SYM
easat-4161	225	8	3	3	NUM
easat-4161	225	9	,	,	PUNCT
easat-4161	225	10	7	7	NUM
easat-4161	225	11	,	,	PUNCT
easat-4161	225	12	11	11	NUM
easat-4161	225	13	,	,	PUNCT
easat-4161	225	14	…	…	PUNCT
easat-4161	225	15	,	,	PUNCT
easat-4161	226	1	𝑛	𝑛	DET
easat-4161	226	2	−	−	NOUN
easat-4161	226	3	2	2	NUM
easat-4161	226	4	.	.	PUNCT
easat-4161	226	5	𝑖	𝑖	ADP
easat-4161	226	6	4	4	NUM
easat-4161	226	7	,	,	PUNCT
easat-4161	226	8	𝑖	𝑖	NOUN
easat-4161	226	9	=	=	SYM
easat-4161	226	10	4	4	NUM
easat-4161	226	11	,	,	PUNCT
easat-4161	226	12	8	8	NUM
easat-4161	226	13	,	,	PUNCT
easat-4161	226	14	12	12	NUM
easat-4161	226	15	,	,	PUNCT
easat-4161	226	16	…	…	PUNCT
easat-4161	226	17	,	,	PUNCT
easat-4161	226	18	𝑛	𝑛	DET
easat-4161	226	19	−	−	NOUN
easat-4161	226	20	1	1	NUM
easat-4161	226	21	.	.	PUNCT
easat-4161	227	1	𝑖−1	𝑖−1	ADP
easat-4161	227	2	4	4	NUM
easat-4161	227	3	,	,	PUNCT
easat-4161	227	4	𝑖	𝑖	NOUN
easat-4161	227	5	=	=	SYM
easat-4161	227	6	5	5	NUM
easat-4161	227	7	,	,	PUNCT
easat-4161	227	8	9	9	NUM
easat-4161	227	9	,	,	PUNCT
easat-4161	227	10	13	13	NUM
easat-4161	227	11	,	,	PUNCT
easat-4161	227	12	…	…	PUNCT
easat-4161	227	13	,	,	PUNCT
easat-4161	227	14	𝑛	𝑛	DET
easat-4161	227	15	−	−	NOUN
easat-4161	227	16	4	4	NUM
easat-4161	227	17	.	.	PUNCT
easat-4161	228	1	𝑖−2	𝑖−2	PROPN
easat-4161	228	2	4	4	NUM
easat-4161	228	3	,	,	PUNCT
easat-4161	228	4	𝑖	𝑖	NOUN
easat-4161	228	5	=	=	SYM
easat-4161	228	6	6	6	NUM
easat-4161	228	7	,	,	PUNCT
easat-4161	228	8	10	10	NUM
easat-4161	228	9	,	,	PUNCT
easat-4161	228	10	14	14	NUM
easat-4161	228	11	,	,	PUNCT
easat-4161	228	12	…	…	PUNCT
easat-4161	228	13	,	,	PUNCT
easat-4161	228	14	𝑛	𝑛	DET
easat-4161	228	15	−	−	NOUN
easat-4161	228	16	3	3	NUM
easat-4161	228	17	.	.	PUNCT
easat-4161	228	18	ℎ(𝑥𝑛𝑦𝑛	ℎ(𝑥𝑛𝑦𝑛	NOUN
easat-4161	228	19	)	)	PUNCT
easat-4161	228	20	=	=	SYM
easat-4161	229	1	𝑛−1	𝑛−1	NUM
easat-4161	229	2	4	4	NUM
easat-4161	229	3	.	.	PUNCT
easat-4161	230	1	ℎ(𝑥2𝑤1	ℎ(𝑥2𝑤1	NOUN
easat-4161	230	2	)	)	PUNCT
easat-4161	231	1	=	=	NOUN
easat-4161	231	2	2𝑠	2𝑠	NOUN
easat-4161	232	1	+	+	CCONJ
easat-4161	232	2	2	2	X
easat-4161	232	3	.	.	X
easat-4161	232	4	ℎ(𝑥3𝑤2	ℎ(𝑥3𝑤2	NOUN
easat-4161	232	5	)	)	PUNCT
easat-4161	233	1	=	=	PRON
easat-4161	233	2	{	{	PUNCT
easat-4161	233	3	3𝑠	3𝑠	NUM
easat-4161	233	4	+	+	CCONJ
easat-4161	233	5	1	1	NUM
easat-4161	233	6	,	,	PUNCT
easat-4161	233	7	𝑠	𝑠	PROPN
easat-4161	233	8	=	=	SYM
easat-4161	233	9	1	1	NUM
easat-4161	233	10	2𝑠	2𝑠	NOUN
easat-4161	233	11	+	+	CCONJ
easat-4161	233	12	3	3	NUM
easat-4161	233	13	,	,	PUNCT
easat-4161	233	14	𝑠	𝑠	PROPN
easat-4161	233	15	=	=	SYM
easat-4161	233	16	2	2	NUM
easat-4161	233	17	,	,	PUNCT
easat-4161	233	18	3	3	NUM
easat-4161	233	19	,	,	PUNCT
easat-4161	233	20	…	…	PUNCT
easat-4161	233	21	ℎ(𝑥𝑖+1𝑤𝑖	ℎ(𝑥𝑖+1𝑤𝑖	NOUN
easat-4161	233	22	)	)	PUNCT
easat-4161	233	23	=	=	SYM
easat-4161	233	24	{	{	PUNCT
easat-4161	233	25	2𝑠	2𝑠	NOUN
easat-4161	234	1	+	+	CCONJ
easat-4161	234	2	3𝑖+3	3𝑖+3	NUM
easat-4161	234	3	4	4	NUM
easat-4161	234	4	+	+	CCONJ
easat-4161	234	5	1	1	NUM
easat-4161	234	6	,	,	PUNCT
easat-4161	234	7	𝑖	𝑖	PRON
easat-4161	234	8	≤	≤	NOUN
easat-4161	234	9	𝑠	𝑠	NUM
easat-4161	234	10	3𝑠	3𝑠	NUM
easat-4161	234	11	+	+	CCONJ
easat-4161	234	12	1	1	NUM
easat-4161	234	13	,	,	PUNCT
easat-4161	234	14	𝑖	𝑖	PROPN
easat-4161	234	15	>	>	X
easat-4161	234	16	𝑠	𝑠	PROPN
easat-4161	234	17	,	,	PUNCT
easat-4161	234	18	𝑖	𝑖	PROPN
easat-4161	234	19	=	=	SYM
easat-4161	234	20	3	3	NUM
easat-4161	234	21	,	,	PUNCT
easat-4161	234	22	7	7	NUM
easat-4161	234	23	,	,	PUNCT
easat-4161	234	24	11	11	NUM
easat-4161	234	25	,	,	PUNCT
easat-4161	234	26	…	…	PUNCT
easat-4161	234	27	,	,	PUNCT
easat-4161	234	28	𝑛	𝑛	DET
easat-4161	234	29	−	−	PROPN
easat-4161	234	30	2	2	NUM
easat-4161	234	31	.	.	PUNCT
easat-4161	234	32	ℎ(𝑥𝑖+1𝑤𝑖	ℎ(𝑥𝑖+1𝑤𝑖	NOUN
easat-4161	234	33	)	)	PUNCT
easat-4161	234	34	=	=	PRON
easat-4161	234	35	{	{	PUNCT
easat-4161	234	36	2𝑠	2𝑠	NOUN
easat-4161	235	1	+	+	CCONJ
easat-4161	235	2	3𝑖+4	3𝑖+4	NUM
easat-4161	235	3	4	4	NUM
easat-4161	235	4	+	+	SYM
easat-4161	235	5	1	1	NUM
easat-4161	235	6	,	,	PUNCT
easat-4161	235	7	𝑖	𝑖	PRON
easat-4161	235	8	≤	≤	NOUN
easat-4161	235	9	𝑠	𝑠	NUM
easat-4161	235	10	3𝑠	3𝑠	NUM
easat-4161	235	11	+	+	CCONJ
easat-4161	235	12	1	1	NUM
easat-4161	235	13	,	,	PUNCT
easat-4161	235	14	𝑖	𝑖	PROPN
easat-4161	235	15	>	>	X
easat-4161	235	16	𝑠	𝑠	PROPN
easat-4161	235	17	,	,	PUNCT
easat-4161	235	18	𝑖	𝑖	X
easat-4161	235	19	=	=	NOUN
easat-4161	235	20	4	4	NUM
easat-4161	235	21	,	,	PUNCT
easat-4161	235	22	8	8	NUM
easat-4161	235	23	,	,	PUNCT
easat-4161	235	24	12	12	NUM
easat-4161	235	25	,	,	PUNCT
easat-4161	235	26	…	…	PUNCT
easat-4161	235	27	,	,	PUNCT
easat-4161	235	28	𝑛	𝑛	DET
easat-4161	235	29	−	−	NOUN
easat-4161	235	30	1	1	NUM
easat-4161	235	31	.	.	PUNCT
easat-4161	235	32	ℎ(𝑥𝑖+1𝑤𝑖	ℎ(𝑥𝑖+1𝑤𝑖	NOUN
easat-4161	235	33	)	)	PUNCT
easat-4161	236	1	=	=	PRON
easat-4161	236	2	{	{	PUNCT
easat-4161	236	3	2𝑠	2𝑠	NOUN
easat-4161	237	1	+	+	CCONJ
easat-4161	237	2	3𝑖+5	3𝑖+5	PROPN
easat-4161	237	3	4	4	NUM
easat-4161	237	4	+	+	SYM
easat-4161	237	5	1	1	NUM
easat-4161	237	6	,	,	PUNCT
easat-4161	237	7	𝑖	𝑖	PRON
easat-4161	237	8	≤	≤	NOUN
easat-4161	237	9	𝑠	𝑠	NUM
easat-4161	237	10	3𝑠	3𝑠	NUM
easat-4161	237	11	+	+	CCONJ
easat-4161	237	12	1	1	NUM
easat-4161	237	13	,	,	PUNCT
easat-4161	237	14	𝑖	𝑖	PROPN
easat-4161	237	15	>	>	X
easat-4161	237	16	𝑠	𝑠	PROPN
easat-4161	237	17	,	,	PUNCT
easat-4161	237	18	𝑖	𝑖	PROPN
easat-4161	237	19	=	=	SYM
easat-4161	237	20	5	5	NUM
easat-4161	237	21	,	,	PUNCT
easat-4161	237	22	9	9	NUM
easat-4161	237	23	,	,	PUNCT
easat-4161	237	24	13	13	NUM
easat-4161	237	25	,	,	PUNCT
easat-4161	237	26	…	…	PUNCT
easat-4161	237	27	,	,	PUNCT
easat-4161	237	28	𝑛	𝑛	DET
easat-4161	237	29	−	−	NOUN
easat-4161	237	30	4	4	NUM
easat-4161	237	31	.	.	PUNCT
easat-4161	237	32	ℎ(𝑥𝑖+1𝑤𝑖	ℎ(𝑥𝑖+1𝑤𝑖	NOUN
easat-4161	237	33	)	)	PUNCT
easat-4161	237	34	=	=	PRON
easat-4161	237	35	{	{	PUNCT
easat-4161	237	36	2𝑠	2𝑠	NOUN
easat-4161	238	1	+	+	CCONJ
easat-4161	238	2	3𝑖+6	3𝑖+6	NUM
easat-4161	238	3	4	4	NUM
easat-4161	238	4	+	+	CCONJ
easat-4161	238	5	1	1	NUM
easat-4161	238	6	,	,	PUNCT
easat-4161	238	7	𝑖	𝑖	PRON
easat-4161	238	8	≤	≤	NOUN
easat-4161	238	9	𝑠	𝑠	NUM
easat-4161	238	10	3𝑠	3𝑠	NUM
easat-4161	238	11	+	+	CCONJ
easat-4161	238	12	1	1	NUM
easat-4161	238	13	,	,	PUNCT
easat-4161	238	14	𝑖	𝑖	PROPN
easat-4161	238	15	>	>	X
easat-4161	238	16	𝑠	𝑠	PROPN
easat-4161	238	17	,	,	PUNCT
easat-4161	238	18	𝑖	𝑖	PROPN
easat-4161	238	19	=	=	SYM
easat-4161	238	20	6	6	NUM
easat-4161	238	21	,	,	PUNCT
easat-4161	238	22	10	10	NUM
easat-4161	238	23	,	,	PUNCT
easat-4161	238	24	14	14	NUM
easat-4161	238	25	,	,	PUNCT
easat-4161	238	26	…	…	PUNCT
easat-4161	238	27	,	,	PUNCT
easat-4161	238	28	𝑛	𝑛	DET
easat-4161	238	29	−	−	NOUN
easat-4161	238	30	3	3	NUM
easat-4161	238	31	.	.	PUNCT
easat-4161	238	32	ℎ(𝑥1𝑤𝑛	ℎ(𝑥1𝑤𝑛	NOUN
easat-4161	238	33	)	)	PUNCT
easat-4161	238	34	=	=	SYM
easat-4161	238	35	ℎ(𝑥𝑛𝑤𝑛−1	ℎ(𝑥𝑛𝑤𝑛−1	PROPN
easat-4161	238	36	)	)	PUNCT
easat-4161	238	37	=	=	SYM
easat-4161	239	1	3𝑛+5	3𝑛+5	NOUN
easat-4161	239	2	4	4	NUM
easat-4161	239	3	−	−	NOUN
easat-4161	239	4	1	1	NUM
easat-4161	239	5	=	=	SYM
easat-4161	239	6	3𝑠	3𝑠	NUM
easat-4161	239	7	+	+	CCONJ
easat-4161	239	8	1	1	X
easat-4161	239	9	.	.	X
easat-4161	239	10	ℎ(𝑥𝑖𝑤𝑖−1	ℎ(𝑥𝑖𝑤𝑖−1	NOUN
easat-4161	239	11	)	)	PUNCT
easat-4161	239	12	=	=	PRON
easat-4161	239	13	{	{	PUNCT
easat-4161	239	14	2𝑠	2𝑠	NOUN
easat-4161	240	1	+	+	CCONJ
easat-4161	240	2	𝑖	𝑖	X
easat-4161	240	3	,	,	PUNCT
easat-4161	240	4	𝑖	𝑖	PROPN
easat-4161	240	5	≤	≤	NUM
easat-4161	240	6	𝑠	𝑠	NUM
easat-4161	240	7	3𝑠	3𝑠	NUM
easat-4161	240	8	+	+	CCONJ
easat-4161	240	9	1	1	NUM
easat-4161	240	10	,	,	PUNCT
easat-4161	240	11	𝑖	𝑖	PROPN
easat-4161	240	12	>	>	X
easat-4161	240	13	𝑠	𝑠	PROPN
easat-4161	240	14	ℎ(𝑥1𝑣2	ℎ(𝑥1𝑣2	PROPN
easat-4161	240	15	)	)	PUNCT
easat-4161	240	16	=	=	SYM
easat-4161	240	17	ℎ(𝑥𝑖𝑣𝑖+1	ℎ(𝑥𝑖𝑣𝑖+1	PROPN
easat-4161	240	18	)	)	PUNCT
easat-4161	240	19	=	=	SYM
easat-4161	240	20	ℎ(𝑥𝑛−1𝑣𝑛	ℎ(𝑥𝑛−1𝑣𝑛	NOUN
easat-4161	240	21	)	)	PUNCT
easat-4161	240	22	=	=	SYM
easat-4161	240	23	ℎ(𝑥𝑛𝑣1	ℎ(𝑥𝑛𝑣1	NOUN
easat-4161	240	24	)	)	PUNCT
easat-4161	240	25	=	=	SYM
easat-4161	240	26	3𝑠	3𝑠	NUM
easat-4161	240	27	+	+	CCONJ
easat-4161	240	28	2	2	X
easat-4161	240	29	.	.	X
easat-4161	240	30	ℎ(𝑦𝑖𝑤𝑖	ℎ(𝑦𝑖𝑤𝑖	NOUN
easat-4161	240	31	)	)	PUNCT
easat-4161	240	32	=	=	SYM
easat-4161	240	33	1	1	NUM
easat-4161	240	34	,	,	PUNCT
easat-4161	240	35	𝑖	𝑖	NOUN
easat-4161	240	36	=	=	SYM
easat-4161	240	37	1	1	NUM
easat-4161	240	38	,	,	PUNCT
easat-4161	240	39	2	2	NUM
easat-4161	240	40	,	,	PUNCT
easat-4161	240	41	…	…	PUNCT
easat-4161	240	42	,	,	PUNCT
easat-4161	240	43	𝑛.	𝑛.	NOUN
easat-4161	240	44	ℎ(𝑦1𝑣1	ℎ(𝑦1𝑣1	NOUN
easat-4161	240	45	)	)	PUNCT
easat-4161	240	46	=	=	SYM
easat-4161	240	47	1	1	X
easat-4161	240	48	.	.	X
easat-4161	240	49	489	489	NUM
easat-4161	240	50	edelweiss	edelweiss	PROPN
easat-4161	240	51	applied	apply	VERB
easat-4161	240	52	science	science	NOUN
easat-4161	240	53	and	and	CCONJ
easat-4161	240	54	technology	technology	NOUN
easat-4161	240	55	issn	issn	PROPN
easat-4161	240	56	:	:	PUNCT
easat-4161	240	57	2576	2576	NUM
easat-4161	240	58	-	-	SYM
easat-4161	240	59	8484	8484	NUM
easat-4161	240	60	vol	vol	NOUN
easat-4161	240	61	.	.	PROPN
easat-4161	241	1	9	9	NUM
easat-4161	241	2	,	,	PUNCT
easat-4161	241	3	no	no	INTJ
easat-4161	241	4	.	.	NOUN
easat-4161	241	5	1	1	NUM
easat-4161	241	6	:	:	PUNCT
easat-4161	241	7	481	481	NUM
easat-4161	241	8	-	-	SYM
easat-4161	241	9	492	492	NUM
easat-4161	241	10	,	,	PUNCT
easat-4161	241	11	2025	2025	NUM
easat-4161	241	12	doi	doi	NOUN
easat-4161	241	13	:	:	PUNCT
easat-4161	241	14	10.55214/25768484.v9i1.4161	10.55214/25768484.v9i1.4161	NUM
easat-4161	241	15	©	©	PROPN
easat-4161	241	16	2025	2025	NUM
easat-4161	241	17	by	by	ADP
easat-4161	241	18	the	the	DET
easat-4161	241	19	authors	author	NOUN
easat-4161	241	20	;	;	PUNCT
easat-4161	241	21	licensee	licensee	PROPN
easat-4161	241	22	learning	learn	VERB
easat-4161	241	23	gate	gate	NOUN
easat-4161	241	24	ℎ(𝑦2𝑣2	ℎ(𝑦2𝑣2	NOUN
easat-4161	241	25	)	)	PUNCT
easat-4161	241	26	=	=	SYM
easat-4161	241	27	2	2	X
easat-4161	241	28	.	.	X
easat-4161	241	29	ℎ(𝑦𝑖𝑣𝑖	ℎ(𝑦𝑖𝑣𝑖	PROPN
easat-4161	241	30	)	)	PUNCT
easat-4161	242	1	=	=	PRON
easat-4161	242	2	{	{	PUNCT
easat-4161	242	3	3𝑖+3	3𝑖+3	PROPN
easat-4161	242	4	4	4	NUM
easat-4161	242	5	,	,	PUNCT
easat-4161	242	6	𝑖	𝑖	PROPN
easat-4161	242	7	=	=	SYM
easat-4161	242	8	3	3	NUM
easat-4161	242	9	,	,	PUNCT
easat-4161	242	10	7	7	NUM
easat-4161	242	11	,	,	PUNCT
easat-4161	242	12	11	11	NUM
easat-4161	242	13	,	,	PUNCT
easat-4161	242	14	…	…	PUNCT
easat-4161	242	15	,	,	PUNCT
easat-4161	242	16	𝑛	𝑛	DET
easat-4161	242	17	−	−	PROPN
easat-4161	242	18	2	2	NUM
easat-4161	242	19	,	,	PUNCT
easat-4161	242	20	3𝑖+4	3𝑖+4	NUM
easat-4161	242	21	4	4	NUM
easat-4161	242	22	,	,	PUNCT
easat-4161	242	23	𝑖	𝑖	NOUN
easat-4161	242	24	=	=	SYM
easat-4161	242	25	4	4	NUM
easat-4161	242	26	,	,	PUNCT
easat-4161	242	27	8	8	NUM
easat-4161	242	28	,	,	PUNCT
easat-4161	242	29	12	12	NUM
easat-4161	242	30	,	,	PUNCT
easat-4161	242	31	…	…	PUNCT
easat-4161	242	32	,	,	PUNCT
easat-4161	242	33	𝑛	𝑛	DET
easat-4161	242	34	−	−	PROPN
easat-4161	242	35	1	1	NUM
easat-4161	242	36	,	,	PUNCT
easat-4161	242	37	3𝑖+5	3𝑖+5	PROPN
easat-4161	242	38	4	4	NUM
easat-4161	242	39	,	,	PUNCT
easat-4161	242	40	𝑖	𝑖	NOUN
easat-4161	242	41	=	=	SYM
easat-4161	242	42	5	5	NUM
easat-4161	242	43	,	,	PUNCT
easat-4161	242	44	9	9	NUM
easat-4161	242	45	,	,	PUNCT
easat-4161	242	46	13	13	NUM
easat-4161	242	47	,	,	PUNCT
easat-4161	242	48	…	…	PUNCT
easat-4161	242	49	,	,	PUNCT
easat-4161	242	50	𝑛	𝑛	DET
easat-4161	242	51	−	−	PROPN
easat-4161	242	52	4	4	NUM
easat-4161	242	53	,	,	PUNCT
easat-4161	242	54	3𝑖+6	3𝑖+6	PROPN
easat-4161	242	55	4	4	NUM
easat-4161	242	56	,	,	PUNCT
easat-4161	242	57	𝑖	𝑖	NOUN
easat-4161	242	58	=	=	SYM
easat-4161	242	59	6	6	NUM
easat-4161	242	60	,	,	PUNCT
easat-4161	242	61	10	10	NUM
easat-4161	242	62	,	,	PUNCT
easat-4161	242	63	14	14	NUM
easat-4161	242	64	,	,	PUNCT
easat-4161	242	65	…	…	PUNCT
easat-4161	242	66	,	,	PUNCT
easat-4161	242	67	𝑛	𝑛	DET
easat-4161	242	68	−	−	PROPN
easat-4161	242	69	3	3	NUM
easat-4161	242	70	,	,	PUNCT
easat-4161	242	71	ℎ(𝑦𝑛𝑣𝑛	ℎ(𝑦𝑛𝑣𝑛	ADJ
easat-4161	242	72	)	)	PUNCT
easat-4161	242	73	=	=	SYM
easat-4161	243	1	3𝑛+5	3𝑛+5	NUM
easat-4161	243	2	4	4	NUM
easat-4161	243	3	.	.	PUNCT
easat-4161	244	1	ℎ(𝑤1𝑣1	ℎ(𝑤1𝑣1	NOUN
easat-4161	244	2	)	)	PUNCT
easat-4161	244	3	=	=	SYM
easat-4161	244	4	ℎ(𝑤2𝑣2	ℎ(𝑤2𝑣2	NOUN
easat-4161	244	5	)	)	PUNCT
easat-4161	244	6	=	=	NOUN
easat-4161	244	7	2𝑠	2𝑠	NOUN
easat-4161	244	8	+	+	CCONJ
easat-4161	244	9	1	1	X
easat-4161	244	10	.	.	X
easat-4161	244	11	ℎ(𝑤𝑖𝑣𝑖	ℎ(𝑤𝑖𝑣𝑖	NOUN
easat-4161	244	12	)	)	PUNCT
easat-4161	245	1	=	=	PRON
easat-4161	245	2	{	{	PUNCT
easat-4161	245	3	𝑖+1	𝑖+1	PUNCT
easat-4161	245	4	4	4	NUM
easat-4161	245	5	+	+	CCONJ
easat-4161	245	6	2𝑠	2𝑠	NOUN
easat-4161	245	7	,	,	PUNCT
easat-4161	245	8	𝑖	𝑖	NOUN
easat-4161	245	9	=	=	SYM
easat-4161	245	10	3	3	NUM
easat-4161	245	11	,	,	PUNCT
easat-4161	245	12	7	7	NUM
easat-4161	245	13	,	,	PUNCT
easat-4161	245	14	11	11	NUM
easat-4161	245	15	,	,	PUNCT
easat-4161	245	16	…	…	PUNCT
easat-4161	245	17	,	,	PUNCT
easat-4161	245	18	𝑛	𝑛	DET
easat-4161	245	19	−	−	PROPN
easat-4161	245	20	2	2	NUM
easat-4161	245	21	,	,	PUNCT
easat-4161	245	22	𝑖	𝑖	PRON
easat-4161	245	23	4	4	NUM
easat-4161	245	24	+	+	CCONJ
easat-4161	245	25	2𝑠	2𝑠	NOUN
easat-4161	245	26	,	,	PUNCT
easat-4161	245	27	𝑖	𝑖	NOUN
easat-4161	245	28	=	=	SYM
easat-4161	245	29	4	4	NUM
easat-4161	245	30	,	,	PUNCT
easat-4161	245	31	8	8	NUM
easat-4161	245	32	,	,	PUNCT
easat-4161	245	33	12	12	NUM
easat-4161	245	34	,	,	PUNCT
easat-4161	245	35	…	…	PUNCT
easat-4161	245	36	,	,	PUNCT
easat-4161	245	37	𝑛	𝑛	DET
easat-4161	245	38	−	−	PROPN
easat-4161	245	39	1	1	NUM
easat-4161	245	40	,	,	PUNCT
easat-4161	245	41	𝑖−1	𝑖−1	PROPN
easat-4161	245	42	4	4	NUM
easat-4161	245	43	+	+	NOUN
easat-4161	245	44	2𝑠	2𝑠	NOUN
easat-4161	245	45	,	,	PUNCT
easat-4161	245	46	𝑖	𝑖	X
easat-4161	245	47	=	=	SYM
easat-4161	245	48	5	5	NUM
easat-4161	245	49	,	,	PUNCT
easat-4161	245	50	9	9	NUM
easat-4161	245	51	,	,	PUNCT
easat-4161	245	52	13	13	NUM
easat-4161	245	53	,	,	PUNCT
easat-4161	245	54	…	…	PUNCT
easat-4161	245	55	,	,	PUNCT
easat-4161	245	56	𝑛	𝑛	DET
easat-4161	245	57	−	−	PROPN
easat-4161	245	58	4	4	NUM
easat-4161	245	59	,	,	PUNCT
easat-4161	245	60	𝑖−2	𝑖−2	PROPN
easat-4161	245	61	4	4	NUM
easat-4161	245	62	+	+	NOUN
easat-4161	245	63	2𝑠	2𝑠	NOUN
easat-4161	245	64	,	,	PUNCT
easat-4161	245	65	𝑖	𝑖	NOUN
easat-4161	245	66	=	=	SYM
easat-4161	245	67	6	6	NUM
easat-4161	245	68	,	,	PUNCT
easat-4161	245	69	10	10	NUM
easat-4161	245	70	,	,	PUNCT
easat-4161	245	71	14	14	NUM
easat-4161	245	72	,	,	PUNCT
easat-4161	245	73	…	…	PUNCT
easat-4161	245	74	,	,	PUNCT
easat-4161	245	75	𝑛	𝑛	DET
easat-4161	245	76	−	−	PROPN
easat-4161	245	77	3	3	NUM
easat-4161	245	78	,	,	PUNCT
easat-4161	245	79	ℎ(𝑤𝑛𝑣𝑛	ℎ(𝑤𝑛𝑣𝑛	NOUN
easat-4161	245	80	)	)	PUNCT
easat-4161	245	81	=	=	SYM
easat-4161	245	82	𝑛	𝑛	DET
easat-4161	245	83	−	−	NUM
easat-4161	245	84	1	1	NUM
easat-4161	245	85	4	4	NUM
easat-4161	245	86	+	+	CCONJ
easat-4161	245	87	2𝑠	2𝑠	NOUN
easat-4161	245	88	based	base	VERB
easat-4161	245	89	on	on	ADP
easat-4161	245	90	this	this	DET
easat-4161	245	91	function	function	NOUN
easat-4161	245	92	,	,	PUNCT
easat-4161	245	93	it	it	PRON
easat-4161	245	94	can	can	AUX
easat-4161	245	95	be	be	AUX
easat-4161	245	96	shown	show	VERB
easat-4161	245	97	that	that	SCONJ
easat-4161	245	98	all	all	DET
easat-4161	245	99	vertices	vertice	VERB
easat-4161	245	100	weights	weight	NOUN
easat-4161	245	101	are	be	AUX
easat-4161	245	102	different	different	ADJ
easat-4161	245	103	and	and	CCONJ
easat-4161	245	104	the	the	DET
easat-4161	245	105	maximum	maximum	ADJ
easat-4161	245	106	value	value	NOUN
easat-4161	245	107	of	of	ADP
easat-4161	245	108	the	the	DET
easat-4161	245	109	function	function	NOUN
easat-4161	245	110	is	be	AUX
easat-4161	245	111	⌈	⌈	SYM
easat-4161	245	112	𝟑+𝟑𝒏	𝟑+𝟑𝒏	NOUN
easat-4161	245	113	𝟒	𝟒	X
easat-4161	245	114	⌉.	⌉.	ADV
easat-4161	245	115	this	this	PRON
easat-4161	245	116	shows	show	VERB
easat-4161	245	117	that	that	SCONJ
easat-4161	245	118	ℎ	ℎ	PROPN
easat-4161	245	119	:	:	PUNCT
easat-4161	245	120	𝑉	𝑉	PROPN
easat-4161	245	121	∪	∪	NOUN
easat-4161	245	122	𝐸	𝐸	PROPN
easat-4161	245	123	→	→	SYM
easat-4161	245	124	{	{	PUNCT
easat-4161	245	125	1	1	NUM
easat-4161	245	126	,	,	PUNCT
easat-4161	245	127	2	2	NUM
easat-4161	245	128	,	,	PUNCT
easat-4161	245	129	3,⋯	3,⋯	NUM
easat-4161	245	130	,	,	PUNCT
easat-4161	245	131	⌈	⌈	X
easat-4161	245	132	𝟑+𝟑𝒏	𝟑+𝟑𝒏	X
easat-4161	245	133	𝟒	𝟒	NUM
easat-4161	245	134	⌉	⌉	NOUN
easat-4161	245	135	}	}	PUNCT
easat-4161	245	136	is	be	AUX
easat-4161	245	137	a	a	DET
easat-4161	245	138	function	function	NOUN
easat-4161	245	139	a	a	DET
easat-4161	245	140	total	total	ADJ
easat-4161	245	141	vertex	vertex	NOUN
easat-4161	245	142	irregular	irregular	ADJ
easat-4161	245	143	𝑘	𝑘	DET
easat-4161	245	144	−	−	NOUN
easat-4161	245	145	𝑙𝑎𝑏𝑒𝑙𝑙𝑖𝑛𝑔	𝑙𝑎𝑏𝑒𝑙𝑙𝑖𝑛𝑔	NOUN
easat-4161	245	146	where	where	SCONJ
easat-4161	245	147	𝑘	𝑘	NOUN
easat-4161	245	148	=	=	PUNCT
easat-4161	245	149	⌈	⌈	NOUN
easat-4161	245	150	𝟑+𝟑𝒏	𝟑+𝟑𝒏	NOUN
easat-4161	245	151	𝟒	𝟒	X
easat-4161	245	152	⌉.	⌉.	ADV
easat-4161	245	153	thus	thus	ADV
easat-4161	245	154	it	it	PRON
easat-4161	245	155	is	be	AUX
easat-4161	245	156	obtained	obtain	VERB
easat-4161	245	157	that	that	SCONJ
easat-4161	245	158	𝒕𝒗𝒔(𝓗𝒏	𝒕𝒗𝒔(𝓗𝒏	NOUN
easat-4161	245	159	)	)	PUNCT
easat-4161	245	160	≤	≤	NOUN
easat-4161	246	1	⌈	⌈	SYM
easat-4161	246	2	𝟑+𝟑𝒏	𝟑+𝟑𝒏	NOUN
easat-4161	246	3	𝟒	𝟒	NUM
easat-4161	246	4	⌉	⌉	X
easat-4161	246	5	for	for	ADP
easat-4161	246	6	𝑛	𝑛	PRON
easat-4161	246	7	=	=	SYM
easat-4161	246	8	4𝑡	4𝑡	NOUN
easat-4161	246	9	+	+	CCONJ
easat-4161	246	10	1	1	NUM
easat-4161	246	11	,	,	PUNCT
easat-4161	246	12	where	where	SCONJ
easat-4161	246	13	𝑡	𝑡	PROPN
easat-4161	246	14	is	be	AUX
easat-4161	246	15	some	some	DET
easat-4161	246	16	positive	positive	ADJ
easat-4161	246	17	integer	integer	NOUN
easat-4161	246	18	.	.	PUNCT
easat-4161	247	1	case	case	NOUN
easat-4161	247	2	4	4	NUM
easat-4161	247	3	.	.	X
easat-4161	248	1	for	for	ADP
easat-4161	248	2	𝑛	𝑛	NOUN
easat-4161	248	3	=	=	SYM
easat-4161	248	4	4𝑡	4𝑡	NOUN
easat-4161	248	5	+	+	CCONJ
easat-4161	248	6	2	2	NUM
easat-4161	248	7	,	,	PUNCT
easat-4161	248	8	where	where	SCONJ
easat-4161	248	9	𝑡	𝑡	PROPN
easat-4161	248	10	is	be	AUX
easat-4161	248	11	some	some	DET
easat-4161	248	12	positive	positive	ADJ
easat-4161	248	13	integer	integer	NOUN
easat-4161	248	14	.	.	PUNCT
easat-4161	249	1	the	the	DET
easat-4161	249	2	total	total	ADJ
easat-4161	249	3	vertex	vertex	NOUN
easat-4161	249	4	labeling	labeling	NOUN
easat-4161	249	5	𝑞	𝑞	X
easat-4161	249	6	is	be	AUX
easat-4161	249	7	𝑞(𝑥1	𝑞(𝑥1	ADV
easat-4161	249	8	)	)	PUNCT
easat-4161	250	1	=	=	SYM
easat-4161	250	2	1	1	X
easat-4161	250	3	.	.	X
easat-4161	250	4	𝑞(𝑥2	𝑞(𝑥2	NOUN
easat-4161	250	5	)	)	PUNCT
easat-4161	251	1	=	=	SYM
easat-4161	251	2	𝑠	𝑠	PROPN
easat-4161	251	3	+	+	NOUN
easat-4161	251	4	1	1	NUM
easat-4161	251	5	.	.	NUM
easat-4161	251	6	𝑞(𝑥𝑖	𝑞(𝑥𝑖	NUM
easat-4161	251	7	)	)	PUNCT
easat-4161	251	8	=	=	PRON
easat-4161	251	9	{	{	PUNCT
easat-4161	251	10	3𝑖+3	3𝑖+3	PROPN
easat-4161	251	11	4	4	NUM
easat-4161	251	12	+	+	CCONJ
easat-4161	251	13	𝑠	𝑠	PROPN
easat-4161	251	14	−	−	NOUN
easat-4161	251	15	𝑖	𝑖	PROPN
easat-4161	252	1	+	+	NOUN
easat-4161	252	2	1	1	NUM
easat-4161	252	3	,	,	PUNCT
easat-4161	252	4	𝑖	𝑖	PRON
easat-4161	252	5	≤	≤	NOUN
easat-4161	252	6	𝑠	𝑠	X
easat-4161	252	7	3𝑖+3	3𝑖+3	PROPN
easat-4161	252	8	4	4	NUM
easat-4161	252	9	,	,	PUNCT
easat-4161	253	1	𝑖	𝑖	PROPN
easat-4161	253	2	>	>	X
easat-4161	253	3	𝑠	𝑠	PROPN
easat-4161	253	4	,	,	PUNCT
easat-4161	253	5	𝑖	𝑖	PROPN
easat-4161	253	6	=	=	SYM
easat-4161	253	7	3	3	NUM
easat-4161	253	8	,	,	PUNCT
easat-4161	253	9	7	7	NUM
easat-4161	253	10	,	,	PUNCT
easat-4161	253	11	11	11	NUM
easat-4161	253	12	,	,	PUNCT
easat-4161	253	13	…	…	PUNCT
easat-4161	253	14	,	,	PUNCT
easat-4161	253	15	𝑛	𝑛	DET
easat-4161	253	16	−	−	PROPN
easat-4161	253	17	3	3	NUM
easat-4161	253	18	.	.	PUNCT
easat-4161	253	19	𝑞(𝑥𝑖	𝑞(𝑥𝑖	NUM
easat-4161	253	20	)	)	PUNCT
easat-4161	253	21	=	=	PRON
easat-4161	253	22	{	{	PUNCT
easat-4161	253	23	3𝑖+4	3𝑖+4	NUM
easat-4161	253	24	4	4	NUM
easat-4161	254	1	+	+	CCONJ
easat-4161	254	2	𝑠	𝑠	PROPN
easat-4161	254	3	−	−	NOUN
easat-4161	254	4	𝑖	𝑖	PROPN
easat-4161	255	1	+	+	NOUN
easat-4161	255	2	1	1	NUM
easat-4161	255	3	,	,	PUNCT
easat-4161	255	4	𝑖	𝑖	PRON
easat-4161	255	5	≤	≤	NUM
easat-4161	255	6	𝑠	𝑠	X
easat-4161	255	7	3𝑖+4	3𝑖+4	PROPN
easat-4161	255	8	4	4	NUM
easat-4161	255	9	,	,	PUNCT
easat-4161	256	1	𝑖	𝑖	PROPN
easat-4161	256	2	>	>	X
easat-4161	256	3	𝑠	𝑠	PROPN
easat-4161	256	4	,	,	PUNCT
easat-4161	256	5	𝑖	𝑖	X
easat-4161	256	6	=	=	NOUN
easat-4161	256	7	4	4	NUM
easat-4161	256	8	,	,	PUNCT
easat-4161	256	9	8	8	NUM
easat-4161	256	10	,	,	PUNCT
easat-4161	256	11	12	12	NUM
easat-4161	256	12	,	,	PUNCT
easat-4161	256	13	…	…	PUNCT
easat-4161	256	14	,	,	PUNCT
easat-4161	257	1	𝑛	𝑛	DET
easat-4161	257	2	−	−	PROPN
easat-4161	257	3	2	2	NUM
easat-4161	257	4	.	.	NUM
easat-4161	257	5	𝑞(𝑥𝑖	𝑞(𝑥𝑖	NUM
easat-4161	257	6	)	)	PUNCT
easat-4161	258	1	=	=	PRON
easat-4161	258	2	{	{	PUNCT
easat-4161	258	3	3𝑖+5	3𝑖+5	PROPN
easat-4161	258	4	4	4	NUM
easat-4161	258	5	+	+	NUM
easat-4161	258	6	𝑠	𝑠	PROPN
easat-4161	258	7	−	−	NOUN
easat-4161	258	8	𝑖	𝑖	PROPN
easat-4161	259	1	+	+	NOUN
easat-4161	259	2	1	1	NUM
easat-4161	259	3	,	,	PUNCT
easat-4161	259	4	𝑖	𝑖	PRON
easat-4161	259	5	≤	≤	NOUN
easat-4161	259	6	𝑠	𝑠	X
easat-4161	259	7	3𝑖+5	3𝑖+5	PROPN
easat-4161	259	8	4	4	NUM
easat-4161	259	9	,	,	PUNCT
easat-4161	259	10	𝑖	𝑖	PROPN
easat-4161	259	11	>	>	X
easat-4161	259	12	𝑠	𝑠	PROPN
easat-4161	259	13	,	,	PUNCT
easat-4161	259	14	𝑖	𝑖	PROPN
easat-4161	259	15	=	=	SYM
easat-4161	259	16	5	5	NUM
easat-4161	259	17	,	,	PUNCT
easat-4161	259	18	9	9	NUM
easat-4161	259	19	,	,	PUNCT
easat-4161	259	20	13	13	NUM
easat-4161	259	21	,	,	PUNCT
easat-4161	259	22	…	…	PUNCT
easat-4161	259	23	,	,	PUNCT
easat-4161	259	24	𝑛	𝑛	DET
easat-4161	259	25	−	−	PROPN
easat-4161	259	26	1	1	NUM
easat-4161	259	27	.	.	PUNCT
easat-4161	259	28	𝑞(𝑥𝑖	𝑞(𝑥𝑖	NUM
easat-4161	259	29	)	)	PUNCT
easat-4161	259	30	=	=	PRON
easat-4161	259	31	{	{	PUNCT
easat-4161	259	32	3𝑖+6	3𝑖+6	PROPN
easat-4161	259	33	4	4	NUM
easat-4161	260	1	+	+	CCONJ
easat-4161	260	2	𝑠	𝑠	PROPN
easat-4161	260	3	−	−	NOUN
easat-4161	260	4	𝑖	𝑖	PROPN
easat-4161	261	1	+	+	NOUN
easat-4161	261	2	1	1	NUM
easat-4161	261	3	,	,	PUNCT
easat-4161	261	4	𝑖	𝑖	DET
easat-4161	261	5	≤	≤	NUM
easat-4161	261	6	𝑠	𝑠	X
easat-4161	262	1	3𝑖+6	3𝑖+6	PROPN
easat-4161	262	2	4	4	NUM
easat-4161	262	3	,	,	PUNCT
easat-4161	262	4	𝑖	𝑖	PROPN
easat-4161	262	5	>	>	X
easat-4161	262	6	𝑠	𝑠	PROPN
easat-4161	262	7	,	,	PUNCT
easat-4161	262	8	𝑖	𝑖	PROPN
easat-4161	262	9	=	=	SYM
easat-4161	262	10	6	6	NUM
easat-4161	262	11	,	,	PUNCT
easat-4161	262	12	10	10	NUM
easat-4161	262	13	,	,	PUNCT
easat-4161	262	14	14	14	NUM
easat-4161	262	15	,	,	PUNCT
easat-4161	262	16	…	…	PUNCT
easat-4161	262	17	,	,	PUNCT
easat-4161	262	18	𝑛	𝑛	DET
easat-4161	262	19	−	−	PROPN
easat-4161	262	20	4	4	NUM
easat-4161	262	21	.	.	PUNCT
easat-4161	262	22	𝑞(𝑥𝑛	𝑞(𝑥𝑛	ADJ
easat-4161	262	23	)	)	PUNCT
easat-4161	262	24	=	=	SYM
easat-4161	263	1	3𝑛+6	3𝑛+6	NOUN
easat-4161	263	2	4	4	NUM
easat-4161	263	3	.	.	PUNCT
easat-4161	264	1	𝑞(𝑦𝑖	𝑞(𝑦𝑖	ADV
easat-4161	264	2	)	)	PUNCT
easat-4161	265	1	=	=	SYM
easat-4161	265	2	1	1	NUM
easat-4161	265	3	,	,	PUNCT
easat-4161	265	4	𝑖	𝑖	NOUN
easat-4161	265	5	=	=	SYM
easat-4161	265	6	1	1	NUM
easat-4161	265	7	,	,	PUNCT
easat-4161	265	8	2	2	NUM
easat-4161	265	9	,	,	PUNCT
easat-4161	265	10	…	…	PUNCT
easat-4161	265	11	,	,	PUNCT
easat-4161	265	12	𝑛.	𝑛.	NOUN
easat-4161	265	13	𝑞(𝑤1	𝑞(𝑤1	NOUN
easat-4161	265	14	)	)	PUNCT
easat-4161	265	15	=	=	SYM
easat-4161	265	16	1	1	X
easat-4161	265	17	.	.	X
easat-4161	265	18	𝑞(𝑤2	𝑞(𝑤2	NOUN
easat-4161	265	19	)	)	PUNCT
easat-4161	265	20	=	=	PRON
easat-4161	265	21	{	{	PUNCT
easat-4161	265	22	2	2	NUM
easat-4161	265	23	,	,	PUNCT
easat-4161	265	24	𝑠	𝑠	PROPN
easat-4161	265	25	=	=	SYM
easat-4161	265	26	1	1	NUM
easat-4161	265	27	1	1	NUM
easat-4161	265	28	,	,	PUNCT
easat-4161	265	29	𝑠	𝑠	PROPN
easat-4161	265	30	=	=	SYM
easat-4161	265	31	2	2	NUM
easat-4161	265	32	,	,	PUNCT
easat-4161	265	33	3	3	NUM
easat-4161	265	34	,	,	PUNCT
easat-4161	265	35	…	…	PUNCT
easat-4161	265	36	490	490	NUM
easat-4161	265	37	edelweiss	edelweiss	PROPN
easat-4161	265	38	applied	apply	VERB
easat-4161	265	39	science	science	NOUN
easat-4161	265	40	and	and	CCONJ
easat-4161	265	41	technology	technology	NOUN
easat-4161	265	42	issn	issn	PROPN
easat-4161	265	43	:	:	PUNCT
easat-4161	265	44	2576	2576	NUM
easat-4161	265	45	-	-	SYM
easat-4161	265	46	8484	8484	NUM
easat-4161	265	47	vol	vol	NOUN
easat-4161	265	48	.	.	PROPN
easat-4161	266	1	9	9	NUM
easat-4161	266	2	,	,	PUNCT
easat-4161	266	3	no	no	INTJ
easat-4161	266	4	.	.	NOUN
easat-4161	266	5	1	1	NUM
easat-4161	266	6	:	:	PUNCT
easat-4161	266	7	481	481	NUM
easat-4161	266	8	-	-	SYM
easat-4161	266	9	492	492	NUM
easat-4161	266	10	,	,	PUNCT
easat-4161	266	11	2025	2025	NUM
easat-4161	266	12	doi	doi	NOUN
easat-4161	266	13	:	:	PUNCT
easat-4161	266	14	10.55214/25768484.v9i1.4161	10.55214/25768484.v9i1.4161	NUM
easat-4161	266	15	©	©	PROPN
easat-4161	266	16	2025	2025	NUM
easat-4161	266	17	by	by	ADP
easat-4161	266	18	the	the	DET
easat-4161	266	19	authors	author	NOUN
easat-4161	266	20	;	;	PUNCT
easat-4161	266	21	licensee	licensee	PROPN
easat-4161	266	22	learning	learning	NOUN
easat-4161	266	23	gate	gate	VERB
easat-4161	266	24	𝑞(𝑤𝑖	𝑞(𝑤𝑖	PROPN
easat-4161	266	25	)	)	PUNCT
easat-4161	266	26	=	=	PRON
easat-4161	266	27	{	{	PUNCT
easat-4161	266	28	1	1	NUM
easat-4161	266	29	,	,	PUNCT
easat-4161	266	30	𝑖	𝑖	PROPN
easat-4161	266	31	≤	≤	NOUN
easat-4161	267	1	𝑠	𝑠	X
easat-4161	267	2	3𝑖+3	3𝑖+3	PROPN
easat-4161	267	3	4	4	NUM
easat-4161	267	4	−	−	NOUN
easat-4161	267	5	𝑠	𝑠	PROPN
easat-4161	267	6	+	+	NOUN
easat-4161	267	7	1	1	NUM
easat-4161	267	8	,	,	PUNCT
easat-4161	267	9	𝑖	𝑖	PROPN
easat-4161	267	10	>	>	X
easat-4161	267	11	𝑠	𝑠	PROPN
easat-4161	267	12	,	,	PUNCT
easat-4161	267	13	𝑖	𝑖	PROPN
easat-4161	267	14	=	=	SYM
easat-4161	267	15	3	3	NUM
easat-4161	267	16	,	,	PUNCT
easat-4161	267	17	7	7	NUM
easat-4161	267	18	,	,	PUNCT
easat-4161	267	19	11	11	NUM
easat-4161	267	20	,	,	PUNCT
easat-4161	267	21	…	…	PUNCT
easat-4161	267	22	,	,	PUNCT
easat-4161	267	23	𝑛	𝑛	DET
easat-4161	267	24	−	−	NOUN
easat-4161	267	25	3	3	NUM
easat-4161	267	26	.	.	PUNCT
easat-4161	267	27	𝑞(𝑤𝑖	𝑞(𝑤𝑖	NUM
easat-4161	267	28	)	)	PUNCT
easat-4161	267	29	=	=	PRON
easat-4161	267	30	{	{	PUNCT
easat-4161	267	31	1	1	NUM
easat-4161	267	32	,	,	PUNCT
easat-4161	267	33	𝑖	𝑖	DET
easat-4161	267	34	≤	≤	NUM
easat-4161	268	1	𝑠	𝑠	X
easat-4161	268	2	3𝑖+4	3𝑖+4	PROPN
easat-4161	268	3	4	4	NUM
easat-4161	268	4	−	−	NOUN
easat-4161	268	5	𝑠	𝑠	PROPN
easat-4161	268	6	+	+	NOUN
easat-4161	268	7	1	1	NUM
easat-4161	268	8	,	,	PUNCT
easat-4161	268	9	𝑖	𝑖	PROPN
easat-4161	268	10	>	>	X
easat-4161	268	11	𝑠	𝑠	PROPN
easat-4161	268	12	,	,	PUNCT
easat-4161	268	13	𝑖	𝑖	X
easat-4161	268	14	=	=	NOUN
easat-4161	268	15	4	4	NUM
easat-4161	268	16	,	,	PUNCT
easat-4161	268	17	8	8	NUM
easat-4161	268	18	,	,	PUNCT
easat-4161	268	19	12	12	NUM
easat-4161	268	20	,	,	PUNCT
easat-4161	268	21	…	…	PUNCT
easat-4161	268	22	,	,	PUNCT
easat-4161	268	23	𝑛	𝑛	DET
easat-4161	268	24	−	−	PROPN
easat-4161	268	25	2	2	NUM
easat-4161	268	26	.	.	PUNCT
easat-4161	268	27	𝑞(𝑤𝑖	𝑞(𝑤𝑖	NUM
easat-4161	268	28	)	)	PUNCT
easat-4161	268	29	=	=	PRON
easat-4161	268	30	{	{	PUNCT
easat-4161	268	31	1	1	NUM
easat-4161	268	32	,	,	PUNCT
easat-4161	268	33	𝑖	𝑖	PRON
easat-4161	268	34	≤	≤	NOUN
easat-4161	268	35	𝑠	𝑠	X
easat-4161	268	36	3𝑖+5	3𝑖+5	PROPN
easat-4161	268	37	4	4	NUM
easat-4161	268	38	−	−	NOUN
easat-4161	268	39	𝑠	𝑠	PROPN
easat-4161	268	40	+	+	NOUN
easat-4161	268	41	1	1	NUM
easat-4161	268	42	,	,	PUNCT
easat-4161	268	43	𝑖	𝑖	PROPN
easat-4161	268	44	>	>	X
easat-4161	268	45	𝑠	𝑠	PROPN
easat-4161	268	46	,	,	PUNCT
easat-4161	268	47	𝑖	𝑖	PROPN
easat-4161	268	48	=	=	SYM
easat-4161	268	49	5	5	NUM
easat-4161	268	50	,	,	PUNCT
easat-4161	268	51	9	9	NUM
easat-4161	268	52	,	,	PUNCT
easat-4161	268	53	13	13	NUM
easat-4161	268	54	,	,	PUNCT
easat-4161	268	55	…	…	PUNCT
easat-4161	268	56	,	,	PUNCT
easat-4161	268	57	𝑛	𝑛	PRON
easat-4161	268	58	−	−	PROPN
easat-4161	268	59	1	1	NUM
easat-4161	268	60	.	.	PUNCT
easat-4161	268	61	𝑞(𝑤𝑖	𝑞(𝑤𝑖	NUM
easat-4161	268	62	)	)	PUNCT
easat-4161	269	1	=	=	PRON
easat-4161	269	2	{	{	PUNCT
easat-4161	269	3	1	1	NUM
easat-4161	269	4	,	,	PUNCT
easat-4161	269	5	𝑖	𝑖	PROPN
easat-4161	269	6	≤	≤	NUM
easat-4161	269	7	𝑠	𝑠	X
easat-4161	270	1	3𝑖+6	3𝑖+6	PROPN
easat-4161	270	2	4	4	NUM
easat-4161	270	3	−	−	NOUN
easat-4161	270	4	𝑠	𝑠	PROPN
easat-4161	270	5	+	+	NOUN
easat-4161	270	6	1	1	NUM
easat-4161	270	7	,	,	PUNCT
easat-4161	270	8	𝑖	𝑖	PROPN
easat-4161	270	9	>	>	X
easat-4161	270	10	𝑠	𝑠	PROPN
easat-4161	270	11	,	,	PUNCT
easat-4161	270	12	𝑖	𝑖	PROPN
easat-4161	270	13	=	=	SYM
easat-4161	270	14	6	6	NUM
easat-4161	270	15	,	,	PUNCT
easat-4161	270	16	10	10	NUM
easat-4161	270	17	,	,	PUNCT
easat-4161	270	18	14	14	NUM
easat-4161	270	19	,	,	PUNCT
easat-4161	270	20	…	…	PUNCT
easat-4161	270	21	,	,	PUNCT
easat-4161	270	22	𝑛	𝑛	DET
easat-4161	270	23	−	−	PROPN
easat-4161	270	24	4	4	NUM
easat-4161	270	25	.	.	NOUN
easat-4161	270	26	𝑞(𝑤𝑛	𝑞(𝑤𝑛	NOUN
easat-4161	270	27	)	)	PUNCT
easat-4161	270	28	=	=	NOUN
easat-4161	270	29	2𝑠	2𝑠	NOUN
easat-4161	270	30	+	+	CCONJ
easat-4161	270	31	4	4	X
easat-4161	270	32	.	.	NUM
easat-4161	270	33	𝑞(𝑣𝑖	𝑞(𝑣𝑖	NUM
easat-4161	270	34	)	)	PUNCT
easat-4161	270	35	=	=	SYM
easat-4161	271	1	3𝑠	3𝑠	NUM
easat-4161	271	2	+	+	CCONJ
easat-4161	271	3	3	3	NUM
easat-4161	271	4	,	,	PUNCT
easat-4161	271	5	𝑖	𝑖	NOUN
easat-4161	271	6	=	=	SYM
easat-4161	271	7	1	1	NUM
easat-4161	271	8	,	,	PUNCT
easat-4161	271	9	2	2	NUM
easat-4161	271	10	,	,	PUNCT
easat-4161	271	11	…	…	PUNCT
easat-4161	271	12	,	,	PUNCT
easat-4161	271	13	𝑛.	𝑛.	NOUN
easat-4161	271	14	𝑞(𝑥1𝑥2	𝑞(𝑥1𝑥2	NOUN
easat-4161	271	15	)	)	PUNCT
easat-4161	271	16	=	=	SYM
easat-4161	271	17	𝑞(𝑥𝑛−1𝑥𝑛	𝑞(𝑥𝑛−1𝑥𝑛	NOUN
easat-4161	271	18	)	)	PUNCT
easat-4161	271	19	=	=	NOUN
easat-4161	271	20	3𝑠	3𝑠	NOUN
easat-4161	271	21	+	+	CCONJ
easat-4161	271	22	1	1	X
easat-4161	271	23	.	.	X
easat-4161	271	24	𝑞(𝑥2𝑥3	𝑞(𝑥2𝑥3	NOUN
easat-4161	271	25	)	)	PUNCT
easat-4161	271	26	=	=	SYM
easat-4161	271	27	𝑞(𝑥𝑛𝑥1	𝑞(𝑥𝑛𝑥1	NOUN
easat-4161	271	28	)	)	PUNCT
easat-4161	271	29	=	=	NOUN
easat-4161	271	30	3𝑠	3𝑠	NUM
easat-4161	271	31	+	+	CCONJ
easat-4161	271	32	2	2	X
easat-4161	271	33	.	.	PUNCT
easat-4161	271	34	𝑞(𝑥𝑖𝑥𝑖+1	𝑞(𝑥𝑖𝑥𝑖+1	PROPN
easat-4161	271	35	)	)	PUNCT
easat-4161	271	36	=	=	SYM
easat-4161	271	37	{	{	PUNCT
easat-4161	271	38	3𝑠	3𝑠	NUM
easat-4161	271	39	+	+	CCONJ
easat-4161	271	40	1	1	NUM
easat-4161	271	41	,	,	PUNCT
easat-4161	271	42	{	{	PUNCT
easat-4161	271	43	𝑖	𝑖	PUNCT
easat-4161	271	44	=	=	SYM
easat-4161	271	45	3	3	NUM
easat-4161	271	46	,	,	PUNCT
easat-4161	271	47	7	7	NUM
easat-4161	271	48	,	,	PUNCT
easat-4161	271	49	11	11	NUM
easat-4161	271	50	,	,	PUNCT
easat-4161	271	51	…	…	PUNCT
easat-4161	271	52	,	,	PUNCT
easat-4161	271	53	𝑛	𝑛	PRON
easat-4161	271	54	−	−	NOUN
easat-4161	271	55	3	3	X
easat-4161	271	56	.	.	PUNCT
easat-4161	271	57	𝑖	𝑖	SYM
easat-4161	272	1	=	=	SYM
easat-4161	272	2	5	5	NUM
easat-4161	272	3	,	,	PUNCT
easat-4161	272	4	9	9	NUM
easat-4161	272	5	,	,	PUNCT
easat-4161	272	6	13,	13,	NUM
easat-4161	272	7	…	…	SYM
easat-4161	272	8	𝑛	𝑛	PRON
easat-4161	272	9	−	−	PROPN
easat-4161	272	10	1	1	NUM
easat-4161	272	11	.	.	PUNCT
easat-4161	273	1	3𝑠	3𝑠	NUM
easat-4161	273	2	+	+	CCONJ
easat-4161	273	3	2	2	NUM
easat-4161	273	4	,	,	PUNCT
easat-4161	273	5	{	{	PUNCT
easat-4161	273	6	𝑖	𝑖	NOUN
easat-4161	273	7	=	=	NOUN
easat-4161	273	8	4	4	NUM
easat-4161	273	9	,	,	PUNCT
easat-4161	273	10	8	8	NUM
easat-4161	273	11	,	,	PUNCT
easat-4161	273	12	12	12	NUM
easat-4161	273	13	,	,	PUNCT
easat-4161	273	14	…	…	PUNCT
easat-4161	273	15	,	,	PUNCT
easat-4161	273	16	𝑛	𝑛	DET
easat-4161	273	17	−	−	NOUN
easat-4161	273	18	2	2	NUM
easat-4161	273	19	.	.	PUNCT
easat-4161	273	20	𝑖	𝑖	SYM
easat-4161	274	1	=	=	NOUN
easat-4161	274	2	6	6	NUM
easat-4161	274	3	,	,	PUNCT
easat-4161	274	4	10	10	NUM
easat-4161	274	5	,	,	PUNCT
easat-4161	274	6	14	14	NUM
easat-4161	274	7	,	,	PUNCT
easat-4161	274	8	…	…	PUNCT
easat-4161	274	9	,	,	PUNCT
easat-4161	274	10	𝑛	𝑛	DET
easat-4161	274	11	−	−	NOUN
easat-4161	274	12	4	4	NUM
easat-4161	274	13	.	.	PUNCT
easat-4161	274	14	𝑞(𝑥𝑖−1𝑥𝑖	𝑞(𝑥𝑖−1𝑥𝑖	VERB
easat-4161	274	15	)	)	PUNCT
easat-4161	274	16	=	=	PRON
easat-4161	274	17	{	{	PUNCT
easat-4161	274	18	3𝑠	3𝑠	NUM
easat-4161	274	19	+	+	CCONJ
easat-4161	274	20	2	2	NUM
easat-4161	274	21	,	,	PUNCT
easat-4161	274	22	{	{	PUNCT
easat-4161	275	1	𝑖	𝑖	PUNCT
easat-4161	275	2	=	=	SYM
easat-4161	275	3	3	3	NUM
easat-4161	275	4	,	,	PUNCT
easat-4161	275	5	7	7	NUM
easat-4161	275	6	,	,	PUNCT
easat-4161	275	7	11	11	NUM
easat-4161	275	8	,	,	PUNCT
easat-4161	275	9	…	…	PUNCT
easat-4161	275	10	,	,	PUNCT
easat-4161	275	11	𝑛	𝑛	DET
easat-4161	275	12	−	−	NOUN
easat-4161	276	1	3	3	X
easat-4161	276	2	.	.	PUNCT
easat-4161	276	3	𝑖	𝑖	SYM
easat-4161	277	1	=	=	SYM
easat-4161	277	2	5	5	NUM
easat-4161	277	3	,	,	PUNCT
easat-4161	277	4	9	9	NUM
easat-4161	277	5	,	,	PUNCT
easat-4161	277	6	13,	13,	NUM
easat-4161	277	7	…	…	SYM
easat-4161	277	8	𝑛	𝑛	PRON
easat-4161	277	9	−	−	PROPN
easat-4161	277	10	1	1	NUM
easat-4161	277	11	.	.	PUNCT
easat-4161	278	1	3𝑠	3𝑠	NUM
easat-4161	278	2	+	+	CCONJ
easat-4161	278	3	1	1	NUM
easat-4161	278	4	,	,	PUNCT
easat-4161	278	5	{	{	PUNCT
easat-4161	278	6	𝑖	𝑖	NOUN
easat-4161	278	7	=	=	NOUN
easat-4161	278	8	4	4	NUM
easat-4161	278	9	,	,	PUNCT
easat-4161	278	10	8	8	NUM
easat-4161	278	11	,	,	PUNCT
easat-4161	278	12	12	12	NUM
easat-4161	278	13	,	,	PUNCT
easat-4161	278	14	…	…	PUNCT
easat-4161	278	15	,	,	PUNCT
easat-4161	278	16	𝑛	𝑛	DET
easat-4161	278	17	−	−	NOUN
easat-4161	278	18	2	2	NUM
easat-4161	278	19	.	.	PUNCT
easat-4161	278	20	𝑖	𝑖	SYM
easat-4161	279	1	=	=	NOUN
easat-4161	279	2	6	6	NUM
easat-4161	279	3	,	,	PUNCT
easat-4161	279	4	10	10	NUM
easat-4161	279	5	,	,	PUNCT
easat-4161	279	6	14	14	NUM
easat-4161	279	7	,	,	PUNCT
easat-4161	279	8	…	…	PUNCT
easat-4161	279	9	,	,	PUNCT
easat-4161	279	10	𝑛	𝑛	DET
easat-4161	279	11	−	−	PROPN
easat-4161	279	12	4	4	NUM
easat-4161	279	13	.	.	PUNCT
easat-4161	279	14	𝑞(𝑥1𝑦1	𝑞(𝑥1𝑦1	NOUN
easat-4161	279	15	)	)	PUNCT
easat-4161	279	16	=	=	SYM
easat-4161	279	17	𝑞(𝑥2𝑦2	𝑞(𝑥2𝑦2	ADJ
easat-4161	279	18	)	)	PUNCT
easat-4161	279	19	=	=	SYM
easat-4161	280	1	1	1	X
easat-4161	280	2	.	.	X
easat-4161	280	3	𝑞(𝑥𝑖𝑦𝑖	𝑞(𝑥𝑖𝑦𝑖	ADJ
easat-4161	280	4	)	)	PUNCT
easat-4161	280	5	=	=	PRON
easat-4161	280	6	{	{	PUNCT
easat-4161	280	7	𝑖+1	𝑖+1	NUM
easat-4161	280	8	4	4	NUM
easat-4161	280	9	,	,	PUNCT
easat-4161	280	10	𝑖	𝑖	NOUN
easat-4161	280	11	=	=	SYM
easat-4161	280	12	3	3	NUM
easat-4161	280	13	,	,	PUNCT
easat-4161	280	14	7	7	NUM
easat-4161	280	15	,	,	PUNCT
easat-4161	280	16	11	11	NUM
easat-4161	280	17	,	,	PUNCT
easat-4161	280	18	…	…	PUNCT
easat-4161	280	19	,	,	PUNCT
easat-4161	281	1	𝑛	𝑛	DET
easat-4161	281	2	−	−	NOUN
easat-4161	281	3	3	3	NUM
easat-4161	281	4	.	.	PUNCT
easat-4161	281	5	𝑖	𝑖	ADP
easat-4161	281	6	4	4	NUM
easat-4161	281	7	,	,	PUNCT
easat-4161	281	8	𝑖	𝑖	NOUN
easat-4161	281	9	=	=	SYM
easat-4161	281	10	4	4	NUM
easat-4161	281	11	,	,	PUNCT
easat-4161	281	12	8	8	NUM
easat-4161	281	13	,	,	PUNCT
easat-4161	281	14	12	12	NUM
easat-4161	281	15	,	,	PUNCT
easat-4161	281	16	…	…	PUNCT
easat-4161	281	17	,	,	PUNCT
easat-4161	281	18	𝑛	𝑛	DET
easat-4161	281	19	−	−	NOUN
easat-4161	281	20	2	2	NUM
easat-4161	281	21	.	.	PUNCT
easat-4161	282	1	𝑖−1	𝑖−1	ADP
easat-4161	282	2	4	4	NUM
easat-4161	282	3	,	,	PUNCT
easat-4161	282	4	𝑖	𝑖	NOUN
easat-4161	282	5	=	=	SYM
easat-4161	282	6	5	5	NUM
easat-4161	282	7	,	,	PUNCT
easat-4161	282	8	9	9	NUM
easat-4161	282	9	,	,	PUNCT
easat-4161	282	10	13	13	NUM
easat-4161	282	11	,	,	PUNCT
easat-4161	282	12	…	…	PUNCT
easat-4161	282	13	,	,	PUNCT
easat-4161	282	14	𝑛	𝑛	DET
easat-4161	282	15	−	−	NOUN
easat-4161	282	16	1	1	NUM
easat-4161	282	17	.	.	PUNCT
easat-4161	283	1	𝑖−2	𝑖−2	PROPN
easat-4161	283	2	4	4	NUM
easat-4161	283	3	,	,	PUNCT
easat-4161	283	4	𝑖	𝑖	NOUN
easat-4161	283	5	=	=	SYM
easat-4161	283	6	6	6	NUM
easat-4161	283	7	,	,	PUNCT
easat-4161	283	8	10	10	NUM
easat-4161	283	9	,	,	PUNCT
easat-4161	283	10	14	14	NUM
easat-4161	283	11	,	,	PUNCT
easat-4161	283	12	…	…	PUNCT
easat-4161	283	13	,	,	PUNCT
easat-4161	283	14	𝑛	𝑛	DET
easat-4161	283	15	−	−	PROPN
easat-4161	283	16	4	4	NUM
easat-4161	283	17	.	.	PUNCT
easat-4161	283	18	𝑞(𝑥𝑛𝑦𝑛	𝑞(𝑥𝑛𝑦𝑛	NUM
easat-4161	283	19	)	)	PUNCT
easat-4161	284	1	=	=	PUNCT
easat-4161	284	2	𝑛−2	𝑛−2	NOUN
easat-4161	284	3	4	4	NUM
easat-4161	284	4	.	.	PUNCT
easat-4161	285	1	𝑞(𝑥2𝑤1	𝑞(𝑥2𝑤1	NOUN
easat-4161	285	2	)	)	PUNCT
easat-4161	286	1	=	=	NOUN
easat-4161	286	2	2𝑠	2𝑠	NOUN
easat-4161	286	3	+	+	CCONJ
easat-4161	286	4	3	3	X
easat-4161	286	5	.	.	X
easat-4161	286	6	𝑞(𝑥3𝑤2	𝑞(𝑥3𝑤2	NOUN
easat-4161	286	7	)	)	PUNCT
easat-4161	287	1	=	=	NOUN
easat-4161	287	2	{	{	PUNCT
easat-4161	287	3	3𝑠	3𝑠	NUM
easat-4161	287	4	+	+	CCONJ
easat-4161	287	5	2	2	NUM
easat-4161	287	6	,	,	PUNCT
easat-4161	287	7	𝑠	𝑠	NOUN
easat-4161	287	8	=	=	SYM
easat-4161	287	9	1	1	NUM
easat-4161	287	10	2𝑠	2𝑠	NOUN
easat-4161	287	11	+	+	CCONJ
easat-4161	287	12	4	4	NUM
easat-4161	287	13	,	,	PUNCT
easat-4161	287	14	𝑠	𝑠	NOUN
easat-4161	287	15	=	=	SYM
easat-4161	287	16	2	2	NUM
easat-4161	287	17	,	,	PUNCT
easat-4161	287	18	3	3	NUM
easat-4161	287	19	,	,	PUNCT
easat-4161	287	20	…	…	PUNCT
easat-4161	287	21	𝑞(𝑥𝑖+1𝑤𝑖	𝑞(𝑥𝑖+1𝑤𝑖	NOUN
easat-4161	287	22	)	)	PUNCT
easat-4161	287	23	=	=	NOUN
easat-4161	287	24	{	{	PUNCT
easat-4161	287	25	2𝑠	2𝑠	NOUN
easat-4161	288	1	+	+	CCONJ
easat-4161	288	2	3𝑖+3	3𝑖+3	NUM
easat-4161	288	3	4	4	NUM
easat-4161	288	4	+	+	CCONJ
easat-4161	288	5	2	2	NUM
easat-4161	288	6	,	,	PUNCT
easat-4161	288	7	𝑖	𝑖	PRON
easat-4161	288	8	≤	≤	NOUN
easat-4161	288	9	𝑠	𝑠	NUM
easat-4161	288	10	3𝑠	3𝑠	NUM
easat-4161	288	11	+	+	CCONJ
easat-4161	288	12	2	2	NUM
easat-4161	288	13	,	,	PUNCT
easat-4161	288	14	𝑖	𝑖	PROPN
easat-4161	288	15	>	>	X
easat-4161	288	16	𝑠	𝑠	PROPN
easat-4161	288	17	,	,	PUNCT
easat-4161	288	18	𝑖	𝑖	PROPN
easat-4161	288	19	=	=	SYM
easat-4161	288	20	3	3	NUM
easat-4161	288	21	,	,	PUNCT
easat-4161	288	22	7	7	NUM
easat-4161	288	23	,	,	PUNCT
easat-4161	288	24	11	11	NUM
easat-4161	288	25	,	,	PUNCT
easat-4161	288	26	…	…	PUNCT
easat-4161	288	27	,	,	PUNCT
easat-4161	288	28	𝑛	𝑛	DET
easat-4161	288	29	−	−	NOUN
easat-4161	288	30	3	3	X
easat-4161	288	31	.	.	PUNCT
easat-4161	288	32	𝑞(𝑥𝑖+1𝑤𝑖	𝑞(𝑥𝑖+1𝑤𝑖	NOUN
easat-4161	288	33	)	)	PUNCT
easat-4161	288	34	=	=	NOUN
easat-4161	288	35	{	{	PUNCT
easat-4161	288	36	2𝑠	2𝑠	NOUN
easat-4161	289	1	+	+	CCONJ
easat-4161	289	2	3𝑖+4	3𝑖+4	NUM
easat-4161	289	3	4	4	NUM
easat-4161	289	4	+	+	SYM
easat-4161	289	5	2	2	NUM
easat-4161	289	6	,	,	PUNCT
easat-4161	289	7	𝑖	𝑖	PRON
easat-4161	289	8	≤	≤	NOUN
easat-4161	289	9	𝑠	𝑠	NUM
easat-4161	289	10	3𝑠	3𝑠	NUM
easat-4161	289	11	+	+	CCONJ
easat-4161	289	12	2	2	NUM
easat-4161	289	13	,	,	PUNCT
easat-4161	289	14	𝑖	𝑖	PROPN
easat-4161	289	15	>	>	X
easat-4161	289	16	𝑠	𝑠	PROPN
easat-4161	289	17	,	,	PUNCT
easat-4161	289	18	𝑖	𝑖	X
easat-4161	289	19	=	=	NOUN
easat-4161	289	20	4	4	NUM
easat-4161	289	21	,	,	PUNCT
easat-4161	289	22	8	8	NUM
easat-4161	289	23	,	,	PUNCT
easat-4161	289	24	12	12	NUM
easat-4161	289	25	,	,	PUNCT
easat-4161	289	26	…	…	PUNCT
easat-4161	289	27	,	,	PUNCT
easat-4161	289	28	𝑛	𝑛	DET
easat-4161	289	29	−	−	PROPN
easat-4161	289	30	2	2	NUM
easat-4161	289	31	.	.	PUNCT
easat-4161	289	32	𝑞(𝑥𝑖+1𝑤𝑖	𝑞(𝑥𝑖+1𝑤𝑖	NOUN
easat-4161	289	33	)	)	PUNCT
easat-4161	289	34	=	=	NOUN
easat-4161	289	35	{	{	PUNCT
easat-4161	289	36	2𝑠	2𝑠	NOUN
easat-4161	290	1	+	+	CCONJ
easat-4161	290	2	3𝑖+5	3𝑖+5	PROPN
easat-4161	290	3	4	4	NUM
easat-4161	290	4	+	+	SYM
easat-4161	290	5	2	2	NUM
easat-4161	290	6	,	,	PUNCT
easat-4161	290	7	𝑖	𝑖	PRON
easat-4161	290	8	≤	≤	NOUN
easat-4161	290	9	𝑠	𝑠	NUM
easat-4161	290	10	3𝑠	3𝑠	NUM
easat-4161	290	11	+	+	CCONJ
easat-4161	290	12	2	2	NUM
easat-4161	290	13	,	,	PUNCT
easat-4161	290	14	𝑖	𝑖	PROPN
easat-4161	290	15	>	>	X
easat-4161	290	16	𝑠	𝑠	PROPN
easat-4161	290	17	,	,	PUNCT
easat-4161	290	18	𝑖	𝑖	PROPN
easat-4161	290	19	=	=	SYM
easat-4161	290	20	5	5	NUM
easat-4161	290	21	,	,	PUNCT
easat-4161	290	22	9	9	NUM
easat-4161	290	23	,	,	PUNCT
easat-4161	290	24	13	13	NUM
easat-4161	290	25	,	,	PUNCT
easat-4161	290	26	…	…	PUNCT
easat-4161	290	27	,	,	PUNCT
easat-4161	290	28	𝑛	𝑛	DET
easat-4161	290	29	−	−	PROPN
easat-4161	290	30	1	1	NUM
easat-4161	290	31	.	.	PUNCT
easat-4161	290	32	𝑞(𝑥𝑖+1𝑤𝑖	𝑞(𝑥𝑖+1𝑤𝑖	NOUN
easat-4161	290	33	)	)	PUNCT
easat-4161	291	1	=	=	NOUN
easat-4161	291	2	{	{	PUNCT
easat-4161	291	3	2𝑠	2𝑠	NOUN
easat-4161	292	1	+	+	CCONJ
easat-4161	292	2	3𝑖+6	3𝑖+6	NUM
easat-4161	292	3	4	4	NUM
easat-4161	292	4	+	+	SYM
easat-4161	292	5	2	2	NUM
easat-4161	292	6	,	,	PUNCT
easat-4161	292	7	𝑖	𝑖	PRON
easat-4161	292	8	≤	≤	NOUN
easat-4161	292	9	𝑠	𝑠	NUM
easat-4161	292	10	3𝑠	3𝑠	NUM
easat-4161	292	11	+	+	CCONJ
easat-4161	292	12	2	2	NUM
easat-4161	292	13	,	,	PUNCT
easat-4161	292	14	𝑖	𝑖	PROPN
easat-4161	292	15	>	>	X
easat-4161	292	16	𝑠	𝑠	PROPN
easat-4161	292	17	,	,	PUNCT
easat-4161	292	18	𝑖	𝑖	PROPN
easat-4161	292	19	=	=	SYM
easat-4161	292	20	6	6	NUM
easat-4161	292	21	,	,	PUNCT
easat-4161	292	22	10	10	NUM
easat-4161	292	23	,	,	PUNCT
easat-4161	292	24	14	14	NUM
easat-4161	292	25	,	,	PUNCT
easat-4161	292	26	…	…	PUNCT
easat-4161	292	27	,	,	PUNCT
easat-4161	292	28	𝑛	𝑛	DET
easat-4161	292	29	−	−	NOUN
easat-4161	292	30	4	4	NUM
easat-4161	292	31	.	.	X
easat-4161	292	32	𝑞(𝑥1𝑤𝑛	𝑞(𝑥1𝑤𝑛	PROPN
easat-4161	292	33	)	)	PUNCT
easat-4161	293	1	=	=	SYM
easat-4161	293	2	𝑞(𝑥𝑛𝑤𝑛−1	𝑞(𝑥𝑛𝑤𝑛−1	NOUN
easat-4161	293	3	)	)	PUNCT
easat-4161	293	4	=	=	PUNCT
easat-4161	294	1	3𝑛+6	3𝑛+6	NOUN
easat-4161	294	2	4	4	NUM
easat-4161	294	3	−	−	NOUN
easat-4161	294	4	1	1	NUM
easat-4161	294	5	=	=	SYM
easat-4161	294	6	3𝑠	3𝑠	NOUN
easat-4161	294	7	+	+	CCONJ
easat-4161	294	8	2	2	NUM
easat-4161	294	9	.	.	NUM
easat-4161	294	10	491	491	NUM
easat-4161	294	11	edelweiss	edelweiss	PROPN
easat-4161	294	12	applied	apply	VERB
easat-4161	294	13	science	science	NOUN
easat-4161	294	14	and	and	CCONJ
easat-4161	294	15	technology	technology	NOUN
easat-4161	294	16	issn	issn	PROPN
easat-4161	294	17	:	:	PUNCT
easat-4161	294	18	2576	2576	NUM
easat-4161	294	19	-	-	SYM
easat-4161	294	20	8484	8484	NUM
easat-4161	294	21	vol	vol	NOUN
easat-4161	294	22	.	.	PROPN
easat-4161	295	1	9	9	NUM
easat-4161	295	2	,	,	PUNCT
easat-4161	295	3	no	no	INTJ
easat-4161	295	4	.	.	NOUN
easat-4161	295	5	1	1	NUM
easat-4161	295	6	:	:	PUNCT
easat-4161	295	7	481	481	NUM
easat-4161	295	8	-	-	SYM
easat-4161	295	9	492	492	NUM
easat-4161	295	10	,	,	PUNCT
easat-4161	295	11	2025	2025	NUM
easat-4161	295	12	doi	doi	NOUN
easat-4161	295	13	:	:	PUNCT
easat-4161	295	14	10.55214/25768484.v9i1.4161	10.55214/25768484.v9i1.4161	NUM
easat-4161	295	15	©	©	PROPN
easat-4161	295	16	2025	2025	NUM
easat-4161	295	17	by	by	ADP
easat-4161	295	18	the	the	DET
easat-4161	295	19	authors	author	NOUN
easat-4161	295	20	;	;	PUNCT
easat-4161	295	21	licensee	licensee	PROPN
easat-4161	295	22	learning	learning	PROPN
easat-4161	295	23	gate	gate	NOUN
easat-4161	295	24	𝑞(𝑥𝑖𝑤𝑖−1	𝑞(𝑥𝑖𝑤𝑖−1	PROPN
easat-4161	295	25	)	)	PUNCT
easat-4161	295	26	=	=	PRON
easat-4161	295	27	{	{	PUNCT
easat-4161	295	28	2𝑠	2𝑠	NOUN
easat-4161	296	1	+	+	CCONJ
easat-4161	296	2	𝑖	𝑖	SYM
easat-4161	297	1	+	+	NOUN
easat-4161	297	2	1	1	NUM
easat-4161	297	3	,	,	PUNCT
easat-4161	297	4	𝑖	𝑖	DET
easat-4161	297	5	≤	≤	NOUN
easat-4161	297	6	𝑠	𝑠	NUM
easat-4161	297	7	3𝑠	3𝑠	NUM
easat-4161	297	8	+	+	CCONJ
easat-4161	297	9	2	2	NUM
easat-4161	297	10	,	,	PUNCT
easat-4161	297	11	𝑖	𝑖	PROPN
easat-4161	297	12	>	>	X
easat-4161	297	13	𝑠	𝑠	PROPN
easat-4161	297	14	𝑞(𝑥1𝑣2	𝑞(𝑥1𝑣2	PROPN
easat-4161	297	15	)	)	PUNCT
easat-4161	297	16	=	=	SYM
easat-4161	298	1	𝑞(𝑥𝑖𝑣𝑖+1	𝑞(𝑥𝑖𝑣𝑖+1	X
easat-4161	298	2	)	)	PUNCT
easat-4161	298	3	=	=	SYM
easat-4161	298	4	𝑞(𝑥𝑛−1𝑣𝑛	𝑞(𝑥𝑛−1𝑣𝑛	NOUN
easat-4161	298	5	)	)	PUNCT
easat-4161	298	6	=	=	SYM
easat-4161	298	7	𝑞(𝑥𝑛𝑣1	𝑞(𝑥𝑛𝑣1	NUM
easat-4161	298	8	)	)	PUNCT
easat-4161	298	9	=	=	SYM
easat-4161	298	10	3𝑠	3𝑠	NUM
easat-4161	298	11	+	+	CCONJ
easat-4161	298	12	3	3	X
easat-4161	298	13	.	.	NUM
easat-4161	298	14	𝑞(𝑦𝑖𝑤𝑖	𝑞(𝑦𝑖𝑤𝑖	NOUN
easat-4161	298	15	)	)	PUNCT
easat-4161	298	16	=	=	SYM
easat-4161	299	1	1	1	NUM
easat-4161	299	2	,	,	PUNCT
easat-4161	299	3	𝑖	𝑖	NOUN
easat-4161	299	4	=	=	SYM
easat-4161	299	5	1	1	NUM
easat-4161	299	6	,	,	PUNCT
easat-4161	299	7	2	2	NUM
easat-4161	299	8	,	,	PUNCT
easat-4161	299	9	…	…	PUNCT
easat-4161	299	10	,	,	PUNCT
easat-4161	299	11	𝑛.	𝑛.	NOUN
easat-4161	299	12	𝑞(𝑦1𝑣1	𝑞(𝑦1𝑣1	NOUN
easat-4161	299	13	)	)	PUNCT
easat-4161	299	14	=	=	SYM
easat-4161	300	1	1	1	X
easat-4161	300	2	.	.	X
easat-4161	300	3	𝑞(𝑦2𝑣2	𝑞(𝑦2𝑣2	NOUN
easat-4161	300	4	)	)	PUNCT
easat-4161	300	5	=	=	SYM
easat-4161	300	6	2	2	X
easat-4161	300	7	.	.	X
easat-4161	300	8	𝑞(𝑦𝑖𝑣𝑖	𝑞(𝑦𝑖𝑣𝑖	NUM
easat-4161	300	9	)	)	PUNCT
easat-4161	301	1	=	=	PRON
easat-4161	301	2	{	{	PUNCT
easat-4161	301	3	3𝑖+3	3𝑖+3	PROPN
easat-4161	301	4	4	4	NUM
easat-4161	301	5	,	,	PUNCT
easat-4161	301	6	𝑖	𝑖	PROPN
easat-4161	301	7	=	=	SYM
easat-4161	301	8	3	3	NUM
easat-4161	301	9	,	,	PUNCT
easat-4161	301	10	7	7	NUM
easat-4161	301	11	,	,	PUNCT
easat-4161	301	12	11	11	NUM
easat-4161	301	13	,	,	PUNCT
easat-4161	301	14	…	…	PUNCT
easat-4161	301	15	,	,	PUNCT
easat-4161	301	16	𝑛	𝑛	DET
easat-4161	301	17	−	−	PROPN
easat-4161	301	18	3	3	NUM
easat-4161	301	19	,	,	PUNCT
easat-4161	301	20	3𝑖+4	3𝑖+4	NUM
easat-4161	301	21	4	4	NUM
easat-4161	301	22	,	,	PUNCT
easat-4161	301	23	𝑖	𝑖	NOUN
easat-4161	301	24	=	=	SYM
easat-4161	301	25	4	4	NUM
easat-4161	301	26	,	,	PUNCT
easat-4161	301	27	8	8	NUM
easat-4161	301	28	,	,	PUNCT
easat-4161	301	29	12	12	NUM
easat-4161	301	30	,	,	PUNCT
easat-4161	301	31	…	…	PUNCT
easat-4161	301	32	,	,	PUNCT
easat-4161	301	33	𝑛	𝑛	DET
easat-4161	301	34	−	−	PROPN
easat-4161	301	35	2	2	NUM
easat-4161	301	36	,	,	PUNCT
easat-4161	301	37	3𝑖+5	3𝑖+5	PROPN
easat-4161	301	38	4	4	NUM
easat-4161	301	39	,	,	PUNCT
easat-4161	301	40	𝑖	𝑖	NOUN
easat-4161	301	41	=	=	SYM
easat-4161	301	42	5	5	NUM
easat-4161	301	43	,	,	PUNCT
easat-4161	301	44	9	9	NUM
easat-4161	301	45	,	,	PUNCT
easat-4161	301	46	13	13	NUM
easat-4161	301	47	,	,	PUNCT
easat-4161	301	48	…	…	PUNCT
easat-4161	301	49	,	,	PUNCT
easat-4161	301	50	𝑛	𝑛	DET
easat-4161	301	51	−	−	PROPN
easat-4161	301	52	1	1	NUM
easat-4161	301	53	,	,	PUNCT
easat-4161	301	54	3𝑖+6	3𝑖+6	NOUN
easat-4161	301	55	4	4	NUM
easat-4161	301	56	,	,	PUNCT
easat-4161	301	57	𝑖	𝑖	NOUN
easat-4161	301	58	=	=	SYM
easat-4161	301	59	6	6	NUM
easat-4161	301	60	,	,	PUNCT
easat-4161	301	61	10	10	NUM
easat-4161	301	62	,	,	PUNCT
easat-4161	301	63	14	14	NUM
easat-4161	301	64	,	,	PUNCT
easat-4161	301	65	…	…	PUNCT
easat-4161	301	66	,	,	PUNCT
easat-4161	301	67	𝑛	𝑛	DET
easat-4161	301	68	−	−	PROPN
easat-4161	301	69	4	4	NUM
easat-4161	301	70	,	,	PUNCT
easat-4161	301	71	𝑞(𝑦𝑛𝑣𝑛	𝑞(𝑦𝑛𝑣𝑛	VERB
easat-4161	301	72	)	)	PUNCT
easat-4161	301	73	=	=	PUNCT
easat-4161	302	1	3𝑛+6	3𝑛+6	NOUN
easat-4161	302	2	4	4	NUM
easat-4161	302	3	.	.	PUNCT
easat-4161	303	1	𝑞(𝑤1𝑣1	𝑞(𝑤1𝑣1	NOUN
easat-4161	303	2	)	)	PUNCT
easat-4161	303	3	=	=	SYM
easat-4161	303	4	𝑞(𝑤2𝑣2	𝑞(𝑤2𝑣2	NOUN
easat-4161	303	5	)	)	PUNCT
easat-4161	303	6	=	=	NOUN
easat-4161	303	7	2𝑠	2𝑠	NOUN
easat-4161	303	8	+	+	CCONJ
easat-4161	303	9	1	1	X
easat-4161	303	10	.	.	X
easat-4161	303	11	𝑞(𝑤𝑖𝑣𝑖	𝑞(𝑤𝑖𝑣𝑖	NOUN
easat-4161	303	12	)	)	PUNCT
easat-4161	304	1	=	=	PRON
easat-4161	304	2	{	{	PUNCT
easat-4161	304	3	𝑖+1	𝑖+1	PUNCT
easat-4161	304	4	4	4	NUM
easat-4161	304	5	+	+	CCONJ
easat-4161	304	6	2𝑠	2𝑠	NOUN
easat-4161	304	7	,	,	PUNCT
easat-4161	304	8	𝑖	𝑖	NOUN
easat-4161	304	9	=	=	SYM
easat-4161	304	10	3	3	NUM
easat-4161	304	11	,	,	PUNCT
easat-4161	304	12	7	7	NUM
easat-4161	304	13	,	,	PUNCT
easat-4161	304	14	11	11	NUM
easat-4161	304	15	,	,	PUNCT
easat-4161	304	16	…	…	PUNCT
easat-4161	304	17	,	,	PUNCT
easat-4161	304	18	𝑛	𝑛	DET
easat-4161	304	19	−	−	PROPN
easat-4161	304	20	3	3	NUM
easat-4161	304	21	,	,	PUNCT
easat-4161	304	22	𝑖	𝑖	PRON
easat-4161	304	23	4	4	NUM
easat-4161	304	24	+	+	CCONJ
easat-4161	304	25	2𝑠	2𝑠	NOUN
easat-4161	304	26	,	,	PUNCT
easat-4161	304	27	𝑖	𝑖	NOUN
easat-4161	304	28	=	=	SYM
easat-4161	304	29	4	4	NUM
easat-4161	304	30	,	,	PUNCT
easat-4161	304	31	8	8	NUM
easat-4161	304	32	,	,	PUNCT
easat-4161	304	33	12	12	NUM
easat-4161	304	34	,	,	PUNCT
easat-4161	304	35	…	…	PUNCT
easat-4161	304	36	,	,	PUNCT
easat-4161	304	37	𝑛	𝑛	DET
easat-4161	304	38	−	−	PROPN
easat-4161	304	39	2	2	NUM
easat-4161	304	40	,	,	PUNCT
easat-4161	304	41	𝑖−1	𝑖−1	PROPN
easat-4161	304	42	4	4	NUM
easat-4161	304	43	+	+	NOUN
easat-4161	304	44	2𝑠	2𝑠	NOUN
easat-4161	304	45	,	,	PUNCT
easat-4161	304	46	𝑖	𝑖	X
easat-4161	304	47	=	=	SYM
easat-4161	304	48	5	5	NUM
easat-4161	304	49	,	,	PUNCT
easat-4161	304	50	9	9	NUM
easat-4161	304	51	,	,	PUNCT
easat-4161	304	52	13	13	NUM
easat-4161	304	53	,	,	PUNCT
easat-4161	304	54	…	…	PUNCT
easat-4161	304	55	,	,	PUNCT
easat-4161	304	56	𝑛	𝑛	DET
easat-4161	304	57	−	−	PROPN
easat-4161	304	58	1	1	NUM
easat-4161	304	59	,	,	PUNCT
easat-4161	304	60	𝑖−2	𝑖−2	PROPN
easat-4161	304	61	4	4	NUM
easat-4161	304	62	+	+	NOUN
easat-4161	304	63	2𝑠	2𝑠	NOUN
easat-4161	304	64	,	,	PUNCT
easat-4161	304	65	𝑖	𝑖	NOUN
easat-4161	304	66	=	=	SYM
easat-4161	304	67	6	6	NUM
easat-4161	304	68	,	,	PUNCT
easat-4161	304	69	10	10	NUM
easat-4161	304	70	,	,	PUNCT
easat-4161	304	71	14	14	NUM
easat-4161	304	72	,	,	PUNCT
easat-4161	304	73	…	…	PUNCT
easat-4161	304	74	,	,	PUNCT
easat-4161	304	75	𝑛	𝑛	DET
easat-4161	304	76	−	−	PROPN
easat-4161	304	77	4	4	NUM
easat-4161	304	78	,	,	PUNCT
easat-4161	304	79	𝑞(𝑤𝑛𝑣𝑛	𝑞(𝑤𝑛𝑣𝑛	NOUN
easat-4161	304	80	)	)	PUNCT
easat-4161	304	81	=	=	SYM
easat-4161	304	82	𝑛	𝑛	DET
easat-4161	304	83	−	−	NUM
easat-4161	304	84	2	2	NUM
easat-4161	304	85	4	4	NUM
easat-4161	304	86	+	+	SYM
easat-4161	304	87	2𝑠.	2𝑠.	NUM
easat-4161	304	88	based	base	VERB
easat-4161	304	89	on	on	ADP
easat-4161	304	90	this	this	DET
easat-4161	304	91	function	function	NOUN
easat-4161	304	92	,	,	PUNCT
easat-4161	304	93	it	it	PRON
easat-4161	304	94	can	can	AUX
easat-4161	304	95	be	be	AUX
easat-4161	304	96	shown	show	VERB
easat-4161	304	97	that	that	SCONJ
easat-4161	304	98	all	all	DET
easat-4161	304	99	vertices	vertice	VERB
easat-4161	304	100	weights	weight	NOUN
easat-4161	304	101	are	be	AUX
easat-4161	304	102	different	different	ADJ
easat-4161	304	103	and	and	CCONJ
easat-4161	304	104	the	the	DET
easat-4161	304	105	maximum	maximum	ADJ
easat-4161	304	106	value	value	NOUN
easat-4161	304	107	of	of	ADP
easat-4161	304	108	the	the	DET
easat-4161	304	109	function	function	NOUN
easat-4161	304	110	is	be	AUX
easat-4161	304	111	⌈	⌈	SYM
easat-4161	304	112	𝟑+𝟑𝒏	𝟑+𝟑𝒏	NOUN
easat-4161	304	113	𝟒	𝟒	X
easat-4161	304	114	⌉.	⌉.	ADV
easat-4161	304	115	this	this	PRON
easat-4161	304	116	shows	show	VERB
easat-4161	304	117	that	that	SCONJ
easat-4161	304	118	𝑞	𝑞	X
easat-4161	304	119	:	:	PUNCT
easat-4161	304	120	𝑉	𝑉	PROPN
easat-4161	304	121	∪	∪	NOUN
easat-4161	304	122	𝐸	𝐸	PROPN
easat-4161	304	123	→	→	SYM
easat-4161	304	124	{	{	PUNCT
easat-4161	304	125	1	1	NUM
easat-4161	304	126	,	,	PUNCT
easat-4161	304	127	2	2	NUM
easat-4161	304	128	,	,	PUNCT
easat-4161	304	129	3,⋯	3,⋯	NUM
easat-4161	304	130	,	,	PUNCT
easat-4161	304	131	⌈	⌈	X
easat-4161	304	132	𝟑+𝟑𝒏	𝟑+𝟑𝒏	X
easat-4161	304	133	𝟒	𝟒	NUM
easat-4161	304	134	⌉	⌉	NOUN
easat-4161	304	135	}	}	PUNCT
easat-4161	304	136	is	be	AUX
easat-4161	304	137	a	a	DET
easat-4161	304	138	function	function	NOUN
easat-4161	304	139	a	a	DET
easat-4161	304	140	total	total	ADJ
easat-4161	304	141	vertex	vertex	NOUN
easat-4161	304	142	irregular	irregular	ADJ
easat-4161	304	143	𝑘	𝑘	DET
easat-4161	304	144	−	−	NOUN
easat-4161	304	145	𝑙𝑎𝑏𝑒𝑙𝑙𝑖𝑛𝑔	𝑙𝑎𝑏𝑒𝑙𝑙𝑖𝑛𝑔	NOUN
easat-4161	304	146	where	where	SCONJ
easat-4161	304	147	𝑘	𝑘	NOUN
easat-4161	304	148	=	=	PUNCT
easat-4161	304	149	⌈	⌈	NOUN
easat-4161	304	150	𝟑+𝟑𝒏	𝟑+𝟑𝒏	NOUN
easat-4161	304	151	𝟒	𝟒	X
easat-4161	304	152	⌉.	⌉.	ADV
easat-4161	304	153	thus	thus	ADV
easat-4161	304	154	it	it	PRON
easat-4161	304	155	is	be	AUX
easat-4161	304	156	obtained	obtain	VERB
easat-4161	304	157	that	that	SCONJ
easat-4161	304	158	𝒕𝒗𝒔(𝓗𝒏	𝒕𝒗𝒔(𝓗𝒏	NOUN
easat-4161	304	159	)	)	PUNCT
easat-4161	304	160	≤	≤	NOUN
easat-4161	305	1	⌈	⌈	SYM
easat-4161	305	2	𝟑+𝟑𝒏	𝟑+𝟑𝒏	NOUN
easat-4161	305	3	𝟒	𝟒	NUM
easat-4161	305	4	⌉	⌉	X
easat-4161	305	5	for	for	ADP
easat-4161	305	6	𝑛	𝑛	PRON
easat-4161	305	7	=	=	SYM
easat-4161	305	8	4𝑡	4𝑡	NOUN
easat-4161	305	9	+	+	CCONJ
easat-4161	305	10	2	2	NUM
easat-4161	305	11	,	,	PUNCT
easat-4161	305	12	where	where	SCONJ
easat-4161	305	13	𝑡	𝑡	PROPN
easat-4161	305	14	is	be	AUX
easat-4161	305	15	some	some	DET
easat-4161	305	16	positive	positive	ADJ
easat-4161	305	17	integer	integer	NOUN
easat-4161	305	18	.	.	PUNCT
easat-4161	306	1	based	base	VERB
easat-4161	306	2	on	on	ADP
easat-4161	306	3	these	these	DET
easat-4161	306	4	four	four	NUM
easat-4161	306	5	cases	case	NOUN
easat-4161	306	6	,	,	PUNCT
easat-4161	306	7	it	it	PRON
easat-4161	306	8	is	be	AUX
easat-4161	306	9	concluded	conclude	VERB
easat-4161	306	10	that	that	SCONJ
easat-4161	306	11	𝑡𝑣𝑠(ℋ𝑛	𝑡𝑣𝑠(ℋ𝑛	NOUN
easat-4161	306	12	)	)	PUNCT
easat-4161	306	13	=	=	PUNCT
easat-4161	307	1	⌈	⌈	SYM
easat-4161	307	2	3	3	NUM
easat-4161	307	3	+	+	SYM
easat-4161	307	4	3𝑛	3𝑛	NUM
easat-4161	307	5	4	4	NUM
easat-4161	307	6	⌉	⌉	X
easat-4161	307	7	for	for	ADP
easat-4161	307	8	𝑛	𝑛	PRON
easat-4161	307	9	≥	≥	NUM
easat-4161	307	10	3	3	NUM
easat-4161	307	11	and	and	CCONJ
easat-4161	307	12	n	n	PRON
easat-4161	307	13	is	be	AUX
easat-4161	307	14	a	a	DET
easat-4161	307	15	positive	positive	ADJ
easat-4161	307	16	integer	integer	NOUN
easat-4161	307	17	number	number	NOUN
easat-4161	307	18	.	.	PUNCT
easat-4161	308	1	4	4	X
easat-4161	308	2	.	.	X
easat-4161	308	3	conclusion	conclusion	NOUN
easat-4161	308	4	this	this	DET
easat-4161	308	5	research	research	NOUN
easat-4161	308	6	contributes	contribute	VERB
easat-4161	308	7	significantly	significantly	ADV
easat-4161	308	8	to	to	ADP
easat-4161	308	9	understanding	understand	VERB
easat-4161	308	10	transportation	transportation	NOUN
easat-4161	308	11	route	route	NOUN
easat-4161	308	12	optimization	optimization	NOUN
easat-4161	308	13	through	through	ADP
easat-4161	308	14	the	the	DET
easat-4161	308	15	lens	lens	NOUN
easat-4161	308	16	of	of	ADP
easat-4161	308	17	graph	graph	NOUN
easat-4161	308	18	theory	theory	NOUN
easat-4161	308	19	,	,	PUNCT
easat-4161	308	20	specifically	specifically	ADV
easat-4161	308	21	focusing	focus	VERB
easat-4161	308	22	on	on	ADP
easat-4161	308	23	graph	graph	NOUN
easat-4161	308	24	labeling	labeling	NOUN
easat-4161	308	25	within	within	ADP
easat-4161	308	26	modified	modified	ADJ
easat-4161	308	27	helm	helm	NOUN
easat-4161	308	28	graph	graph	NOUN
easat-4161	308	29	topologies	topology	NOUN
easat-4161	308	30	.	.	PUNCT
easat-4161	309	1	by	by	ADP
easat-4161	309	2	applying	apply	VERB
easat-4161	309	3	irregular	irregular	ADJ
easat-4161	309	4	labeling	labeling	NOUN
easat-4161	309	5	,	,	PUNCT
easat-4161	309	6	this	this	DET
easat-4161	309	7	study	study	NOUN
easat-4161	309	8	explores	explore	VERB
easat-4161	309	9	the	the	DET
easat-4161	309	10	vertex	vertex	NOUN
easat-4161	309	11	irregularity	irregularity	NOUN
easat-4161	309	12	strength	strength	NOUN
easat-4161	309	13	required	require	VERB
easat-4161	309	14	for	for	ADP
easat-4161	309	15	efficient	efficient	ADJ
easat-4161	309	16	transportation	transportation	NOUN
easat-4161	309	17	network	network	NOUN
easat-4161	309	18	configurations	configuration	NOUN
easat-4161	309	19	,	,	PUNCT
easat-4161	309	20	which	which	PRON
easat-4161	309	21	is	be	AUX
easat-4161	309	22	critical	critical	ADJ
easat-4161	309	23	in	in	ADP
easat-4161	309	24	addressing	address	VERB
easat-4161	309	25	the	the	DET
easat-4161	309	26	increasing	increase	VERB
easat-4161	309	27	congestion	congestion	NOUN
easat-4161	309	28	in	in	ADP
easat-4161	309	29	urban	urban	ADJ
easat-4161	309	30	transportation	transportation	NOUN
easat-4161	309	31	systems	system	NOUN
easat-4161	309	32	.	.	PUNCT
easat-4161	310	1	the	the	DET
easat-4161	310	2	findings	finding	NOUN
easat-4161	310	3	establish	establish	VERB
easat-4161	310	4	the	the	DET
easat-4161	310	5	lower	low	ADJ
easat-4161	310	6	and	and	CCONJ
easat-4161	310	7	upper	upper	ADJ
easat-4161	310	8	bounds	bound	NOUN
easat-4161	310	9	of	of	ADP
easat-4161	310	10	vertex	vertex	NOUN
easat-4161	310	11	irregularity	irregularity	NOUN
easat-4161	310	12	strength	strength	NOUN
easat-4161	310	13	within	within	ADP
easat-4161	310	14	these	these	DET
easat-4161	310	15	graph	graph	NOUN
easat-4161	310	16	structures	structure	NOUN
easat-4161	310	17	,	,	PUNCT
easat-4161	310	18	providing	provide	VERB
easat-4161	310	19	foundational	foundational	ADJ
easat-4161	310	20	parameters	parameter	NOUN
easat-4161	310	21	for	for	ADP
easat-4161	310	22	further	further	ADJ
easat-4161	310	23	modeling	modeling	NOUN
easat-4161	310	24	and	and	CCONJ
easat-4161	310	25	practical	practical	ADJ
easat-4161	310	26	application	application	NOUN
easat-4161	310	27	in	in	ADP
easat-4161	310	28	real	real	ADJ
easat-4161	310	29	-	-	PUNCT
easat-4161	310	30	world	world	NOUN
easat-4161	310	31	transportation	transportation	NOUN
easat-4161	310	32	networks	network	NOUN
easat-4161	310	33	.	.	PUNCT
easat-4161	311	1	these	these	DET
easat-4161	311	2	insights	insight	NOUN
easat-4161	311	3	enhance	enhance	VERB
easat-4161	311	4	theoretical	theoretical	ADJ
easat-4161	311	5	perspectives	perspective	NOUN
easat-4161	311	6	in	in	ADP
easat-4161	311	7	graph	graph	NOUN
easat-4161	311	8	theory	theory	NOUN
easat-4161	311	9	and	and	CCONJ
easat-4161	311	10	offer	offer	VERB
easat-4161	311	11	a	a	DET
easat-4161	311	12	pathway	pathway	NOUN
easat-4161	311	13	for	for	ADP
easat-4161	311	14	developing	develop	VERB
easat-4161	311	15	algorithms	algorithm	NOUN
easat-4161	311	16	that	that	PRON
easat-4161	311	17	can	can	AUX
easat-4161	311	18	be	be	AUX
easat-4161	311	19	used	use	VERB
easat-4161	311	20	to	to	PART
easat-4161	311	21	optimize	optimize	VERB
easat-4161	311	22	route	route	NOUN
easat-4161	311	23	navigation	navigation	NOUN
easat-4161	311	24	in	in	ADP
easat-4161	311	25	complex	complex	ADJ
easat-4161	311	26	transportation	transportation	NOUN
easat-4161	311	27	systems	system	NOUN
easat-4161	311	28	.	.	PUNCT
easat-4161	312	1	transparency	transparency	NOUN
easat-4161	312	2	:	:	PUNCT
easat-4161	312	3	the	the	DET
easat-4161	312	4	authors	author	NOUN
easat-4161	312	5	confirm	confirm	VERB
easat-4161	312	6	that	that	SCONJ
easat-4161	312	7	the	the	DET
easat-4161	312	8	manuscript	manuscript	NOUN
easat-4161	312	9	is	be	AUX
easat-4161	312	10	an	an	DET
easat-4161	312	11	honest	honest	ADJ
easat-4161	312	12	,	,	PUNCT
easat-4161	312	13	accurate	accurate	ADJ
easat-4161	312	14	,	,	PUNCT
easat-4161	312	15	and	and	CCONJ
easat-4161	312	16	transparent	transparent	ADJ
easat-4161	312	17	account	account	NOUN
easat-4161	312	18	of	of	ADP
easat-4161	312	19	the	the	DET
easat-4161	312	20	study	study	NOUN
easat-4161	312	21	;	;	PUNCT
easat-4161	312	22	that	that	SCONJ
easat-4161	312	23	no	no	DET
easat-4161	312	24	vital	vital	ADJ
easat-4161	312	25	features	feature	NOUN
easat-4161	312	26	of	of	ADP
easat-4161	312	27	the	the	DET
easat-4161	312	28	study	study	NOUN
easat-4161	312	29	have	have	AUX
easat-4161	312	30	been	be	AUX
easat-4161	312	31	omitted	omit	VERB
easat-4161	312	32	;	;	PUNCT
easat-4161	312	33	and	and	CCONJ
easat-4161	312	34	that	that	SCONJ
easat-4161	312	35	any	any	DET
easat-4161	312	36	discrepancies	discrepancy	NOUN
easat-4161	312	37	from	from	ADP
easat-4161	312	38	the	the	DET
easat-4161	312	39	study	study	NOUN
easat-4161	312	40	as	as	SCONJ
easat-4161	312	41	planned	plan	VERB
easat-4161	312	42	have	have	AUX
easat-4161	312	43	been	be	AUX
easat-4161	312	44	explained	explain	VERB
easat-4161	312	45	.	.	PUNCT
easat-4161	313	1	this	this	DET
easat-4161	313	2	study	study	NOUN
easat-4161	313	3	followed	follow	VERB
easat-4161	313	4	all	all	DET
easat-4161	313	5	ethical	ethical	ADJ
easat-4161	313	6	practices	practice	NOUN
easat-4161	313	7	during	during	ADP
easat-4161	313	8	writing	writing	NOUN
easat-4161	313	9	.	.	PUNCT
easat-4161	314	1	492	492	NUM
easat-4161	314	2	edelweiss	edelweiss	PROPN
easat-4161	314	3	applied	apply	VERB
easat-4161	314	4	science	science	NOUN
easat-4161	314	5	and	and	CCONJ
easat-4161	314	6	technology	technology	NOUN
easat-4161	314	7	issn	issn	PROPN
easat-4161	314	8	:	:	PUNCT
easat-4161	314	9	2576	2576	NUM
easat-4161	314	10	-	-	SYM
easat-4161	314	11	8484	8484	NUM
easat-4161	314	12	vol	vol	NOUN
easat-4161	314	13	.	.	PROPN
easat-4161	315	1	9	9	NUM
easat-4161	315	2	,	,	PUNCT
easat-4161	315	3	no	no	INTJ
easat-4161	315	4	.	.	NOUN
easat-4161	315	5	1	1	NUM
easat-4161	315	6	:	:	PUNCT
easat-4161	315	7	481	481	NUM
easat-4161	315	8	-	-	SYM
easat-4161	315	9	492	492	NUM
easat-4161	315	10	,	,	PUNCT
easat-4161	315	11	2025	2025	NUM
easat-4161	315	12	doi	doi	NOUN
easat-4161	315	13	:	:	PUNCT
easat-4161	315	14	10.55214/25768484.v9i1.4161	10.55214/25768484.v9i1.4161	NUM
easat-4161	315	15	©	©	PROPN
easat-4161	315	16	2025	2025	NUM
easat-4161	315	17	by	by	ADP
easat-4161	315	18	the	the	DET
easat-4161	315	19	authors	author	NOUN
easat-4161	315	20	;	;	PUNCT
easat-4161	316	1	licensee	licensee	PROPN
easat-4161	316	2	learning	learn	VERB
easat-4161	316	3	gate	gate	NOUN
easat-4161	316	4	acknowledgments	acknowledgment	NOUN
easat-4161	316	5	:	:	PUNCT
easat-4161	316	6	this	this	DET
easat-4161	316	7	research	research	NOUN
easat-4161	316	8	was	be	AUX
easat-4161	316	9	funded	fund	VERB
easat-4161	316	10	by	by	ADP
easat-4161	316	11	ministry	ministry	PROPN
easat-4161	316	12	of	of	ADP
easat-4161	316	13	education	education	PROPN
easat-4161	316	14	,	,	PUNCT
easat-4161	316	15	culture	culture	NOUN
easat-4161	316	16	,	,	PUNCT
easat-4161	316	17	research	research	NOUN
easat-4161	316	18	and	and	CCONJ
easat-4161	316	19	technology	technology	NOUN
easat-4161	316	20	of	of	ADP
easat-4161	316	21	the	the	DET
easat-4161	316	22	republic	republic	NOUN
easat-4161	316	23	of	of	ADP
easat-4161	316	24	indonesia	indonesia	PROPN
easat-4161	316	25	,	,	PUNCT
easat-4161	316	26	grant	grant	VERB
easat-4161	316	27	number	number	NOUN
easat-4161	316	28	124	124	NUM
easat-4161	316	29	/	/	SYM
easat-4161	316	30	e5	e5	PROPN
easat-4161	316	31	/	/	SYM
easat-4161	316	32	pg.02.00.pl/2023	pg.02.00.pl/2023	PROPN
easat-4161	316	33	.	.	PUNCT
easat-4161	317	1	copyright	copyright	NOUN
easat-4161	317	2	:	:	PUNCT
easat-4161	317	3	©	©	PROPN
easat-4161	317	4	2025	2025	NUM
easat-4161	317	5	by	by	ADP
easat-4161	317	6	the	the	DET
easat-4161	317	7	authors	author	NOUN
easat-4161	317	8	.	.	PUNCT
easat-4161	318	1	this	this	DET
easat-4161	318	2	open	open	ADJ
easat-4161	318	3	-	-	PUNCT
easat-4161	318	4	access	access	NOUN
easat-4161	318	5	article	article	NOUN
easat-4161	318	6	is	be	AUX
easat-4161	318	7	distributed	distribute	VERB
easat-4161	318	8	under	under	ADP
easat-4161	318	9	the	the	DET
easat-4161	318	10	terms	term	NOUN
easat-4161	318	11	and	and	CCONJ
easat-4161	318	12	conditions	condition	NOUN
easat-4161	318	13	of	of	ADP
easat-4161	318	14	the	the	DET
easat-4161	318	15	creative	creative	ADJ
easat-4161	318	16	commons	common	NOUN
easat-4161	318	17	attribution	attribution	NOUN
easat-4161	318	18	(	(	PUNCT
easat-4161	318	19	cc	cc	NOUN
easat-4161	318	20	by	by	ADP
easat-4161	318	21	)	)	PUNCT
easat-4161	318	22	license	license	NOUN
easat-4161	318	23	(	(	PUNCT
easat-4161	318	24	https://creativecommons.org/licenses/by/4.0/	https://creativecommons.org/licenses/by/4.0/	PROPN
easat-4161	318	25	)	)	PUNCT
easat-4161	318	26	.	.	PUNCT
easat-4161	319	1	references	reference	NOUN
easat-4161	319	2	[	[	X
easat-4161	319	3	1	1	X
easat-4161	319	4	]	]	PUNCT
easat-4161	319	5	j.	j.	PROPN
easat-4161	319	6	a.	a.	PROPN
easat-4161	319	7	gallian	gallian	PROPN
easat-4161	319	8	,	,	PUNCT
easat-4161	319	9	"	"	PUNCT
easat-4161	319	10	a	a	DET
easat-4161	319	11	dynamic	dynamic	ADJ
easat-4161	319	12	survey	survey	NOUN
easat-4161	319	13	of	of	ADP
easat-4161	319	14	graph	graph	NOUN
easat-4161	319	15	labelling	labelling	NOUN
easat-4161	319	16	,	,	PUNCT
easat-4161	319	17	"	"	PUNCT
easat-4161	319	18	the	the	DET
easat-4161	319	19	electronic	electronic	ADJ
easat-4161	319	20	journal	journal	NOUN
easat-4161	319	21	of	of	ADP
easat-4161	319	22	combinatorics	combinatorics	PROPN
easat-4161	319	23	,	,	PUNCT
easat-4161	319	24	vol	vol	NOUN
easat-4161	319	25	.	.	PROPN
easat-4161	320	1	6	6	NUM
easat-4161	320	2	,	,	PUNCT
easat-4161	320	3	no	no	INTJ
easat-4161	320	4	.	.	NOUN
easat-4161	320	5	25	25	NUM
easat-4161	320	6	,	,	PUNCT
easat-4161	320	7	pp	pp	ADJ
easat-4161	320	8	.	.	PUNCT
easat-4161	321	1	4	4	NUM
easat-4161	321	2	–	–	PUNCT
easat-4161	321	3	623	623	NUM
easat-4161	321	4	,	,	PUNCT
easat-4161	321	5	2024	2024	NUM
easat-4161	321	6	.	.	PUNCT
easat-4161	322	1	[	[	X
easat-4161	322	2	2	2	X
easat-4161	322	3	]	]	X
easat-4161	322	4	g.	g.	PROPN
easat-4161	322	5	chartrand	chartrand	PROPN
easat-4161	322	6	,	,	PUNCT
easat-4161	322	7	m.	m.	PROPN
easat-4161	322	8	s.	s.	PROPN
easat-4161	322	9	jacobson	jacobson	PROPN
easat-4161	322	10	,	,	PUNCT
easat-4161	322	11	j.	j.	PROPN
easat-4161	322	12	lehel	lehel	PROPN
easat-4161	322	13	,	,	PUNCT
easat-4161	322	14	o.	o.	PROPN
easat-4161	322	15	r.	r.	PROPN
easat-4161	322	16	oellermann	oellermann	PROPN
easat-4161	322	17	,	,	PUNCT
easat-4161	322	18	s.	s.	PROPN
easat-4161	322	19	ruiz	ruiz	PROPN
easat-4161	322	20	,	,	PUNCT
easat-4161	322	21	and	and	CCONJ
easat-4161	322	22	f.	f.	PROPN
easat-4161	322	23	saba	saba	PROPN
easat-4161	322	24	,	,	PUNCT
easat-4161	322	25	"	"	PUNCT
easat-4161	322	26	irregular	irregular	ADJ
easat-4161	322	27	network	network	NOUN
easat-4161	322	28	,	,	PUNCT
easat-4161	322	29	"	"	PUNCT
easat-4161	322	30	congruent	congruent	ADJ
easat-4161	322	31	numbers	number	NOUN
easat-4161	322	32	,	,	PUNCT
easat-4161	322	33	vol	vol	NOUN
easat-4161	322	34	.	.	PROPN
easat-4161	322	35	64	64	NUM
easat-4161	322	36	,	,	PUNCT
easat-4161	322	37	pp	pp	ADJ
easat-4161	322	38	.	.	PUNCT
easat-4161	323	1	187	187	NUM
easat-4161	323	2	-	-	SYM
easat-4161	323	3	192	192	NUM
easat-4161	323	4	,	,	PUNCT
easat-4161	323	5	1988	1988	NUM
easat-4161	323	6	.	.	PUNCT
easat-4161	324	1	[	[	X
easat-4161	324	2	3	3	X
easat-4161	324	3	]	]	PUNCT
easat-4161	324	4	m.	m.	NOUN
easat-4161	324	5	bac	bac	PROPN
easat-4161	324	6	̆a	̆a	PROPN
easat-4161	324	7	,	,	PUNCT
easat-4161	324	8	s.	s.	PROPN
easat-4161	324	9	jendrol	jendrol	PROPN
easat-4161	324	10	,	,	PUNCT
easat-4161	324	11	m.	m.	NOUN
easat-4161	324	12	miller	miller	PROPN
easat-4161	324	13	,	,	PUNCT
easat-4161	324	14	and	and	CCONJ
easat-4161	324	15	j.	j.	PROPN
easat-4161	324	16	ryan	ryan	PROPN
easat-4161	324	17	,	,	PUNCT
easat-4161	324	18	"	"	PUNCT
easat-4161	324	19	on	on	ADP
easat-4161	324	20	irregular	irregular	ADJ
easat-4161	324	21	total	total	ADJ
easat-4161	324	22	labeling	labeling	NOUN
easat-4161	324	23	,	,	PUNCT
easat-4161	324	24	"	"	PUNCT
easat-4161	324	25	discrete	discrete	ADJ
easat-4161	324	26	mathematics	mathematic	NOUN
easat-4161	324	27	,	,	PUNCT
easat-4161	324	28	vol	vol	NOUN
easat-4161	324	29	.	.	PROPN
easat-4161	324	30	307	307	NUM
easat-4161	324	31	,	,	PUNCT
easat-4161	324	32	pp	pp	ADJ
easat-4161	324	33	.	.	PUNCT
easat-4161	324	34	1378	1378	NUM
easat-4161	324	35	–	–	PUNCT
easat-4161	324	36	1388	1388	NUM
easat-4161	324	37	,	,	PUNCT
easat-4161	324	38	2007	2007	NUM
easat-4161	324	39	.	.	PUNCT
easat-4161	325	1	https://doi.org/10.1016/j.disc.2005.11.075	https://doi.org/10.1016/j.disc.2005.11.075	VERB
easat-4161	326	1	[	[	X
easat-4161	326	2	4	4	X
easat-4161	326	3	]	]	PUNCT
easat-4161	326	4	m.	m.	NOUN
easat-4161	326	5	z.	z.	PROPN
easat-4161	326	6	nurdin	nurdin	PROPN
easat-4161	326	7	,	,	PUNCT
easat-4161	326	8	"	"	PUNCT
easat-4161	326	9	firman,“vertex	firman,“vertex	ADJ
easat-4161	326	10	-	-	PUNCT
easat-4161	326	11	irregular	irregular	ADJ
easat-4161	326	12	labeling	labeling	NOUN
easat-4161	326	13	and	and	CCONJ
easat-4161	326	14	vertex	vertex	NOUN
easat-4161	326	15	-	-	PUNCT
easat-4161	326	16	irregular	irregular	ADJ
easat-4161	326	17	total	total	ADJ
easat-4161	326	18	labeling	labeling	NOUN
easat-4161	326	19	on	on	ADP
easat-4161	326	20	caterpillar	caterpillar	ADJ
easat-4161	326	21	graph	graph	NOUN
easat-4161	326	22	,	,	PUNCT
easat-4161	326	23	"	"	PUNCT
easat-4161	326	24	international	international	ADJ
easat-4161	326	25	journal	journal	NOUN
easat-4161	326	26	of	of	ADP
easat-4161	326	27	applied	apply	VERB
easat-4161	326	28	mathematics	mathematic	NOUN
easat-4161	326	29	and	and	CCONJ
easat-4161	326	30	statistics	statistic	NOUN
easat-4161	326	31	,	,	PUNCT
easat-4161	326	32	vol	vol	NOUN
easat-4161	326	33	.	.	PROPN
easat-4161	326	34	40	40	NUM
easat-4161	326	35	,	,	PUNCT
easat-4161	326	36	no	no	INTJ
easat-4161	326	37	.	.	NOUN
easat-4161	326	38	10	10	NUM
easat-4161	326	39	,	,	PUNCT
easat-4161	326	40	pp	pp	ADJ
easat-4161	326	41	.	.	PUNCT
easat-4161	327	1	99	99	NUM
easat-4161	327	2	-	-	SYM
easat-4161	327	3	105	105	NUM
easat-4161	327	4	,	,	PUNCT
easat-4161	327	5	2013	2013	NUM
easat-4161	327	6	.	.	PUNCT
easat-4161	328	1	[	[	X
easat-4161	328	2	5	5	X
easat-4161	328	3	]	]	PUNCT
easat-4161	328	4	s.	s.	PROPN
easat-4161	328	5	aarthi	aarthi	PROPN
easat-4161	328	6	,	,	PUNCT
easat-4161	328	7	"	"	PUNCT
easat-4161	328	8	stability	stability	NOUN
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easat-4161	328	10	total	total	ADJ
easat-4161	328	11	irregularity	irregularity	NOUN
easat-4161	328	12	strength	strength	NOUN
easat-4161	328	13	of	of	ADP
easat-4161	328	14	helm	helm	NOUN
easat-4161	328	15	graphs	graph	NOUN
easat-4161	328	16	,	,	PUNCT
easat-4161	328	17	"	"	PUNCT
easat-4161	328	18	ijesc	ijesc	NOUN
easat-4161	328	19	,	,	PUNCT
easat-4161	328	20	vol	vol	NOUN
easat-4161	328	21	.	.	PROPN
easat-4161	328	22	7	7	NUM
easat-4161	328	23	,	,	PUNCT
easat-4161	328	24	no	no	INTJ
easat-4161	328	25	.	.	NOUN
easat-4161	328	26	8	8	NUM
easat-4161	328	27	,	,	PUNCT
easat-4161	328	28	2017	2017	NUM
easat-4161	328	29	.	.	PUNCT
easat-4161	329	1	[	[	X
easat-4161	329	2	6	6	NUM
easat-4161	329	3	]	]	PUNCT
easat-4161	329	4	a.	a.	NOUN
easat-4161	329	5	ahmad	ahmad	PROPN
easat-4161	329	6	,	,	PUNCT
easat-4161	329	7	e.	e.	PROPN
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easat-4161	329	9	,	,	PUNCT
easat-4161	329	10	and	and	CCONJ
easat-4161	329	11	m.	m.	NOUN
easat-4161	329	12	imran	imran	PROPN
easat-4161	329	13	,	,	PUNCT
easat-4161	329	14	"	"	PUNCT
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easat-4161	329	18	strength	strength	NOUN
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easat-4161	329	21	union	union	PROPN
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easat-4161	329	26	"	"	PUNCT
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easat-4161	329	29	graph	graph	NOUN
easat-4161	329	30	theory	theory	NOUN
easat-4161	329	31	,	,	PUNCT
easat-4161	329	32	vol	vol	NOUN
easat-4161	329	33	.	.	PROPN
easat-4161	330	1	32	32	NUM
easat-4161	330	2	,	,	PUNCT
easat-4161	330	3	no	no	INTJ
easat-4161	330	4	.	.	NOUN
easat-4161	330	5	3	3	NUM
easat-4161	330	6	,	,	PUNCT
easat-4161	330	7	pp	pp	ADJ
easat-4161	330	8	.	.	PUNCT
easat-4161	331	1	427	427	NUM
easat-4161	331	2	-	-	SYM
easat-4161	331	3	434	434	NUM
easat-4161	331	4	,	,	PUNCT
easat-4161	331	5	2012	2012	NUM
easat-4161	331	6	.	.	PUNCT
easat-4161	332	1	https://doi.org/10.7151/dmgt.1619	https://doi.org/10.7151/dmgt.1619	PRON
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easat-4161	332	3	7	7	X
easat-4161	332	4	]	]	X
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easat-4161	332	7	widodo	widodo	PROPN
easat-4161	332	8	,	,	PUNCT
easat-4161	332	9	i.	i.	PROPN
easat-4161	332	10	e.	e.	PROPN
easat-4161	332	11	wijayanti	wijayanti	PROPN
easat-4161	332	12	,	,	PUNCT
easat-4161	332	13	k.	k.	PROPN
easat-4161	332	14	a.	a.	PROPN
easat-4161	332	15	sugeng	sugeng	PROPN
easat-4161	332	16	,	,	PUNCT
easat-4161	332	17	m.	m.	NOUN
easat-4161	332	18	bača	bača	PROPN
easat-4161	332	19	,	,	PUNCT
easat-4161	332	20	and	and	CCONJ
easat-4161	332	21	a.	a.	PROPN
easat-4161	332	22	s.	s.	PROPN
easat-4161	332	23	fenovcikova	fenovcikova	PROPN
easat-4161	332	24	,	,	PUNCT
easat-4161	332	25	"	"	PUNCT
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easat-4161	332	27	total	total	ADJ
easat-4161	332	28	vertex	vertex	NOUN
easat-4161	332	29	irregularity	irregularity	NOUN
easat-4161	332	30	strength	strength	NOUN
easat-4161	332	31	of	of	ADP
easat-4161	332	32	generalized	generalized	ADJ
easat-4161	332	33	helm	helm	NOUN
easat-4161	332	34	graphs	graph	NOUN
easat-4161	332	35	and	and	CCONJ
easat-4161	332	36	prisms	prism	NOUN
easat-4161	332	37	with	with	ADP
easat-4161	332	38	outer	outer	ADJ
easat-4161	332	39	pendant	pendant	ADJ
easat-4161	332	40	edges	edge	NOUN
easat-4161	332	41	,	,	PUNCT
easat-4161	332	42	"	"	PUNCT
easat-4161	332	43	australian	australian	ADJ
easat-4161	332	44	hair	hair	NOUN
easat-4161	332	45	comb	comb	NOUN
easat-4161	332	46	,	,	PUNCT
easat-4161	332	47	vol	vol	NOUN
easat-4161	332	48	.	.	PROPN
easat-4161	332	49	65	65	NUM
easat-4161	332	50	,	,	PUNCT
easat-4161	332	51	no	no	INTJ
easat-4161	332	52	.	.	NOUN
easat-4161	332	53	1	1	NUM
easat-4161	332	54	,	,	PUNCT
easat-4161	332	55	pp	pp	ADJ
easat-4161	332	56	.	.	PUNCT
easat-4161	332	57	14–26	14–26	NUM
easat-4161	332	58	,	,	PUNCT
easat-4161	332	59	2016	2016	NUM
easat-4161	332	60	.	.	PUNCT
easat-4161	333	1	[	[	X
easat-4161	333	2	8	8	NUM
easat-4161	333	3	]	]	X
easat-4161	333	4	n.	n.	NOUN
easat-4161	333	5	hinding	hinding	NOUN
easat-4161	333	6	,	,	PUNCT
easat-4161	333	7	d.	d.	PROPN
easat-4161	333	8	firmayasari	firmayasari	PROPN
easat-4161	333	9	,	,	PUNCT
easat-4161	333	10	h.	h.	PROPN
easat-4161	333	11	basir	basir	PROPN
easat-4161	333	12	,	,	PUNCT
easat-4161	333	13	m.	m.	NOUN
easat-4161	333	14	bača	bača	PROPN
easat-4161	333	15	,	,	PUNCT
easat-4161	333	16	and	and	CCONJ
easat-4161	333	17	a.	a.	PROPN
easat-4161	333	18	semaničová	semaničová	PROPN
easat-4161	333	19	-	-	PUNCT
easat-4161	333	20	feňovčíková	feňovčíková	PROPN
easat-4161	333	21	,	,	PUNCT
easat-4161	333	22	"	"	PUNCT
easat-4161	333	23	on	on	ADP
easat-4161	333	24	irregularity	irregularity	NOUN
easat-4161	333	25	strength	strength	NOUN
easat-4161	333	26	of	of	ADP
easat-4161	333	27	diamond	diamond	NOUN
easat-4161	333	28	network	network	NOUN
easat-4161	333	29	,	,	PUNCT
easat-4161	333	30	"	"	PUNCT
easat-4161	333	31	akce	akce	PROPN
easat-4161	333	32	international	international	PROPN
easat-4161	333	33	journal	journal	NOUN
easat-4161	333	34	of	of	ADP
easat-4161	333	35	graphs	graph	NOUN
easat-4161	333	36	and	and	CCONJ
easat-4161	333	37	combinatorics	combinatoric	NOUN
easat-4161	333	38	,	,	PUNCT
easat-4161	333	39	vol	vol	NOUN
easat-4161	333	40	.	.	PROPN
easat-4161	333	41	15	15	NUM
easat-4161	333	42	,	,	PUNCT
easat-4161	333	43	no	no	INTJ
easat-4161	333	44	.	.	NOUN
easat-4161	333	45	3	3	NUM
easat-4161	333	46	,	,	PUNCT
easat-4161	333	47	pp	pp	ADJ
easat-4161	333	48	.	.	PUNCT
easat-4161	333	49	291	291	NUM
easat-4161	333	50	-	-	SYM
easat-4161	333	51	297	297	NUM
easat-4161	333	52	,	,	PUNCT
easat-4161	333	53	2018	2018	NUM
easat-4161	333	54	.	.	PUNCT
easat-4161	334	1	https://doi.org/10.1016/j.akcej.2017.10.003	https://doi.org/10.1016/j.akcej.2017.10.003	NUM
easat-4161	334	2	[	[	X
easat-4161	335	1	9	9	NUM
easat-4161	335	2	]	]	PUNCT
easat-4161	335	3	m.	m.	NOUN
easat-4161	335	4	k.	k.	PROPN
easat-4161	335	5	siddiqui	siddiqui	PROPN
easat-4161	335	6	nurdin	nurdin	PROPN
easat-4161	335	7	and	and	CCONJ
easat-4161	335	8	e.	e.	PROPN
easat-4161	335	9	t.	t.	PROPN
easat-4161	335	10	baskoro	baskoro	PROPN
easat-4161	335	11	,	,	PUNCT
easat-4161	335	12	"	"	PUNCT
easat-4161	335	13	total	total	ADJ
easat-4161	335	14	edge	edge	NOUN
easat-4161	335	15	irregularity	irregularity	NOUN
easat-4161	335	16	strength	strength	NOUN
easat-4161	335	17	of	of	ADP
easat-4161	335	18	the	the	DET
easat-4161	335	19	disjoint	disjoint	PROPN
easat-4161	335	20	union	union	PROPN
easat-4161	335	21	of	of	ADP
easat-4161	335	22	helm	helm	NOUN
easat-4161	335	23	graph	graph	NOUN
easat-4161	335	24	,	,	PUNCT
easat-4161	335	25	"	"	PUNCT
easat-4161	335	26	journal	journal	NOUN
easat-4161	335	27	of	of	ADP
easat-4161	335	28	mathematical	mathematical	ADJ
easat-4161	335	29	and	and	CCONJ
easat-4161	335	30	fundamental	fundamental	ADJ
easat-4161	335	31	sciences	science	NOUN
easat-4161	335	32	,	,	PUNCT
easat-4161	335	33	vol	vol	NOUN
easat-4161	335	34	.	.	PROPN
easat-4161	336	1	42	42	NUM
easat-4161	336	2	,	,	PUNCT
easat-4161	336	3	no	no	INTJ
easat-4161	336	4	.	.	NOUN
easat-4161	336	5	2	2	NUM
easat-4161	336	6	,	,	PUNCT
easat-4161	336	7	pp	pp	ADJ
easat-4161	336	8	.	.	PUNCT
easat-4161	337	1	163–171	163–171	NUM
easat-4161	337	2	,	,	PUNCT
easat-4161	337	3	2013	2013	NUM
easat-4161	337	4	.	.	PUNCT
easat-4161	338	1	https://creativecommons.org/licenses/by/4.0/	https://creativecommons.org/licenses/by/4.0/	PROPN
easat-4161	338	2	https://doi.org/10.1016/j.disc.2005.11.075	https://doi.org/10.1016/j.disc.2005.11.075	VERB
easat-4161	338	3	https://doi.org/10.7151/dmgt.1619	https://doi.org/10.7151/dmgt.1619	ADJ
easat-4161	338	4	https://doi.org/10.1016/j.akcej.2017.10.003	https://doi.org/10.1016/j.akcej.2017.10.003	NUM