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Дискретна математика 2 семестр

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Знайти роз'єднувальні вершини графа.

b , d , f , j , l

Image failed to load: b

b , c , f , i , l

b , c , f , j , l

b , c , e , j , l

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Задати орієнтований граф за допомогою матриці суміжності.

	a	Image failed to load: b b	Image failed to load: c c	Image failed to load: d d	f	Image failed to load: g g	Image failed to load: h h	Image failed to load: j j
a	0	1	1	1	0	0	0	0
b	0	0	0	1	0	2	1	0
c	0	0	0	0	0	1	0	0
d	1	0	0	1	0		1	1
Image failed to load: f f	0	1	0	0	0	1	1	0
g	1	0	0	0	2	0	0	0
h	0	0	0	0	1	0	0	1
j	0	0	0	0	0	0	2	1

	a	b	c	d	f	g	h	j
a	0	1	1	1	0	0	0	0
b	0	0	0	1	0	1	2	0
c	0	0	0	0	0	1	0	0
d	1	0	0	1	0	0	1	1
f	0	0	0	0	1	1	1	0
g	1	0	0	0	2	0	0	0
h	0	0	0	0	1	0	0	0
j	0	0	0	0	0	0	1	2

	a	b	c	d	f	g	h	j
Image failed to load: a a	0	1	1	1	0	0	0	0
Image failed to load: b b	0	0	0	1	0	1	2	0
c	0	0	0	0	0	1	0	0
d	1	0	0	1	0	0	1	1
f	0	1	0	0	1	1	1	0
Image failed to load: g g	1	0	0	0	2	0	0	0
h	0	0	0	0	1	0	0	1
Image failed to load: j j	0	0	0	0	0	0	2	1

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Задати граф за допомогою матриці суміжності.

	a	b	c	d	g	f	h	j
Image failed to load: a a	0	0	1	3	1	0	0	0
b	0	1	1	0	1	2	0	0
c	1	1	0	0	0	0	0	0
Image failed to load: d d	3	0	0	0	1	0	1	2
g	1	1	0	1	0	3	1	0
f	0	2	0	0	3	1	2	0
h	0	0	0	1	1	2	0	1
j	0	0	0	2	0	0	1	1

	a	Image failed to load: b b	Image failed to load: c c	d	Image failed to load: g g	Image failed to load: f f	Image failed to load: h h	Image failed to load: j j
a	0	0	3	1	1	0	0	0
b	0	1	1	0	1	2	0	0
c	1	1	0	0	0	0	0	0
d	1	0	0	0	3	0	1	2
g	1	1	0	1	0	1	3	0
f	0	2	0	0	3	1	2	0
h	0	0	0	1	1	2	0	1
j	0	0	0	2	0	0	1	1

	a	b	c	d	g	f	h	j
a	0	0	1	3	1	0	0	0
b	0	2	0	0	1	2	0	0
c	1	1	0	0	0	0	0	0
d	3	0	0	0	1	0	1	2
g	1	1	0	1	0	3	1	0
f	0	2	0	0	3	2	1	0
h	0	0	0	1	1	2	0	1
j	0	0	0	1	0	0	2	1

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Задати орієнтований граф за допомогою матриці інцидентності.

	e_1	Image failed to load: e_2 e_2	e_3	e_4	e_5	e_6	e_7	e_8	e_9	$e_{10}$ e_{10}	$e_{11}$ e_{11}	$e_{12}$ e_{12}	$e_{13}$ e_{13}	$e_{14}$ e_{14}	$e_{15}$ e_{15}	Image failed to load: e_{16} e_{16}
Image failed to load: a a	-1	1	1	0	0	0	0	0	1	0	0	0	0	0	0	0
Image failed to load: b b	0	0	-1	0	1	1	1	-1	0	0	0	0	0	1	0	0
Image failed to load: c c	0	-1	0	1	0	0	0	0	0	0	0	0	0	0	0	0
Image failed to load: d d	1	0	0	0	-1	0	0	0	-1	0	1	1	0	0	0	0
Image failed to load: f f	0	0	0	0	0	0	-1	1	0	1	0	0	0	0	0	2
Image failed to load: g g	0	0	0	-1	0	-1	1	0	0	0	0	0	0	0	0	0
Image failed to load: h h	0	0	0	0	0	0	0	0	0	-1	-1	0	1	-1	0	0
Image failed to load: j j	0	0	0	0	0	0	0	0	0	0	0	-1	-1	0	2	0

	e_1	e_2	Image failed to load: e_3 e_3	Image failed to load: e_4 e_4	Image failed to load: e_5 e_5	Image failed to load: e_6 e_6	Image failed to load: e_7 e_7	Image failed to load: e_8 e_8	Image failed to load: e_9 e_9	Image failed to load: e_{10} e_{10}	Image failed to load: e_{11} e_{11}	Image failed to load: e_{12} e_{12}	Image failed to load: e_{13} e_{13}	Image failed to load: e_{14} e_{14}	Image failed to load: e_{15} e_{15}	$e_{16}$ e_{16}
a	-1	1	1	0	0	0	0	0	1	0	0	0	0	0	0	0
b	0	0	-1	0	1	1	0	-1	0	0	0	0	0	1	0	0
c	0	-1	0	1	0	0	0	0	0	0	0	0	0	0	0	0
d	1	0	0	0	-1	0	0	0	-1	0	1	1	0	0	0	0
f	0	0	0	0	0	0	-1	1	0	1	0	0	0	0	0	2
g	0	0	0	-1	0	-1	1	0	0	0	0	0	0	0	0	0
h	0	0	0	0	0	0	0	0	0	-1	-1	0	1	-1	0	0
j	0	0	0	0	0	0	0	0	0	0	0	-1	-1	0	2	0

	Image failed to load: e_1 e_1	e_2	e_3	e_4	e_5	e_6	e_7	e_8	e_9	$e_{10}$ e_{10}	$e_{11}$ e_{11}	$e_{12}$ e_{12}	$e_{13}$ e_{13}	$e_{14}$ e_{14}	$e_{15}$ e_{15}	$e_{16}$ e_{16}
a	-1	1	1	0	0	0	0	0	1	0	0	0	0	0	0	0
b	0	0	-1	0	1	1	0	-1	0	0	0	0	0	1	0	0
c	0	-1	0	1	0	0	0	0	0	0	0	0	0	0	0	0
d	1	0	0	0	-1	0	0	0	-1	0	-1	1	0	0	0	0
f	0	0	0	0	0	0	-1	1	0	1	0	0	0	0	0	2
g	0	0	0	-1	0	-1	1	0	0	0	0	0	0	0	0	0
h	0	0	0	0	0	0	0	0	0	-1	1	0	1	-1	0	0
j	0	0	0	0	0	0	0	0	0	0	0	-1	-1	0	2	0

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Задати неорієнтований граф за допомогою матриці інцидентності.

	e_1	Image failed to load: e_2 e_2	Image failed to load: e_3 e_3	Image failed to load: e_4 e_4	Image failed to load: e_5 e_5	Image failed to load: e_6 e_6	Image failed to load: e_7 e_7	Image failed to load: e_8 e_8	Image failed to load: e_9 e_9	$e_{10}$ e_{10}	$e_{11}$ e_{11}	$e_{1 2}$ e_{1 2}	$e_{1 3}$ e_{1 3}	Image failed to load: e_{14} e_{14}	Image failed to load: e_{1 5} e_{1 5}	Image failed to load: e_{1 6} e_{1 6}
Image failed to load: a a	1	1	1	0	0	0	0	0	1	0	0	0	0	0	0	0
Image failed to load: b b	0	0	1	0	1	1	0	1	0	0	0	0	0	1	0	0
Image failed to load: c c	0	1	0	1	0	0	0	0	0	0	0	0	0	0	0	0
Image failed to load: d d	1	0	0	0	1	0	0	0	1	0	1	1	0	0	0	0
Image failed to load: f f	0	0	0	0	0	0	1	1	0	1	0	0	0	0	0	2
Image failed to load: g g	0	0	0	1	0	1	1	0	0	0	0	0	0	0	0	0
Image failed to load: h h	0	0	0	0	0	0	0	0	0	1	1	0	1	1	0	0
Image failed to load: j j	0	0	0	0	0	0	0	0	0	0	0	1	1	0	2	0

	e_1	e_2	e_3	e_4	e_5	e_6	e_7	e_8	e_9	Image failed to load: e_{10} e_{10}	Image failed to load: e_{11} e_{11}	Image failed to load: e_{1 2} e_{1 2}	Image failed to load: e_{1 3} e_{1 3}	$e_{14}$ e_{14}	$e_{1 5}$ e_{1 5}	$e_{1 6}$ e_{1 6}
a	1	1	1	0	0	0	0	0	1	0	0	0	0	0	0	0
b	0	0	0	0	1	1	0	1	0	0	0	0	0	1	0	0
c	0	1	0	1	0	0	0	0	0	0	0	0	0	0	0	0
d	1	0	0	0	1	0	0	0	1	0	1	1	0	0	0	0
f	0	0	1	0	0	0	1	1	0	1	0	0	0	0	0	2
g	0	0	0	1	0	1	1	0	0	0	0	0	0	0	0	0
h	0	0	0	0	0	0	0	0	0	1	1	0	1	1	0	0
j	0	0	0	0	0	0	0	0	0	0	0	1	1	0	2	0

	Image failed to load: e_1 e_1	e_2	e_3	e_4	e_5	e_6	e_7	e_8	e_9	$e_{10}$ e_{10}	$e_{11}$ e_{11}	$e_{1 2}$ e_{1 2}	$e_{1 3}$ e_{1 3}	$e_{14}$ e_{14}	$e_{1 5}$ e_{1 5}	$e_{1 6}$ e_{1 6}
a	1	1	1	0	0	0	0	1	1	0	0	0	0	0	0	0
b	0	0	1	0	1	1	0	1	0	0	0	0	0	1	0	0
c	0	1	0	1	0	0	0	0	0	0	0	0	0	0	0	0
d	1	0	0	0	1	0	0	0	1	0	1	1	0	0	0	0
f	0	0	0	0	0	0	1	1	0	1	0	0	0	0	0	2
g	0	0	0	1	0	1	1	0	0	0	0	0	0	0	0	0
h	0	0	0	0	0	0	0	0	0	1	1	0	1	1	0	0
j	0	0	0	0	0	0	0	0	0	0	0	1	1	0	2	0

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Знайти всі мости у графі

Вибрати кілька відповідей.

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Знайти роз'єднувальні вершини графа.

b , d , f , j , l

b , c , f , l , m

b , c , f , i , l

b , c , f , j , l

b , c , e , j , l

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Задати орієнтований граф за допомогою матриці суміжності.

	a	b	c	d	f	g	h	j
a	0	1	1	1	0	0	0	0
b	0	0	0	1	0	2	1	0
c	0	0	0	0	0	1	0	0
d	1	0	0	1	0		1	1
f	0	1	0	0	0	1	1	0
g	1	0	0	0	2	0	0	0
h	0	0	0	0	1	0	0	1
j	0	0	0	0	0	0	2	1

	Image failed to load: a a	Image failed to load: b b	Image failed to load: c c	Image failed to load: d d	Image failed to load: f f	g	Image failed to load: h h	j
a	0	1	1	1	0	0	0	0
b	0	0	0	1	0	1	2	0
Image failed to load: c c	0	0	0	0	0	1	0	0
Image failed to load: d d	1	0	0	1	0	0	1	1
f	0	0	0	0	1	1	1	0
Image failed to load: g g	1	0	0	0	2	0	0	0
h	0	0	0	0	1	0	0	0
Image failed to load: j j	0	0	0	0	0	0	1	2

	a	b	c	d	f	g	h	j
a	0	1	1	1	0	0	0	0
b	0	0	0	1	0	1	2	0
c	0	0	0	0	0	1	0	0
d	1	0	0	1	0	0	1	1
f	0	1	0	0	1	1	1	0
g	1	0	0	0	2	0	0	0
h	0	0	0	0	1	0	0	1
j	0	0	0	0	0	0	2	1

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Задати граф за допомогою матриці суміжності.

	Image failed to load: a a	b	c	d	g	f	h	j
a	0	0	1	3	1	0	0	0
b	0	1	1	0	1	2	0	0
c	1	1	0	0	0	0	0	0
d	3	0	0	0	1	0	1	2
g	1	1	0	1	0	3	1	0
f	0	2	0	0	3	1	2	0
h	0	0	0	1	1	2	0	1
j	0	0	0	2	0	0	1	1

	a	b	c	d	g	f	h	j
a	0	0	3	1	1	0	0	0
Image failed to load: b b	0	1	1	0	1	2	0	0
c	1	1	0	0	0	0	0	0
Image failed to load: d d	1	0	0	0	3	0	1	2
Image failed to load: g g	1	1	0	1	0	1	3	0
f	0	2	0	0	3	1	2	0
Image failed to load: h h	0	0	0	1	1	2	0	1
Image failed to load: j j	0	0	0	2	0	0	1	1

	a	b	Image failed to load: c c	d	g	f	h	j
a	0	0	1	3	1	0	0	0
b	0	2	0	0	1	2	0	0
c	1	1	0	0	0	0	0	0
d	3	0	0	0	1	0	1	2
g	1	1	0	1	0	3	1	0
f	0	2	0	0	3	2	1	0
h	0	0	0	1	1	2	0	1
j	0	0	0	1	0	0	2	1

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Задати неорієнтований граф за допомогою матриці інцидентності.

	e_1	e_2	e_3	e_4	e_5	e_6	e_7	e_8	e_9	$e_{10}$ e_{10}	$e_{11}$ e_{11}	$e_{1 2}$ e_{1 2}	$e_{1 3}$ e_{1 3}	$e_{14}$ e_{14}	$e_{1 5}$ e_{1 5}	$e_{1 6}$ e_{1 6}
a	1	1	1	0	0	0	0	0	1	0	0	0	0	0	0	0
b	0	0	1	0	1	1	0	1	0	0	0	0	0	1	0	0
c	0	1	0	1	0	0	0	0	0	0	0	0	0	0	0	0
d	1	0	0	0	1	0	0	0	1	0	1	1	0	0	0	0
f	0	0	0	0	0	0	1	1	0	1	0	0	0	0	0	2
g	0	0	0	1	0	1	1	0	0	0	0	0	0	0	0	0
h	0	0	0	0	0	0	0	0	0	1	1	0	1	1	0	0
j	0	0	0	0	0	0	0	0	0	0	0	1	1	0	2	0

	e_1	e_2	e_3	e_4	e_5	e_6	e_7	e_8	e_9	$e_{10}$ e_{10}	$e_{11}$ e_{11}	$e_{1 2}$ e_{1 2}	$e_{1 3}$ e_{1 3}	$e_{14}$ e_{14}	$e_{1 5}$ e_{1 5}	$e_{1 6}$ e_{1 6}
a	1	1	1	0	0	0	0	0	1	0	0	0	0	0	0	0
b	0	0	0	0	1	1	0	1	0	0	0	0	0	1	0	0
c	0	1	0	1	0	0	0	0	0	0	0	0	0	0	0	0
d	1	0	0	0	1	0	0	0	1	0	1	1	0	0	0	0
f	0	0	1	0	0	0	1	1	0	1	0	0	0	0	0	2
g	0	0	0	1	0	1	1	0	0	0	0	0	0	0	0	0
h	0	0	0	0	0	0	0	0	0	1	1	0	1	1	0	0
j	0	0	0	0	0	0	0	0	0	0	0	1	1	0	2	0

	e_1	e_2	e_3	e_4	e_5	e_6	e_7	e_8	e_9	$e_{10}$ e_{10}	$e_{11}$ e_{11}	$e_{1 2}$ e_{1 2}	$e_{1 3}$ e_{1 3}	$e_{14}$ e_{14}	$e_{1 5}$ e_{1 5}	$e_{1 6}$ e_{1 6}
a	1	1	1	0	0	0	0	1	1	0	0	0	0	0	0	0
b	0	0	1	0	1	1	0	1	0	0	0	0	0	1	0	0
c	0	1	0	1	0	0	0	0	0	0	0	0	0	0	0	0
d	1	0	0	0	1	0	0	0	1	0	1	1	0	0	0	0
f	0	0	0	0	0	0	1	1	0	1	0	0	0	0	0	2
g	0	0	0	1	0	1	1	0	0	0	0	0	0	0	0	0
h	0	0	0	0	0	0	0	0	0	1	1	0	1	1	0	0
j	0	0	0	0	0	0	0	0	0	0	0	1	1	0	2	0

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	a	b	c	d	f	g	h	j
a	0	1	1	1	0	0	0	0
b	0	0	0	1	0	1	2	0
c	0	0	0	0	0	1	0	0
d	1	0	0	1	0	0	1	1
f	0	0	0	0	1	1	1	0
g	1	0	0	0	2	0	0	0
h	0	0	0	0	1	0	0	0
j	0	0	0	0	0	0	1	2

	a	Image failed to load: b b	Image failed to load: c c	d	Image failed to load: g g	Image failed to load: f f	Image failed to load: h h	Image failed to load: j j
a	0	0	3	1	1	0	0	0
b	0	1	1	0	1	2	0	0
c	1	1	0	0	0	0	0	0
d	1	0	0	0	3	0	1	2
g	1	1	0	1	0	1	3	0
f	0	2	0	0	3	1	2	0
h	0	0	0	1	1	2	0	1
j	0	0	0	2	0	0	1	1

	a	b	c	d	g	f	h	j
a	0	0	1	3	1	0	0	0
b	0	2	0	0	1	2	0	0
c	1	1	0	0	0	0	0	0
d	3	0	0	0	1	0	1	2
g	1	1	0	1	0	3	1	0
f	0	2	0	0	3	2	1	0
h	0	0	0	1	1	2	0	1
j	0	0	0	1	0	0	2	1

	e_1	e_2	Image failed to load: e_3 e_3	Image failed to load: e_4 e_4	Image failed to load: e_5 e_5	Image failed to load: e_6 e_6	Image failed to load: e_7 e_7	Image failed to load: e_8 e_8	Image failed to load: e_9 e_9	Image failed to load: e_{10} e_{10}	Image failed to load: e_{11} e_{11}	Image failed to load: e_{12} e_{12}	Image failed to load: e_{13} e_{13}	Image failed to load: e_{14} e_{14}	Image failed to load: e_{15} e_{15}	$e_{16}$ e_{16}
a	-1	1	1	0	0	0	0	0	1	0	0	0	0	0	0	0
b	0	0	-1	0	1	1	0	-1	0	0	0	0	0	1	0	0
c	0	-1	0	1	0	0	0	0	0	0	0	0	0	0	0	0
d	1	0	0	0	-1	0	0	0	-1	0	1	1	0	0	0	0
f	0	0	0	0	0	0	-1	1	0	1	0	0	0	0	0	2
g	0	0	0	-1	0	-1	1	0	0	0	0	0	0	0	0	0
h	0	0	0	0	0	0	0	0	0	-1	-1	0	1	-1	0	0
j	0	0	0	0	0	0	0	0	0	0	0	-1	-1	0	2	0

	Image failed to load: e_1 e_1	e_2	e_3	e_4	e_5	e_6	e_7	e_8	e_9	$e_{10}$ e_{10}	$e_{11}$ e_{11}	$e_{12}$ e_{12}	$e_{13}$ e_{13}	$e_{14}$ e_{14}	$e_{15}$ e_{15}	$e_{16}$ e_{16}
a	-1	1	1	0	0	0	0	0	1	0	0	0	0	0	0	0
b	0	0	-1	0	1	1	0	-1	0	0	0	0	0	1	0	0
c	0	-1	0	1	0	0	0	0	0	0	0	0	0	0	0	0
d	1	0	0	0	-1	0	0	0	-1	0	-1	1	0	0	0	0
f	0	0	0	0	0	0	-1	1	0	1	0	0	0	0	0	2
g	0	0	0	-1	0	-1	1	0	0	0	0	0	0	0	0	0
h	0	0	0	0	0	0	0	0	0	-1	1	0	1	-1	0	0
j	0	0	0	0	0	0	0	0	0	0	0	-1	-1	0	2	0

	e_1	e_2	e_3	e_4	e_5	e_6	e_7	e_8	e_9	Image failed to load: e_{10} e_{10}	Image failed to load: e_{11} e_{11}	Image failed to load: e_{1 2} e_{1 2}	Image failed to load: e_{1 3} e_{1 3}	$e_{14}$ e_{14}	$e_{1 5}$ e_{1 5}	$e_{1 6}$ e_{1 6}
a	1	1	1	0	0	0	0	0	1	0	0	0	0	0	0	0
b	0	0	0	0	1	1	0	1	0	0	0	0	0	1	0	0
c	0	1	0	1	0	0	0	0	0	0	0	0	0	0	0	0
d	1	0	0	0	1	0	0	0	1	0	1	1	0	0	0	0
f	0	0	1	0	0	0	1	1	0	1	0	0	0	0	0	2
g	0	0	0	1	0	1	1	0	0	0	0	0	0	0	0	0
h	0	0	0	0	0	0	0	0	0	1	1	0	1	1	0	0
j	0	0	0	0	0	0	0	0	0	0	0	1	1	0	2	0

	Image failed to load: e_1 e_1	e_2	e_3	e_4	e_5	e_6	e_7	e_8	e_9	$e_{10}$ e_{10}	$e_{11}$ e_{11}	$e_{1 2}$ e_{1 2}	$e_{1 3}$ e_{1 3}	$e_{14}$ e_{14}	$e_{1 5}$ e_{1 5}	$e_{1 6}$ e_{1 6}
a	1	1	1	0	0	0	0	1	1	0	0	0	0	0	0	0
b	0	0	1	0	1	1	0	1	0	0	0	0	0	1	0	0
c	0	1	0	1	0	0	0	0	0	0	0	0	0	0	0	0
d	1	0	0	0	1	0	0	0	1	0	1	1	0	0	0	0
f	0	0	0	0	0	0	1	1	0	1	0	0	0	0	0	2
g	0	0	0	1	0	1	1	0	0	0	0	0	0	0	0	0
h	0	0	0	0	0	0	0	0	0	1	1	0	1	1	0	0
j	0	0	0	0	0	0	0	0	0	0	0	1	1	0	2	0

	a	b	c	d	f	g	h	j
a	0	1	1	1	0	0	0	0
b	0	0	0	1	0	2	1	0
c	0	0	0	0	0	1	0	0
d	1	0	0	1	0		1	1
f	0	1	0	0	0	1	1	0
g	1	0	0	0	2	0	0	0
h	0	0	0	0	1	0	0	1
j	0	0	0	0	0	0	2	1

	a	b	c	d	f	g	h	j
a	0	1	1	1	0	0	0	0
b	0	0	0	1	0	1	2	0
c	0	0	0	0	0	1	0	0
d	1	0	0	1	0	0	1	1
f	0	1	0	0	1	1	1	0
g	1	0	0	0	2	0	0	0
h	0	0	0	0	1	0	0	1
j	0	0	0	0	0	0	2	1

	Image failed to load: a a	b	c	d	g	f	h	j
a	0	0	1	3	1	0	0	0
b	0	1	1	0	1	2	0	0
c	1	1	0	0	0	0	0	0
d	3	0	0	0	1	0	1	2
g	1	1	0	1	0	3	1	0
f	0	2	0	0	3	1	2	0
h	0	0	0	1	1	2	0	1
j	0	0	0	2	0	0	1	1

	a	b	c	d	f	g	h	j
a	0	1	1	1	0	0	0	0
b	0	0	0	1	0	1	2	0
c	0	0	0	0	0	1	0	0
d	1	0	0	1	0	0	1	1
f	0	0	0	0	1	1	1	0
g	1	0	0	0	2	0	0	0
h	0	0	0	0	1	0	0	0
j	0	0	0	0	0	0	1	2

	a	Image failed to load: b b	Image failed to load: c c	d	Image failed to load: g g	Image failed to load: f f	Image failed to load: h h	Image failed to load: j j
a	0	0	3	1	1	0	0	0
b	0	1	1	0	1	2	0	0
c	1	1	0	0	0	0	0	0
d	1	0	0	0	3	0	1	2
g	1	1	0	1	0	1	3	0
f	0	2	0	0	3	1	2	0
h	0	0	0	1	1	2	0	1
j	0	0	0	2	0	0	1	1

	a	b	c	d	g	f	h	j
a	0	0	1	3	1	0	0	0
b	0	2	0	0	1	2	0	0
c	1	1	0	0	0	0	0	0
d	3	0	0	0	1	0	1	2
g	1	1	0	1	0	3	1	0
f	0	2	0	0	3	2	1	0
h	0	0	0	1	1	2	0	1
j	0	0	0	1	0	0	2	1

	e_1	e_2	Image failed to load: e_3 e_3	Image failed to load: e_4 e_4	Image failed to load: e_5 e_5	Image failed to load: e_6 e_6	Image failed to load: e_7 e_7	Image failed to load: e_8 e_8	Image failed to load: e_9 e_9	Image failed to load: e_{10} e_{10}	Image failed to load: e_{11} e_{11}	Image failed to load: e_{12} e_{12}	Image failed to load: e_{13} e_{13}	Image failed to load: e_{14} e_{14}	Image failed to load: e_{15} e_{15}	$e_{16}$ e_{16}
a	-1	1	1	0	0	0	0	0	1	0	0	0	0	0	0	0
b	0	0	-1	0	1	1	0	-1	0	0	0	0	0	1	0	0
c	0	-1	0	1	0	0	0	0	0	0	0	0	0	0	0	0
d	1	0	0	0	-1	0	0	0	-1	0	1	1	0	0	0	0
f	0	0	0	0	0	0	-1	1	0	1	0	0	0	0	0	2
g	0	0	0	-1	0	-1	1	0	0	0	0	0	0	0	0	0
h	0	0	0	0	0	0	0	0	0	-1	-1	0	1	-1	0	0
j	0	0	0	0	0	0	0	0	0	0	0	-1	-1	0	2	0

	Image failed to load: e_1 e_1	e_2	e_3	e_4	e_5	e_6	e_7	e_8	e_9	$e_{10}$ e_{10}	$e_{11}$ e_{11}	$e_{12}$ e_{12}	$e_{13}$ e_{13}	$e_{14}$ e_{14}	$e_{15}$ e_{15}	$e_{16}$ e_{16}
a	-1	1	1	0	0	0	0	0	1	0	0	0	0	0	0	0
b	0	0	-1	0	1	1	0	-1	0	0	0	0	0	1	0	0
c	0	-1	0	1	0	0	0	0	0	0	0	0	0	0	0	0
d	1	0	0	0	-1	0	0	0	-1	0	-1	1	0	0	0	0
f	0	0	0	0	0	0	-1	1	0	1	0	0	0	0	0	2
g	0	0	0	-1	0	-1	1	0	0	0	0	0	0	0	0	0
h	0	0	0	0	0	0	0	0	0	-1	1	0	1	-1	0	0
j	0	0	0	0	0	0	0	0	0	0	0	-1	-1	0	2	0

	e_1	e_2	e_3	e_4	e_5	e_6	e_7	e_8	e_9	Image failed to load: e_{10} e_{10}	Image failed to load: e_{11} e_{11}	Image failed to load: e_{1 2} e_{1 2}	Image failed to load: e_{1 3} e_{1 3}	$e_{14}$ e_{14}	$e_{1 5}$ e_{1 5}	$e_{1 6}$ e_{1 6}
a	1	1	1	0	0	0	0	0	1	0	0	0	0	0	0	0
b	0	0	0	0	1	1	0	1	0	0	0	0	0	1	0	0
c	0	1	0	1	0	0	0	0	0	0	0	0	0	0	0	0
d	1	0	0	0	1	0	0	0	1	0	1	1	0	0	0	0
f	0	0	1	0	0	0	1	1	0	1	0	0	0	0	0	2
g	0	0	0	1	0	1	1	0	0	0	0	0	0	0	0	0
h	0	0	0	0	0	0	0	0	0	1	1	0	1	1	0	0
j	0	0	0	0	0	0	0	0	0	0	0	1	1	0	2	0

	Image failed to load: e_1 e_1	e_2	e_3	e_4	e_5	e_6	e_7	e_8	e_9	$e_{10}$ e_{10}	$e_{11}$ e_{11}	$e_{1 2}$ e_{1 2}	$e_{1 3}$ e_{1 3}	$e_{14}$ e_{14}	$e_{1 5}$ e_{1 5}	$e_{1 6}$ e_{1 6}
a	1	1	1	0	0	0	0	1	1	0	0	0	0	0	0	0
b	0	0	1	0	1	1	0	1	0	0	0	0	0	1	0	0
c	0	1	0	1	0	0	0	0	0	0	0	0	0	0	0	0
d	1	0	0	0	1	0	0	0	1	0	1	1	0	0	0	0
f	0	0	0	0	0	0	1	1	0	1	0	0	0	0	0	2
g	0	0	0	1	0	1	1	0	0	0	0	0	0	0	0	0
h	0	0	0	0	0	0	0	0	0	1	1	0	1	1	0	0
j	0	0	0	0	0	0	0	0	0	0	0	1	1	0	2	0

	a	b	c	d	f	g	h	j
a	0	1	1	1	0	0	0	0
b	0	0	0	1	0	2	1	0
c	0	0	0	0	0	1	0	0
d	1	0	0	1	0		1	1
f	0	1	0	0	0	1	1	0
g	1	0	0	0	2	0	0	0
h	0	0	0	0	1	0	0	1
j	0	0	0	0	0	0	2	1

	a	b	c	d	f	g	h	j
a	0	1	1	1	0	0	0	0
b	0	0	0	1	0	1	2	0
c	0	0	0	0	0	1	0	0
d	1	0	0	1	0	0	1	1
f	0	1	0	0	1	1	1	0
g	1	0	0	0	2	0	0	0
h	0	0	0	0	1	0	0	1
j	0	0	0	0	0	0	2	1

	Image failed to load: a a	b	c	d	g	f	h	j
a	0	0	1	3	1	0	0	0
b	0	1	1	0	1	2	0	0
c	1	1	0	0	0	0	0	0
d	3	0	0	0	1	0	1	2
g	1	1	0	1	0	3	1	0
f	0	2	0	0	3	1	2	0
h	0	0	0	1	1	2	0	1
j	0	0	0	2	0	0	1	1

	a	b	c	d	f	g	h	j
a	0	1	1	1	0	0	0	0
b	0	0	0	1	0	1	2	0
c	0	0	0	0	0	1	0	0
d	1	0	0	1	0	0	1	1
f	0	0	0	0	1	1	1	0
g	1	0	0	0	2	0	0	0
h	0	0	0	0	1	0	0	0
j	0	0	0	0	0	0	1	2

	a	Image failed to load: b b	Image failed to load: c c	d	Image failed to load: g g	Image failed to load: f f	Image failed to load: h h	Image failed to load: j j
a	0	0	3	1	1	0	0	0
b	0	1	1	0	1	2	0	0
c	1	1	0	0	0	0	0	0
d	1	0	0	0	3	0	1	2
g	1	1	0	1	0	1	3	0
f	0	2	0	0	3	1	2	0
h	0	0	0	1	1	2	0	1
j	0	0	0	2	0	0	1	1

	a	b	c	d	g	f	h	j
a	0	0	1	3	1	0	0	0
b	0	2	0	0	1	2	0	0
c	1	1	0	0	0	0	0	0
d	3	0	0	0	1	0	1	2
g	1	1	0	1	0	3	1	0
f	0	2	0	0	3	2	1	0
h	0	0	0	1	1	2	0	1
j	0	0	0	1	0	0	2	1

	e_1	e_2	Image failed to load: e_3 e_3	Image failed to load: e_4 e_4	Image failed to load: e_5 e_5	Image failed to load: e_6 e_6	Image failed to load: e_7 e_7	Image failed to load: e_8 e_8	Image failed to load: e_9 e_9	Image failed to load: e_{10} e_{10}	Image failed to load: e_{11} e_{11}	Image failed to load: e_{12} e_{12}	Image failed to load: e_{13} e_{13}	Image failed to load: e_{14} e_{14}	Image failed to load: e_{15} e_{15}	$e_{16}$ e_{16}
a	-1	1	1	0	0	0	0	0	1	0	0	0	0	0	0	0
b	0	0	-1	0	1	1	0	-1	0	0	0	0	0	1	0	0
c	0	-1	0	1	0	0	0	0	0	0	0	0	0	0	0	0
d	1	0	0	0	-1	0	0	0	-1	0	1	1	0	0	0	0
f	0	0	0	0	0	0	-1	1	0	1	0	0	0	0	0	2
g	0	0	0	-1	0	-1	1	0	0	0	0	0	0	0	0	0
h	0	0	0	0	0	0	0	0	0	-1	-1	0	1	-1	0	0
j	0	0	0	0	0	0	0	0	0	0	0	-1	-1	0	2	0

	Image failed to load: e_1 e_1	e_2	e_3	e_4	e_5	e_6	e_7	e_8	e_9	$e_{10}$ e_{10}	$e_{11}$ e_{11}	$e_{12}$ e_{12}	$e_{13}$ e_{13}	$e_{14}$ e_{14}	$e_{15}$ e_{15}	$e_{16}$ e_{16}
a	-1	1	1	0	0	0	0	0	1	0	0	0	0	0	0	0
b	0	0	-1	0	1	1	0	-1	0	0	0	0	0	1	0	0
c	0	-1	0	1	0	0	0	0	0	0	0	0	0	0	0	0
d	1	0	0	0	-1	0	0	0	-1	0	-1	1	0	0	0	0
f	0	0	0	0	0	0	-1	1	0	1	0	0	0	0	0	2
g	0	0	0	-1	0	-1	1	0	0	0	0	0	0	0	0	0
h	0	0	0	0	0	0	0	0	0	-1	1	0	1	-1	0	0
j	0	0	0	0	0	0	0	0	0	0	0	-1	-1	0	2	0

	e_1	e_2	e_3	e_4	e_5	e_6	e_7	e_8	e_9	Image failed to load: e_{10} e_{10}	Image failed to load: e_{11} e_{11}	Image failed to load: e_{1 2} e_{1 2}	Image failed to load: e_{1 3} e_{1 3}	$e_{14}$ e_{14}	$e_{1 5}$ e_{1 5}	$e_{1 6}$ e_{1 6}
a	1	1	1	0	0	0	0	0	1	0	0	0	0	0	0	0
b	0	0	0	0	1	1	0	1	0	0	0	0	0	1	0	0
c	0	1	0	1	0	0	0	0	0	0	0	0	0	0	0	0
d	1	0	0	0	1	0	0	0	1	0	1	1	0	0	0	0
f	0	0	1	0	0	0	1	1	0	1	0	0	0	0	0	2
g	0	0	0	1	0	1	1	0	0	0	0	0	0	0	0	0
h	0	0	0	0	0	0	0	0	0	1	1	0	1	1	0	0
j	0	0	0	0	0	0	0	0	0	0	0	1	1	0	2	0

	Image failed to load: e_1 e_1	e_2	e_3	e_4	e_5	e_6	e_7	e_8	e_9	$e_{10}$ e_{10}	$e_{11}$ e_{11}	$e_{1 2}$ e_{1 2}	$e_{1 3}$ e_{1 3}	$e_{14}$ e_{14}	$e_{1 5}$ e_{1 5}	$e_{1 6}$ e_{1 6}
a	1	1	1	0	0	0	0	1	1	0	0	0	0	0	0	0
b	0	0	1	0	1	1	0	1	0	0	0	0	0	1	0	0
c	0	1	0	1	0	0	0	0	0	0	0	0	0	0	0	0
d	1	0	0	0	1	0	0	0	1	0	1	1	0	0	0	0
f	0	0	0	0	0	0	1	1	0	1	0	0	0	0	0	2
g	0	0	0	1	0	1	1	0	0	0	0	0	0	0	0	0
h	0	0	0	0	0	0	0	0	0	1	1	0	1	1	0	0
j	0	0	0	0	0	0	0	0	0	0	0	1	1	0	2	0

	a	b	c	d	f	g	h	j
a	0	1	1	1	0	0	0	0
b	0	0	0	1	0	2	1	0
c	0	0	0	0	0	1	0	0
d	1	0	0	1	0		1	1
f	0	1	0	0	0	1	1	0
g	1	0	0	0	2	0	0	0
h	0	0	0	0	1	0	0	1
j	0	0	0	0	0	0	2	1

	a	b	c	d	f	g	h	j
a	0	1	1	1	0	0	0	0
b	0	0	0	1	0	1	2	0
c	0	0	0	0	0	1	0	0
d	1	0	0	1	0	0	1	1
f	0	1	0	0	1	1	1	0
g	1	0	0	0	2	0	0	0
h	0	0	0	0	1	0	0	1
j	0	0	0	0	0	0	2	1

	Image failed to load: a a	b	c	d	g	f	h	j
a	0	0	1	3	1	0	0	0
b	0	1	1	0	1	2	0	0
c	1	1	0	0	0	0	0	0
d	3	0	0	0	1	0	1	2
g	1	1	0	1	0	3	1	0
f	0	2	0	0	3	1	2	0
h	0	0	0	1	1	2	0	1
j	0	0	0	2	0	0	1	1