searching the database
Your data matches 8 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
(click to perform a complete search on your data)
Matching statistic: St001424
(load all 5 compositions to match this statistic)
(load all 5 compositions to match this statistic)
St001424: Binary words ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
0 => 0
1 => 0
00 => 1
01 => 0
10 => 0
11 => 1
000 => 1
001 => 1
010 => 0
011 => 1
100 => 1
101 => 0
110 => 1
111 => 1
0000 => 2
0001 => 1
0010 => 1
0011 => 2
0100 => 1
0101 => 1
0110 => 1
0111 => 1
1000 => 1
1001 => 1
1010 => 1
1011 => 1
1100 => 2
1101 => 1
1110 => 1
1111 => 2
00000 => 2
00001 => 2
00010 => 1
00011 => 2
00100 => 1
00101 => 2
00110 => 2
00111 => 2
01000 => 1
01001 => 1
01010 => 2
01011 => 2
01100 => 2
01101 => 1
01110 => 1
01111 => 2
10000 => 2
10001 => 1
10010 => 1
10011 => 2
Description
The number of distinct squares in a binary word.
A factor of a word is a sequence of consecutive letters. This statistic records the number of distinct non-empty words $u$ such that $uu$ is a factor of the word.
Note that every word of length at least four contains a square.
Matching statistic: St001335
Values
0 => ([(0,1)],2)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 0
1 => ([(0,1)],2)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 0
00 => ([(0,2),(2,1)],3)
=> ([(0,2),(1,2)],3)
=> ([(0,2),(1,2)],3)
=> 0
01 => ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> 1
10 => ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> 1
11 => ([(0,2),(2,1)],3)
=> ([(0,2),(1,2)],3)
=> ([(0,2),(1,2)],3)
=> 0
000 => ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(1,2),(2,3)],4)
=> ([(0,3),(1,2),(2,3)],4)
=> 0
001 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,5),(3,4),(4,5)],6)
=> 1
010 => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6)
=> 1
011 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,5),(3,4),(4,5)],6)
=> 1
100 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,5),(3,4),(4,5)],6)
=> 1
101 => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6)
=> 1
110 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,5),(3,4),(4,5)],6)
=> 1
111 => ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(1,2),(2,3)],4)
=> ([(0,3),(1,2),(2,3)],4)
=> 0
0000 => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> 1
0001 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,3),(0,7),(1,2),(1,4),(2,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ([(0,3),(0,5),(0,6),(0,7),(1,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6),(6,7)],8)
=> 1
0010 => ([(0,2),(0,3),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,5),(8,5),(8,6)],9)
=> ([(0,5),(0,8),(1,4),(1,6),(2,6),(2,8),(3,4),(3,5),(3,8),(4,7),(5,7),(6,7),(7,8)],9)
=> ([(0,2),(0,3),(0,4),(0,8),(1,5),(1,6),(1,7),(1,8),(2,3),(2,4),(2,5),(2,6),(3,4),(3,7),(3,8),(4,6),(4,7),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9)
=> ? ∊ {1,1,1,1,2,2,2,2}
0011 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,6),(0,7),(1,4),(1,5),(2,5),(2,7),(3,4),(3,6),(4,8),(5,8),(6,8),(7,8)],9)
=> ([(0,5),(0,6),(0,7),(0,8),(1,2),(1,3),(1,4),(1,7),(1,8),(2,3),(2,4),(2,5),(2,6),(3,4),(3,6),(3,8),(4,5),(4,7),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9)
=> ? ∊ {1,1,1,1,2,2,2,2}
0100 => ([(0,2),(0,3),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,5),(8,5),(8,6)],9)
=> ([(0,5),(0,8),(1,4),(1,6),(2,6),(2,8),(3,4),(3,5),(3,8),(4,7),(5,7),(6,7),(7,8)],9)
=> ([(0,2),(0,3),(0,4),(0,8),(1,5),(1,6),(1,7),(1,8),(2,3),(2,4),(2,5),(2,6),(3,4),(3,7),(3,8),(4,6),(4,7),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9)
=> ? ∊ {1,1,1,1,2,2,2,2}
0101 => ([(0,1),(0,2),(1,6),(1,7),(2,6),(2,7),(4,3),(5,3),(6,4),(6,5),(7,4),(7,5)],8)
=> ([(0,4),(0,5),(1,2),(1,3),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
=> ([(0,1),(0,6),(0,7),(1,6),(1,7),(2,3),(2,4),(2,5),(2,7),(3,4),(3,5),(3,7),(4,5),(4,6),(5,6),(6,7)],8)
=> 1
0110 => ([(0,2),(0,3),(1,5),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,6),(8,5)],9)
=> ([(0,5),(0,6),(1,7),(1,8),(2,5),(2,6),(2,8),(3,6),(3,7),(3,8),(4,5),(4,7),(4,8)],9)
=> ([(0,4),(0,5),(0,6),(0,8),(1,2),(1,3),(1,4),(1,7),(1,8),(2,3),(2,6),(2,7),(2,8),(3,5),(3,7),(3,8),(4,5),(4,6),(4,8),(5,6),(5,7),(6,7),(7,8)],9)
=> ? ∊ {1,1,1,1,2,2,2,2}
0111 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,3),(0,7),(1,2),(1,4),(2,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ([(0,3),(0,5),(0,6),(0,7),(1,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6),(6,7)],8)
=> 1
1000 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,3),(0,7),(1,2),(1,4),(2,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ([(0,3),(0,5),(0,6),(0,7),(1,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6),(6,7)],8)
=> 1
1001 => ([(0,2),(0,3),(1,5),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,6),(8,5)],9)
=> ([(0,5),(0,6),(1,7),(1,8),(2,5),(2,6),(2,8),(3,6),(3,7),(3,8),(4,5),(4,7),(4,8)],9)
=> ([(0,4),(0,5),(0,6),(0,8),(1,2),(1,3),(1,4),(1,7),(1,8),(2,3),(2,6),(2,7),(2,8),(3,5),(3,7),(3,8),(4,5),(4,6),(4,8),(5,6),(5,7),(6,7),(7,8)],9)
=> ? ∊ {1,1,1,1,2,2,2,2}
1010 => ([(0,1),(0,2),(1,6),(1,7),(2,6),(2,7),(4,3),(5,3),(6,4),(6,5),(7,4),(7,5)],8)
=> ([(0,4),(0,5),(1,2),(1,3),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
=> ([(0,1),(0,6),(0,7),(1,6),(1,7),(2,3),(2,4),(2,5),(2,7),(3,4),(3,5),(3,7),(4,5),(4,6),(5,6),(6,7)],8)
=> 1
1011 => ([(0,2),(0,3),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,5),(8,5),(8,6)],9)
=> ([(0,5),(0,8),(1,4),(1,6),(2,6),(2,8),(3,4),(3,5),(3,8),(4,7),(5,7),(6,7),(7,8)],9)
=> ([(0,2),(0,3),(0,4),(0,8),(1,5),(1,6),(1,7),(1,8),(2,3),(2,4),(2,5),(2,6),(3,4),(3,7),(3,8),(4,6),(4,7),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9)
=> ? ∊ {1,1,1,1,2,2,2,2}
1100 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,6),(0,7),(1,4),(1,5),(2,5),(2,7),(3,4),(3,6),(4,8),(5,8),(6,8),(7,8)],9)
=> ([(0,5),(0,6),(0,7),(0,8),(1,2),(1,3),(1,4),(1,7),(1,8),(2,3),(2,4),(2,5),(2,6),(3,4),(3,6),(3,8),(4,5),(4,7),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9)
=> ? ∊ {1,1,1,1,2,2,2,2}
1101 => ([(0,2),(0,3),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,5),(8,5),(8,6)],9)
=> ([(0,5),(0,8),(1,4),(1,6),(2,6),(2,8),(3,4),(3,5),(3,8),(4,7),(5,7),(6,7),(7,8)],9)
=> ([(0,2),(0,3),(0,4),(0,8),(1,5),(1,6),(1,7),(1,8),(2,3),(2,4),(2,5),(2,6),(3,4),(3,7),(3,8),(4,6),(4,7),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9)
=> ? ∊ {1,1,1,1,2,2,2,2}
1110 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,3),(0,7),(1,2),(1,4),(2,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ([(0,3),(0,5),(0,6),(0,7),(1,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6),(6,7)],8)
=> 1
1111 => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> 1
00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> ([(0,1),(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 1
00001 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ([(0,3),(0,7),(1,2),(1,6),(2,8),(3,9),(4,5),(4,8),(4,9),(5,6),(5,7),(6,8),(7,9)],10)
=> ([(0,1),(0,3),(0,5),(0,6),(0,7),(0,9),(1,2),(1,5),(1,6),(1,7),(1,8),(2,3),(2,4),(2,6),(2,8),(2,9),(3,4),(3,7),(3,8),(3,9),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,7),(6,8),(7,9),(8,9)],10)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
00010 => ([(0,3),(0,4),(1,2),(1,11),(2,8),(3,9),(3,10),(4,1),(4,9),(4,10),(6,7),(7,5),(8,5),(9,6),(10,6),(10,11),(11,7),(11,8)],12)
=> ([(0,7),(0,11),(1,5),(1,8),(2,6),(2,8),(3,4),(3,7),(3,11),(4,5),(4,9),(5,10),(6,10),(6,11),(7,9),(8,10),(9,10),(9,11)],12)
=> ([(0,3),(0,4),(0,5),(0,6),(0,9),(0,10),(0,11),(1,2),(1,4),(1,5),(1,7),(1,8),(1,10),(1,11),(2,6),(2,7),(2,8),(2,9),(2,10),(2,11),(3,4),(3,5),(3,6),(3,7),(3,8),(3,9),(3,11),(4,5),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,9),(5,10),(6,9),(6,10),(6,11),(7,8),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
00011 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ([(0,5),(0,9),(1,4),(1,9),(2,6),(2,8),(3,7),(3,8),(4,6),(4,10),(5,7),(5,10),(6,11),(7,11),(8,11),(9,10),(10,11)],12)
=> ([(0,3),(0,6),(0,7),(0,8),(0,9),(0,10),(0,11),(1,2),(1,4),(1,5),(1,8),(1,9),(1,10),(1,11),(2,3),(2,4),(2,5),(2,6),(2,7),(2,8),(2,9),(3,4),(3,5),(3,6),(3,7),(3,10),(3,11),(4,5),(4,7),(4,8),(4,9),(4,11),(5,6),(5,8),(5,9),(5,10),(6,7),(6,8),(6,10),(6,11),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
00100 => ([(0,2),(0,3),(1,5),(1,6),(2,10),(2,11),(3,1),(3,10),(3,11),(5,8),(6,7),(7,4),(8,4),(9,7),(9,8),(10,6),(10,9),(11,5),(11,9)],12)
=> ([(0,7),(0,11),(1,5),(1,6),(2,3),(2,4),(2,11),(3,6),(3,9),(4,5),(4,8),(5,10),(6,10),(7,8),(7,9),(8,10),(8,11),(9,10),(9,11)],12)
=> ([(0,3),(0,4),(0,5),(0,6),(0,8),(0,9),(0,11),(1,2),(1,5),(1,6),(1,7),(1,9),(1,10),(1,11),(2,5),(2,6),(2,7),(2,8),(2,10),(2,11),(3,4),(3,7),(3,8),(3,9),(3,10),(3,11),(4,5),(4,6),(4,7),(4,8),(4,9),(4,11),(5,6),(5,7),(5,8),(5,10),(6,7),(6,9),(6,10),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
00101 => ([(0,2),(0,3),(1,8),(2,10),(2,11),(3,1),(3,10),(3,11),(5,6),(6,4),(7,4),(8,7),(9,6),(9,7),(10,5),(10,9),(11,5),(11,8),(11,9)],12)
=> ([(0,5),(0,6),(1,7),(1,10),(2,4),(2,10),(3,6),(3,8),(3,11),(4,5),(4,11),(5,9),(6,9),(7,8),(7,11),(8,9),(8,10),(9,11),(10,11)],12)
=> ([(0,3),(0,7),(0,8),(0,9),(0,10),(0,11),(1,2),(1,4),(1,5),(1,6),(1,7),(1,8),(1,11),(2,4),(2,5),(2,6),(2,9),(2,10),(2,11),(3,5),(3,7),(3,8),(3,9),(3,10),(3,11),(4,5),(4,6),(4,7),(4,8),(4,9),(4,11),(5,6),(5,7),(5,10),(5,11),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(8,9),(8,10),(9,10),(9,11),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
00110 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ([(0,11),(0,12),(1,8),(1,12),(2,6),(2,7),(3,4),(3,11),(3,12),(4,5),(4,6),(5,9),(5,11),(6,9),(7,8),(7,9),(8,10),(9,10),(10,11),(10,12)],13)
=> ([(0,4),(0,5),(0,6),(0,7),(0,9),(0,10),(0,11),(0,12),(1,2),(1,3),(1,4),(1,6),(1,7),(1,8),(1,9),(1,12),(2,3),(2,6),(2,7),(2,8),(2,9),(2,11),(2,12),(3,5),(3,8),(3,9),(3,10),(3,11),(3,12),(4,5),(4,6),(4,7),(4,8),(4,10),(4,11),(4,12),(5,6),(5,7),(5,8),(5,10),(5,11),(5,12),(6,7),(6,9),(6,10),(6,11),(7,8),(7,10),(7,11),(8,9),(8,10),(8,12),(9,10),(9,11),(9,12),(10,11),(10,12),(11,12)],13)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
00111 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ([(0,5),(0,9),(1,4),(1,9),(2,6),(2,8),(3,7),(3,8),(4,6),(4,10),(5,7),(5,10),(6,11),(7,11),(8,11),(9,10),(10,11)],12)
=> ([(0,3),(0,6),(0,7),(0,8),(0,9),(0,10),(0,11),(1,2),(1,4),(1,5),(1,8),(1,9),(1,10),(1,11),(2,3),(2,4),(2,5),(2,6),(2,7),(2,8),(2,9),(3,4),(3,5),(3,6),(3,7),(3,10),(3,11),(4,5),(4,7),(4,8),(4,9),(4,11),(5,6),(5,8),(5,9),(5,10),(6,7),(6,8),(6,10),(6,11),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
01000 => ([(0,3),(0,4),(1,2),(1,11),(2,8),(3,9),(3,10),(4,1),(4,9),(4,10),(6,7),(7,5),(8,5),(9,6),(10,6),(10,11),(11,7),(11,8)],12)
=> ([(0,7),(0,11),(1,5),(1,8),(2,6),(2,8),(3,4),(3,7),(3,11),(4,5),(4,9),(5,10),(6,10),(6,11),(7,9),(8,10),(9,10),(9,11)],12)
=> ([(0,3),(0,4),(0,5),(0,6),(0,9),(0,10),(0,11),(1,2),(1,4),(1,5),(1,7),(1,8),(1,10),(1,11),(2,6),(2,7),(2,8),(2,9),(2,10),(2,11),(3,4),(3,5),(3,6),(3,7),(3,8),(3,9),(3,11),(4,5),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,9),(5,10),(6,9),(6,10),(6,11),(7,8),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
01001 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
=> ([(0,7),(0,11),(1,5),(1,6),(2,3),(2,10),(2,11),(3,5),(3,8),(4,6),(4,8),(4,9),(5,10),(6,10),(7,8),(7,9),(8,11),(9,10),(9,11)],12)
=> ([(0,2),(0,4),(0,5),(0,7),(0,8),(0,9),(0,11),(1,3),(1,6),(1,7),(1,8),(1,9),(1,10),(1,11),(2,3),(2,4),(2,5),(2,8),(2,10),(2,11),(3,6),(3,7),(3,9),(3,10),(3,11),(4,5),(4,6),(4,7),(4,8),(4,9),(4,11),(5,6),(5,7),(5,8),(5,10),(5,11),(6,7),(6,9),(6,10),(6,11),(7,9),(7,10),(8,9),(8,10),(8,11),(9,10),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
01010 => ([(0,1),(0,2),(1,8),(1,9),(2,8),(2,9),(4,3),(5,3),(6,4),(6,5),(7,4),(7,5),(8,6),(8,7),(9,6),(9,7)],10)
=> ([(0,4),(0,5),(1,2),(1,3),(2,6),(2,7),(3,6),(3,7),(4,8),(4,9),(5,8),(5,9),(6,8),(6,9),(7,8),(7,9)],10)
=> ([(0,1),(0,4),(0,5),(0,8),(0,9),(1,4),(1,5),(1,8),(1,9),(2,3),(2,6),(2,7),(2,8),(2,9),(3,6),(3,7),(3,8),(3,9),(4,5),(4,6),(4,7),(4,9),(5,6),(5,7),(5,9),(6,7),(6,8),(7,8),(8,9)],10)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
01011 => ([(0,2),(0,3),(1,8),(2,10),(2,11),(3,1),(3,10),(3,11),(5,6),(6,4),(7,4),(8,7),(9,6),(9,7),(10,5),(10,9),(11,5),(11,8),(11,9)],12)
=> ([(0,5),(0,6),(1,7),(1,10),(2,4),(2,10),(3,6),(3,8),(3,11),(4,5),(4,11),(5,9),(6,9),(7,8),(7,11),(8,9),(8,10),(9,11),(10,11)],12)
=> ([(0,3),(0,7),(0,8),(0,9),(0,10),(0,11),(1,2),(1,4),(1,5),(1,6),(1,7),(1,8),(1,11),(2,4),(2,5),(2,6),(2,9),(2,10),(2,11),(3,5),(3,7),(3,8),(3,9),(3,10),(3,11),(4,5),(4,6),(4,7),(4,8),(4,9),(4,11),(5,6),(5,7),(5,10),(5,11),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(8,9),(8,10),(9,10),(9,11),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
01100 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ([(0,11),(0,12),(1,8),(1,12),(2,6),(2,7),(3,4),(3,11),(3,12),(4,5),(4,6),(5,9),(5,11),(6,9),(7,8),(7,9),(8,10),(9,10),(10,11),(10,12)],13)
=> ([(0,4),(0,5),(0,6),(0,7),(0,9),(0,10),(0,11),(0,12),(1,2),(1,3),(1,4),(1,6),(1,7),(1,8),(1,9),(1,12),(2,3),(2,6),(2,7),(2,8),(2,9),(2,11),(2,12),(3,5),(3,8),(3,9),(3,10),(3,11),(3,12),(4,5),(4,6),(4,7),(4,8),(4,10),(4,11),(4,12),(5,6),(5,7),(5,8),(5,10),(5,11),(5,12),(6,7),(6,9),(6,10),(6,11),(7,8),(7,10),(7,11),(8,9),(8,10),(8,12),(9,10),(9,11),(9,12),(10,11),(10,12),(11,12)],13)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
01101 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
=> ([(0,7),(0,11),(1,5),(1,6),(2,3),(2,10),(2,11),(3,5),(3,8),(4,6),(4,8),(4,9),(5,10),(6,10),(7,8),(7,9),(8,11),(9,10),(9,11)],12)
=> ([(0,2),(0,4),(0,5),(0,7),(0,8),(0,9),(0,11),(1,3),(1,6),(1,7),(1,8),(1,9),(1,10),(1,11),(2,3),(2,4),(2,5),(2,8),(2,10),(2,11),(3,6),(3,7),(3,9),(3,10),(3,11),(4,5),(4,6),(4,7),(4,8),(4,9),(4,11),(5,6),(5,7),(5,8),(5,10),(5,11),(6,7),(6,9),(6,10),(6,11),(7,9),(7,10),(8,9),(8,10),(8,11),(9,10),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
01110 => ([(0,3),(0,4),(1,2),(1,10),(1,11),(2,8),(2,9),(3,6),(3,7),(4,1),(4,6),(4,7),(6,11),(7,10),(8,5),(9,5),(10,8),(11,9)],12)
=> ([(0,9),(0,11),(1,7),(1,8),(2,5),(2,9),(2,11),(3,4),(3,9),(3,11),(4,7),(4,10),(5,8),(5,10),(6,7),(6,8),(6,10),(10,11)],12)
=> ([(0,2),(0,3),(0,4),(0,7),(0,8),(0,9),(0,11),(1,5),(1,6),(1,7),(1,8),(1,9),(1,10),(1,11),(2,3),(2,4),(2,5),(2,6),(2,7),(2,10),(2,11),(3,4),(3,6),(3,7),(3,9),(3,10),(3,11),(4,5),(4,7),(4,8),(4,10),(4,11),(5,6),(5,8),(5,9),(5,10),(5,11),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,11),(8,9),(8,10),(9,10),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
01111 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ([(0,3),(0,7),(1,2),(1,6),(2,8),(3,9),(4,5),(4,8),(4,9),(5,6),(5,7),(6,8),(7,9)],10)
=> ([(0,1),(0,3),(0,5),(0,6),(0,7),(0,9),(1,2),(1,5),(1,6),(1,7),(1,8),(2,3),(2,4),(2,6),(2,8),(2,9),(3,4),(3,7),(3,8),(3,9),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,7),(6,8),(7,9),(8,9)],10)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ([(0,3),(0,7),(1,2),(1,6),(2,8),(3,9),(4,5),(4,8),(4,9),(5,6),(5,7),(6,8),(7,9)],10)
=> ([(0,1),(0,3),(0,5),(0,6),(0,7),(0,9),(1,2),(1,5),(1,6),(1,7),(1,8),(2,3),(2,4),(2,6),(2,8),(2,9),(3,4),(3,7),(3,8),(3,9),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,7),(6,8),(7,9),(8,9)],10)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
10001 => ([(0,3),(0,4),(1,2),(1,10),(1,11),(2,8),(2,9),(3,6),(3,7),(4,1),(4,6),(4,7),(6,11),(7,10),(8,5),(9,5),(10,8),(11,9)],12)
=> ([(0,9),(0,11),(1,7),(1,8),(2,5),(2,9),(2,11),(3,4),(3,9),(3,11),(4,7),(4,10),(5,8),(5,10),(6,7),(6,8),(6,10),(10,11)],12)
=> ([(0,2),(0,3),(0,4),(0,7),(0,8),(0,9),(0,11),(1,5),(1,6),(1,7),(1,8),(1,9),(1,10),(1,11),(2,3),(2,4),(2,5),(2,6),(2,7),(2,10),(2,11),(3,4),(3,6),(3,7),(3,9),(3,10),(3,11),(4,5),(4,7),(4,8),(4,10),(4,11),(5,6),(5,8),(5,9),(5,10),(5,11),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,11),(8,9),(8,10),(9,10),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
10010 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
=> ([(0,7),(0,11),(1,5),(1,6),(2,3),(2,10),(2,11),(3,5),(3,8),(4,6),(4,8),(4,9),(5,10),(6,10),(7,8),(7,9),(8,11),(9,10),(9,11)],12)
=> ([(0,2),(0,4),(0,5),(0,7),(0,8),(0,9),(0,11),(1,3),(1,6),(1,7),(1,8),(1,9),(1,10),(1,11),(2,3),(2,4),(2,5),(2,8),(2,10),(2,11),(3,6),(3,7),(3,9),(3,10),(3,11),(4,5),(4,6),(4,7),(4,8),(4,9),(4,11),(5,6),(5,7),(5,8),(5,10),(5,11),(6,7),(6,9),(6,10),(6,11),(7,9),(7,10),(8,9),(8,10),(8,11),(9,10),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
10011 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ([(0,11),(0,12),(1,8),(1,12),(2,6),(2,7),(3,4),(3,11),(3,12),(4,5),(4,6),(5,9),(5,11),(6,9),(7,8),(7,9),(8,10),(9,10),(10,11),(10,12)],13)
=> ([(0,4),(0,5),(0,6),(0,7),(0,9),(0,10),(0,11),(0,12),(1,2),(1,3),(1,4),(1,6),(1,7),(1,8),(1,9),(1,12),(2,3),(2,6),(2,7),(2,8),(2,9),(2,11),(2,12),(3,5),(3,8),(3,9),(3,10),(3,11),(3,12),(4,5),(4,6),(4,7),(4,8),(4,10),(4,11),(4,12),(5,6),(5,7),(5,8),(5,10),(5,11),(5,12),(6,7),(6,9),(6,10),(6,11),(7,8),(7,10),(7,11),(8,9),(8,10),(8,12),(9,10),(9,11),(9,12),(10,11),(10,12),(11,12)],13)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
10100 => ([(0,2),(0,3),(1,8),(2,10),(2,11),(3,1),(3,10),(3,11),(5,6),(6,4),(7,4),(8,7),(9,6),(9,7),(10,5),(10,9),(11,5),(11,8),(11,9)],12)
=> ([(0,5),(0,6),(1,7),(1,10),(2,4),(2,10),(3,6),(3,8),(3,11),(4,5),(4,11),(5,9),(6,9),(7,8),(7,11),(8,9),(8,10),(9,11),(10,11)],12)
=> ([(0,3),(0,7),(0,8),(0,9),(0,10),(0,11),(1,2),(1,4),(1,5),(1,6),(1,7),(1,8),(1,11),(2,4),(2,5),(2,6),(2,9),(2,10),(2,11),(3,5),(3,7),(3,8),(3,9),(3,10),(3,11),(4,5),(4,6),(4,7),(4,8),(4,9),(4,11),(5,6),(5,7),(5,10),(5,11),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(8,9),(8,10),(9,10),(9,11),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
10101 => ([(0,1),(0,2),(1,8),(1,9),(2,8),(2,9),(4,3),(5,3),(6,4),(6,5),(7,4),(7,5),(8,6),(8,7),(9,6),(9,7)],10)
=> ([(0,4),(0,5),(1,2),(1,3),(2,6),(2,7),(3,6),(3,7),(4,8),(4,9),(5,8),(5,9),(6,8),(6,9),(7,8),(7,9)],10)
=> ([(0,1),(0,4),(0,5),(0,8),(0,9),(1,4),(1,5),(1,8),(1,9),(2,3),(2,6),(2,7),(2,8),(2,9),(3,6),(3,7),(3,8),(3,9),(4,5),(4,6),(4,7),(4,9),(5,6),(5,7),(5,9),(6,7),(6,8),(7,8),(8,9)],10)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
10110 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
=> ([(0,7),(0,11),(1,5),(1,6),(2,3),(2,10),(2,11),(3,5),(3,8),(4,6),(4,8),(4,9),(5,10),(6,10),(7,8),(7,9),(8,11),(9,10),(9,11)],12)
=> ([(0,2),(0,4),(0,5),(0,7),(0,8),(0,9),(0,11),(1,3),(1,6),(1,7),(1,8),(1,9),(1,10),(1,11),(2,3),(2,4),(2,5),(2,8),(2,10),(2,11),(3,6),(3,7),(3,9),(3,10),(3,11),(4,5),(4,6),(4,7),(4,8),(4,9),(4,11),(5,6),(5,7),(5,8),(5,10),(5,11),(6,7),(6,9),(6,10),(6,11),(7,9),(7,10),(8,9),(8,10),(8,11),(9,10),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
10111 => ([(0,3),(0,4),(1,2),(1,11),(2,8),(3,9),(3,10),(4,1),(4,9),(4,10),(6,7),(7,5),(8,5),(9,6),(10,6),(10,11),(11,7),(11,8)],12)
=> ([(0,7),(0,11),(1,5),(1,8),(2,6),(2,8),(3,4),(3,7),(3,11),(4,5),(4,9),(5,10),(6,10),(6,11),(7,9),(8,10),(9,10),(9,11)],12)
=> ([(0,3),(0,4),(0,5),(0,6),(0,9),(0,10),(0,11),(1,2),(1,4),(1,5),(1,7),(1,8),(1,10),(1,11),(2,6),(2,7),(2,8),(2,9),(2,10),(2,11),(3,4),(3,5),(3,6),(3,7),(3,8),(3,9),(3,11),(4,5),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,9),(5,10),(6,9),(6,10),(6,11),(7,8),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
11000 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ([(0,5),(0,9),(1,4),(1,9),(2,6),(2,8),(3,7),(3,8),(4,6),(4,10),(5,7),(5,10),(6,11),(7,11),(8,11),(9,10),(10,11)],12)
=> ([(0,3),(0,6),(0,7),(0,8),(0,9),(0,10),(0,11),(1,2),(1,4),(1,5),(1,8),(1,9),(1,10),(1,11),(2,3),(2,4),(2,5),(2,6),(2,7),(2,8),(2,9),(3,4),(3,5),(3,6),(3,7),(3,10),(3,11),(4,5),(4,7),(4,8),(4,9),(4,11),(5,6),(5,8),(5,9),(5,10),(6,7),(6,8),(6,10),(6,11),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
11001 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ([(0,11),(0,12),(1,8),(1,12),(2,6),(2,7),(3,4),(3,11),(3,12),(4,5),(4,6),(5,9),(5,11),(6,9),(7,8),(7,9),(8,10),(9,10),(10,11),(10,12)],13)
=> ([(0,4),(0,5),(0,6),(0,7),(0,9),(0,10),(0,11),(0,12),(1,2),(1,3),(1,4),(1,6),(1,7),(1,8),(1,9),(1,12),(2,3),(2,6),(2,7),(2,8),(2,9),(2,11),(2,12),(3,5),(3,8),(3,9),(3,10),(3,11),(3,12),(4,5),(4,6),(4,7),(4,8),(4,10),(4,11),(4,12),(5,6),(5,7),(5,8),(5,10),(5,11),(5,12),(6,7),(6,9),(6,10),(6,11),(7,8),(7,10),(7,11),(8,9),(8,10),(8,12),(9,10),(9,11),(9,12),(10,11),(10,12),(11,12)],13)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
11010 => ([(0,2),(0,3),(1,8),(2,10),(2,11),(3,1),(3,10),(3,11),(5,6),(6,4),(7,4),(8,7),(9,6),(9,7),(10,5),(10,9),(11,5),(11,8),(11,9)],12)
=> ([(0,5),(0,6),(1,7),(1,10),(2,4),(2,10),(3,6),(3,8),(3,11),(4,5),(4,11),(5,9),(6,9),(7,8),(7,11),(8,9),(8,10),(9,11),(10,11)],12)
=> ([(0,3),(0,7),(0,8),(0,9),(0,10),(0,11),(1,2),(1,4),(1,5),(1,6),(1,7),(1,8),(1,11),(2,4),(2,5),(2,6),(2,9),(2,10),(2,11),(3,5),(3,7),(3,8),(3,9),(3,10),(3,11),(4,5),(4,6),(4,7),(4,8),(4,9),(4,11),(5,6),(5,7),(5,10),(5,11),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(8,9),(8,10),(9,10),(9,11),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
11011 => ([(0,2),(0,3),(1,5),(1,6),(2,10),(2,11),(3,1),(3,10),(3,11),(5,8),(6,7),(7,4),(8,4),(9,7),(9,8),(10,6),(10,9),(11,5),(11,9)],12)
=> ([(0,7),(0,11),(1,5),(1,6),(2,3),(2,4),(2,11),(3,6),(3,9),(4,5),(4,8),(5,10),(6,10),(7,8),(7,9),(8,10),(8,11),(9,10),(9,11)],12)
=> ([(0,3),(0,4),(0,5),(0,6),(0,8),(0,9),(0,11),(1,2),(1,5),(1,6),(1,7),(1,9),(1,10),(1,11),(2,5),(2,6),(2,7),(2,8),(2,10),(2,11),(3,4),(3,7),(3,8),(3,9),(3,10),(3,11),(4,5),(4,6),(4,7),(4,8),(4,9),(4,11),(5,6),(5,7),(5,8),(5,10),(6,7),(6,9),(6,10),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
11100 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ([(0,5),(0,9),(1,4),(1,9),(2,6),(2,8),(3,7),(3,8),(4,6),(4,10),(5,7),(5,10),(6,11),(7,11),(8,11),(9,10),(10,11)],12)
=> ([(0,3),(0,6),(0,7),(0,8),(0,9),(0,10),(0,11),(1,2),(1,4),(1,5),(1,8),(1,9),(1,10),(1,11),(2,3),(2,4),(2,5),(2,6),(2,7),(2,8),(2,9),(3,4),(3,5),(3,6),(3,7),(3,10),(3,11),(4,5),(4,7),(4,8),(4,9),(4,11),(5,6),(5,8),(5,9),(5,10),(6,7),(6,8),(6,10),(6,11),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
11101 => ([(0,3),(0,4),(1,2),(1,11),(2,8),(3,9),(3,10),(4,1),(4,9),(4,10),(6,7),(7,5),(8,5),(9,6),(10,6),(10,11),(11,7),(11,8)],12)
=> ([(0,7),(0,11),(1,5),(1,8),(2,6),(2,8),(3,4),(3,7),(3,11),(4,5),(4,9),(5,10),(6,10),(6,11),(7,9),(8,10),(9,10),(9,11)],12)
=> ([(0,3),(0,4),(0,5),(0,6),(0,9),(0,10),(0,11),(1,2),(1,4),(1,5),(1,7),(1,8),(1,10),(1,11),(2,6),(2,7),(2,8),(2,9),(2,10),(2,11),(3,4),(3,5),(3,6),(3,7),(3,8),(3,9),(3,11),(4,5),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,9),(5,10),(6,9),(6,10),(6,11),(7,8),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
11110 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ([(0,3),(0,7),(1,2),(1,6),(2,8),(3,9),(4,5),(4,8),(4,9),(5,6),(5,7),(6,8),(7,9)],10)
=> ([(0,1),(0,3),(0,5),(0,6),(0,7),(0,9),(1,2),(1,5),(1,6),(1,7),(1,8),(2,3),(2,4),(2,6),(2,8),(2,9),(3,4),(3,7),(3,8),(3,9),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,7),(6,8),(7,9),(8,9)],10)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> ([(0,1),(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 1
000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
=> ([(0,1),(0,3),(0,4),(0,6),(1,2),(1,4),(1,5),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 1
000001 => ([(0,2),(0,6),(1,8),(2,7),(3,5),(3,9),(4,3),(4,11),(5,1),(5,10),(6,4),(6,7),(7,11),(9,10),(10,8),(11,9)],12)
=> ([(0,3),(0,11),(1,2),(1,8),(2,9),(3,10),(4,5),(4,6),(4,8),(5,7),(5,9),(6,7),(6,10),(7,11),(8,9),(10,11)],12)
=> ([(0,2),(0,3),(0,5),(0,6),(0,7),(0,9),(0,10),(0,11),(1,2),(1,3),(1,4),(1,6),(1,7),(1,8),(1,10),(1,11),(2,4),(2,5),(2,6),(2,8),(2,9),(2,10),(3,4),(3,5),(3,7),(3,8),(3,9),(3,11),(4,7),(4,8),(4,9),(4,10),(4,11),(5,6),(5,8),(5,9),(5,10),(5,11),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11),(8,10),(8,11),(9,10),(9,11)],12)
=> ? ∊ {1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3}
000010 => ([(0,4),(0,5),(1,3),(1,12),(2,11),(3,2),(3,14),(4,10),(4,13),(5,1),(5,10),(5,13),(7,8),(8,9),(9,6),(10,7),(11,6),(12,8),(12,14),(13,7),(13,12),(14,9),(14,11)],15)
=> ([(0,9),(0,14),(1,7),(1,10),(2,8),(2,10),(3,4),(3,9),(3,14),(4,5),(4,11),(5,7),(5,13),(6,8),(6,13),(6,14),(7,12),(8,12),(9,11),(10,12),(11,13),(11,14),(12,13)],15)
=> ([(0,3),(0,5),(0,6),(0,8),(0,9),(0,10),(0,11),(0,12),(0,13),(0,14),(1,2),(1,4),(1,7),(1,8),(1,9),(1,10),(1,11),(1,12),(1,13),(1,14),(2,3),(2,4),(2,6),(2,7),(2,8),(2,9),(2,10),(2,13),(2,14),(3,4),(3,5),(3,6),(3,7),(3,11),(3,12),(3,13),(3,14),(4,5),(4,6),(4,7),(4,8),(4,9),(4,10),(4,13),(4,14),(5,6),(5,7),(5,8),(5,10),(5,11),(5,12),(5,13),(5,14),(6,8),(6,9),(6,11),(6,12),(6,13),(6,14),(7,8),(7,9),(7,10),(7,12),(7,13),(7,14),(8,9),(8,10),(8,11),(8,12),(9,10),(9,11),(9,12),(9,13),(10,11),(10,12),(10,14),(11,12),(11,13),(11,14),(12,13),(12,14),(13,14)],15)
=> ? ∊ {1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3}
000011 => ([(0,5),(0,6),(1,4),(1,14),(2,11),(3,10),(4,3),(4,12),(5,1),(5,13),(6,2),(6,13),(8,9),(9,7),(10,7),(11,8),(12,9),(12,10),(13,11),(13,14),(14,8),(14,12)],15)
=> ([(0,7),(0,11),(1,6),(1,10),(2,8),(2,10),(3,9),(3,11),(4,8),(4,9),(4,14),(5,6),(5,7),(5,14),(6,12),(7,13),(8,12),(9,13),(10,12),(11,13),(12,14),(13,14)],15)
=> ([(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,11),(0,12),(0,13),(0,14),(1,2),(1,4),(1,7),(1,8),(1,9),(1,10),(1,11),(1,12),(1,13),(1,14),(2,3),(2,5),(2,6),(2,9),(2,10),(2,11),(2,12),(2,13),(2,14),(3,4),(3,5),(3,6),(3,7),(3,8),(3,9),(3,10),(3,11),(3,12),(4,5),(4,6),(4,7),(4,8),(4,9),(4,10),(4,13),(4,14),(5,6),(5,7),(5,8),(5,10),(5,11),(5,12),(5,14),(6,7),(6,8),(6,9),(6,11),(6,12),(6,13),(7,8),(7,9),(7,11),(7,13),(7,14),(8,10),(8,12),(8,13),(8,14),(9,10),(9,11),(9,12),(9,13),(9,14),(10,11),(10,12),(10,13),(10,14),(11,12),(11,13),(11,14),(12,13),(12,14),(13,14)],15)
=> ? ∊ {1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3}
000100 => ([(0,3),(0,4),(1,10),(2,1),(2,6),(2,12),(3,14),(3,15),(4,2),(4,14),(4,15),(6,7),(7,8),(8,5),(9,5),(10,9),(11,7),(11,13),(12,10),(12,13),(13,8),(13,9),(14,6),(14,11),(15,11),(15,12)],16)
=> ([(0,7),(0,15),(1,5),(1,14),(2,6),(2,8),(3,4),(3,13),(3,15),(4,6),(4,10),(5,12),(5,13),(6,11),(7,8),(7,9),(8,11),(9,11),(9,12),(9,15),(10,11),(10,12),(10,13),(12,14),(13,14),(14,15)],16)
=> ([(0,1),(0,3),(0,4),(0,5),(0,7),(0,8),(0,9),(0,11),(0,13),(0,14),(0,15),(1,4),(1,5),(1,6),(1,7),(1,10),(1,11),(1,12),(1,13),(1,14),(1,15),(2,3),(2,5),(2,6),(2,8),(2,9),(2,10),(2,11),(2,12),(2,13),(2,14),(2,15),(3,6),(3,7),(3,8),(3,9),(3,10),(3,12),(3,13),(3,14),(3,15),(4,5),(4,7),(4,8),(4,9),(4,10),(4,11),(4,13),(4,14),(4,15),(5,7),(5,8),(5,9),(5,11),(5,12),(5,13),(5,15),(6,7),(6,8),(6,9),(6,10),(6,11),(6,12),(6,13),(6,14),(7,9),(7,11),(7,12),(7,13),(7,14),(7,15),(8,9),(8,10),(8,11),(8,12),(8,14),(8,15),(9,10),(9,12),(9,14),(9,15),(10,11),(10,12),(10,13),(10,14),(10,15),(11,12),(11,13),(11,15),(12,13),(12,14),(13,14),(13,15),(14,15)],16)
=> ? ∊ {1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3}
000101 => ([(0,3),(0,4),(1,2),(1,14),(2,6),(3,13),(3,15),(4,1),(4,13),(4,15),(6,9),(7,8),(8,10),(9,5),(10,5),(11,8),(11,12),(12,9),(12,10),(13,7),(13,11),(14,6),(14,12),(15,7),(15,11),(15,14)],16)
=> ([(0,5),(0,7),(1,6),(1,8),(2,9),(2,14),(3,4),(3,8),(3,13),(4,10),(4,15),(5,6),(5,11),(6,12),(7,11),(7,14),(8,12),(9,10),(9,15),(10,13),(10,14),(11,12),(11,15),(12,13),(13,15),(14,15)],16)
=> ([(0,4),(0,5),(0,8),(0,9),(0,10),(0,11),(0,12),(0,13),(0,14),(0,15),(1,2),(1,3),(1,6),(1,7),(1,8),(1,9),(1,11),(1,12),(1,13),(1,14),(1,15),(2,3),(2,5),(2,6),(2,7),(2,9),(2,10),(2,11),(2,12),(2,14),(2,15),(3,4),(3,6),(3,7),(3,10),(3,11),(3,12),(3,13),(3,14),(3,15),(4,5),(4,8),(4,9),(4,10),(4,11),(4,12),(4,13),(4,14),(4,15),(5,6),(5,7),(5,8),(5,9),(5,10),(5,13),(5,14),(5,15),(6,7),(6,8),(6,9),(6,10),(6,11),(6,12),(6,14),(6,15),(7,8),(7,9),(7,11),(7,12),(7,13),(7,14),(7,15),(8,9),(8,10),(8,11),(8,12),(8,13),(8,15),(9,10),(9,11),(9,13),(9,15),(10,12),(10,13),(10,14),(10,15),(11,12),(11,13),(11,14),(12,13),(12,14),(13,14),(13,15),(14,15)],16)
=> ? ∊ {1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3}
000110 => ([(0,4),(0,5),(1,11),(2,1),(2,13),(3,7),(3,14),(4,2),(4,12),(4,16),(5,3),(5,12),(5,16),(7,8),(8,9),(9,6),(10,6),(11,10),(12,7),(13,11),(13,15),(14,8),(14,15),(15,9),(15,10),(16,13),(16,14)],17)
=> ([(0,15),(0,16),(1,7),(1,10),(2,8),(2,9),(3,4),(3,5),(3,6),(4,15),(4,16),(5,11),(5,15),(6,8),(6,11),(7,14),(7,16),(8,13),(9,10),(9,13),(10,14),(11,12),(11,13),(12,14),(12,15),(12,16),(13,14)],17)
=> ([(0,3),(0,6),(0,7),(0,8),(0,9),(0,10),(0,11),(0,12),(0,13),(0,14),(0,15),(0,16),(1,2),(1,4),(1,5),(1,6),(1,7),(1,8),(1,9),(1,12),(1,13),(1,14),(1,15),(1,16),(2,4),(2,5),(2,7),(2,8),(2,10),(2,11),(2,12),(2,13),(2,14),(2,15),(2,16),(3,4),(3,5),(3,6),(3,9),(3,10),(3,11),(3,12),(3,13),(3,14),(3,15),(3,16),(4,5),(4,6),(4,7),(4,8),(4,9),(4,11),(4,13),(4,15),(4,16),(5,7),(5,8),(5,9),(5,10),(5,11),(5,13),(5,15),(5,16),(6,7),(6,8),(6,9),(6,10),(6,11),(6,12),(6,13),(6,14),(6,16),(7,8),(7,9),(7,10),(7,12),(7,13),(7,14),(7,15),(8,10),(8,11),(8,12),(8,13),(8,14),(8,15),(9,10),(9,11),(9,12),(9,13),(9,14),(9,16),(10,11),(10,12),(10,14),(10,15),(10,16),(11,12),(11,14),(11,15),(11,16),(12,14),(12,15),(12,16),(13,14),(13,15),(13,16),(14,15),(14,16),(15,16)],17)
=> ? ∊ {1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3}
000111 => ([(0,5),(0,6),(1,4),(1,15),(2,3),(2,14),(3,8),(4,9),(5,2),(5,13),(6,1),(6,13),(8,10),(9,11),(10,7),(11,7),(12,10),(12,11),(13,14),(13,15),(14,8),(14,12),(15,9),(15,12)],16)
=> ([(0,10),(0,11),(1,6),(1,7),(2,5),(2,9),(3,4),(3,8),(4,6),(4,13),(5,7),(5,14),(6,12),(7,12),(8,10),(8,13),(9,11),(9,14),(10,15),(11,15),(12,13),(12,14),(13,15),(14,15)],16)
=> ([(0,3),(0,6),(0,7),(0,8),(0,9),(0,10),(0,11),(0,12),(0,13),(0,14),(0,15),(1,2),(1,4),(1,5),(1,6),(1,7),(1,9),(1,11),(1,12),(1,13),(1,14),(1,15),(2,4),(2,5),(2,6),(2,7),(2,8),(2,10),(2,12),(2,13),(2,14),(2,15),(3,4),(3,5),(3,8),(3,9),(3,10),(3,11),(3,12),(3,13),(3,14),(3,15),(4,5),(4,6),(4,7),(4,8),(4,10),(4,11),(4,13),(4,14),(4,15),(5,6),(5,7),(5,9),(5,10),(5,11),(5,13),(5,14),(5,15),(6,7),(6,8),(6,9),(6,10),(6,12),(6,14),(6,15),(7,8),(7,9),(7,11),(7,12),(7,14),(7,15),(8,9),(8,10),(8,11),(8,12),(8,13),(8,14),(9,10),(9,11),(9,12),(9,13),(9,15),(10,11),(10,12),(10,13),(10,14),(11,12),(11,13),(11,15),(12,13),(12,14),(12,15),(13,14),(13,15),(14,15)],16)
=> ? ∊ {1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3}
001000 => ([(0,3),(0,4),(1,10),(2,1),(2,6),(2,12),(3,14),(3,15),(4,2),(4,14),(4,15),(6,7),(7,8),(8,5),(9,5),(10,9),(11,7),(11,13),(12,10),(12,13),(13,8),(13,9),(14,6),(14,11),(15,11),(15,12)],16)
=> ([(0,7),(0,15),(1,5),(1,14),(2,6),(2,8),(3,4),(3,13),(3,15),(4,6),(4,10),(5,12),(5,13),(6,11),(7,8),(7,9),(8,11),(9,11),(9,12),(9,15),(10,11),(10,12),(10,13),(12,14),(13,14),(14,15)],16)
=> ([(0,1),(0,3),(0,4),(0,5),(0,7),(0,8),(0,9),(0,11),(0,13),(0,14),(0,15),(1,4),(1,5),(1,6),(1,7),(1,10),(1,11),(1,12),(1,13),(1,14),(1,15),(2,3),(2,5),(2,6),(2,8),(2,9),(2,10),(2,11),(2,12),(2,13),(2,14),(2,15),(3,6),(3,7),(3,8),(3,9),(3,10),(3,12),(3,13),(3,14),(3,15),(4,5),(4,7),(4,8),(4,9),(4,10),(4,11),(4,13),(4,14),(4,15),(5,7),(5,8),(5,9),(5,11),(5,12),(5,13),(5,15),(6,7),(6,8),(6,9),(6,10),(6,11),(6,12),(6,13),(6,14),(7,9),(7,11),(7,12),(7,13),(7,14),(7,15),(8,9),(8,10),(8,11),(8,12),(8,14),(8,15),(9,10),(9,12),(9,14),(9,15),(10,11),(10,12),(10,13),(10,14),(10,15),(11,12),(11,13),(11,15),(12,13),(12,14),(13,14),(13,15),(14,15)],16)
=> ? ∊ {1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3}
001001 => ([(0,2),(0,3),(1,11),(1,12),(2,13),(2,14),(3,1),(3,13),(3,14),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,9),(11,6),(11,9),(12,5),(12,6),(13,10),(13,11),(14,10),(14,12)],15)
=> ([(0,5),(0,14),(1,6),(1,7),(2,12),(2,13),(2,14),(3,6),(3,12),(3,13),(4,7),(4,11),(4,13),(5,8),(5,9),(6,10),(7,10),(8,11),(8,13),(8,14),(9,11),(9,12),(9,14),(10,11),(10,12)],15)
=> ([(0,1),(0,2),(0,4),(0,5),(0,6),(0,7),(0,8),(0,12),(0,13),(0,14),(1,3),(1,4),(1,6),(1,7),(1,8),(1,10),(1,12),(1,13),(1,14),(2,3),(2,5),(2,6),(2,9),(2,10),(2,11),(2,12),(2,13),(2,14),(3,5),(3,7),(3,8),(3,9),(3,10),(3,11),(3,13),(3,14),(4,6),(4,7),(4,8),(4,9),(4,11),(4,12),(4,13),(4,14),(5,7),(5,8),(5,9),(5,10),(5,11),(5,13),(5,14),(6,7),(6,8),(6,9),(6,10),(6,12),(6,13),(7,8),(7,10),(7,11),(7,12),(7,14),(8,9),(8,11),(8,12),(8,14),(9,10),(9,11),(9,12),(9,13),(9,14),(10,11),(10,12),(10,13),(10,14),(11,12),(11,13),(11,14),(12,13),(13,14)],15)
=> ? ∊ {1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3}
001010 => ([(0,2),(0,3),(1,9),(2,12),(2,14),(3,1),(3,12),(3,14),(5,7),(6,8),(7,4),(8,4),(9,5),(10,6),(10,11),(11,7),(11,8),(12,10),(12,13),(13,5),(13,6),(13,11),(14,9),(14,10),(14,13)],15)
=> ([(0,6),(0,7),(1,8),(1,12),(2,5),(2,12),(3,5),(3,7),(3,14),(4,6),(4,11),(4,14),(5,13),(6,9),(7,9),(8,10),(8,13),(9,11),(9,14),(10,11),(10,12),(10,14),(11,13),(12,13),(13,14)],15)
=> ([(0,2),(0,5),(0,7),(0,9),(0,10),(0,11),(0,12),(0,13),(0,14),(1,3),(1,4),(1,6),(1,8),(1,10),(1,11),(1,12),(1,13),(1,14),(2,5),(2,7),(2,8),(2,9),(2,10),(2,11),(2,12),(2,13),(2,14),(3,4),(3,6),(3,8),(3,9),(3,10),(3,11),(3,12),(3,13),(3,14),(4,5),(4,6),(4,7),(4,8),(4,9),(4,10),(4,11),(4,12),(5,6),(5,7),(5,8),(5,9),(5,12),(5,13),(5,14),(6,7),(6,8),(6,9),(6,10),(6,11),(6,12),(6,13),(7,8),(7,9),(7,11),(7,12),(7,13),(7,14),(8,10),(8,11),(8,12),(8,14),(9,10),(9,12),(9,13),(9,14),(10,11),(10,13),(10,14),(11,13),(11,14),(12,13),(12,14),(13,14)],15)
=> ? ∊ {1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3}
001011 => ([(0,3),(0,4),(1,11),(2,10),(3,2),(3,15),(3,16),(4,1),(4,15),(4,16),(6,8),(7,9),(8,5),(9,5),(10,6),(11,7),(12,6),(12,14),(13,7),(13,14),(14,8),(14,9),(15,12),(15,13),(16,10),(16,11),(16,12),(16,13)],17)
=> ([(0,8),(0,9),(1,7),(1,15),(2,6),(2,14),(3,14),(3,15),(4,6),(4,8),(4,12),(5,7),(5,9),(5,13),(6,16),(7,16),(8,10),(9,10),(10,12),(10,13),(11,12),(11,13),(11,14),(11,15),(12,16),(13,16),(14,16),(15,16)],17)
=> ([(0,5),(0,6),(0,9),(0,10),(0,11),(0,12),(0,13),(0,14),(0,15),(0,16),(1,2),(1,3),(1,4),(1,7),(1,8),(1,9),(1,10),(1,12),(1,13),(1,14),(1,15),(1,16),(2,3),(2,4),(2,7),(2,8),(2,9),(2,10),(2,11),(2,13),(2,14),(2,15),(2,16),(3,4),(3,5),(3,7),(3,8),(3,9),(3,10),(3,11),(3,12),(3,13),(3,14),(4,5),(4,7),(4,8),(4,9),(4,10),(4,11),(4,12),(4,13),(4,15),(5,6),(5,7),(5,8),(5,11),(5,12),(5,13),(5,14),(5,15),(5,16),(6,7),(6,8),(6,9),(6,10),(6,11),(6,12),(6,13),(6,14),(6,15),(6,16),(7,8),(7,9),(7,10),(7,11),(7,13),(7,14),(7,16),(8,9),(8,10),(8,12),(8,13),(8,15),(8,16),(9,10),(9,11),(9,14),(9,15),(9,16),(10,12),(10,14),(10,15),(10,16),(11,12),(11,13),(11,14),(11,15),(11,16),(12,13),(12,14),(12,15),(12,16),(13,14),(13,15),(13,16),(14,15),(14,16),(15,16)],17)
=> ? ∊ {1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3}
001100 => ([(0,3),(0,4),(1,15),(1,16),(2,10),(2,11),(3,1),(3,13),(3,14),(4,2),(4,13),(4,14),(6,9),(7,8),(8,5),(9,5),(10,7),(11,6),(12,8),(12,9),(13,10),(13,15),(14,11),(14,16),(15,7),(15,12),(16,6),(16,12)],17)
=> ([(0,15),(0,16),(1,8),(1,9),(2,3),(2,4),(2,16),(3,6),(3,11),(4,5),(4,10),(5,8),(5,12),(6,9),(6,13),(7,12),(7,13),(7,15),(8,14),(9,14),(10,12),(10,15),(10,16),(11,13),(11,15),(11,16),(12,14),(13,14)],17)
=> ([(0,1),(0,5),(0,6),(0,7),(0,8),(0,9),(0,10),(0,11),(0,12),(0,14),(0,15),(0,16),(1,4),(1,6),(1,7),(1,8),(1,9),(1,10),(1,11),(1,12),(1,13),(1,15),(1,16),(2,3),(2,4),(2,5),(2,6),(2,8),(2,9),(2,10),(2,11),(2,12),(2,13),(2,14),(2,16),(3,4),(3,5),(3,6),(3,7),(3,9),(3,10),(3,11),(3,12),(3,13),(3,14),(3,16),(4,5),(4,8),(4,9),(4,11),(4,12),(4,13),(4,14),(4,15),(4,16),(5,8),(5,10),(5,11),(5,12),(5,13),(5,14),(5,15),(5,16),(6,7),(6,8),(6,9),(6,10),(6,13),(6,14),(6,15),(6,16),(7,8),(7,9),(7,10),(7,11),(7,12),(7,13),(7,14),(7,15),(7,16),(8,9),(8,10),(8,11),(8,12),(8,15),(8,16),(9,10),(9,11),(9,13),(9,15),(9,16),(10,12),(10,14),(10,15),(10,16),(11,12),(11,13),(11,14),(11,15),(12,13),(12,14),(12,15),(13,14),(13,15),(13,16),(14,15),(14,16),(15,16)],17)
=> ? ∊ {1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3}
111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
=> ([(0,1),(0,3),(0,4),(0,6),(1,2),(1,4),(1,5),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 1
Description
The cardinality of a minimal cycle-isolating set of a graph.
Let $\mathcal F$ be a set of graphs. A set of vertices $S$ is $\mathcal F$-isolating, if the subgraph induced by the vertices in the complement of the closed neighbourhood of $S$ does not contain any graph in $\mathcal F$.
This statistic returns the cardinality of the smallest isolating set when $\mathcal F$ contains all cycles.
Matching statistic: St001323
Values
0 => ([(0,1)],2)
=> ([(0,1)],2)
=> 0
1 => ([(0,1)],2)
=> ([(0,1)],2)
=> 0
00 => ([(0,2),(2,1)],3)
=> ([(0,2),(1,2)],3)
=> 1
01 => ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> 0
10 => ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> 0
11 => ([(0,2),(2,1)],3)
=> ([(0,2),(1,2)],3)
=> 1
000 => ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(1,2),(2,3)],4)
=> 0
001 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
=> 1
010 => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
=> 1
011 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
=> 1
100 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
=> 1
101 => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
=> 1
110 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
=> 1
111 => ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(1,2),(2,3)],4)
=> 0
0000 => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> 1
0001 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,3),(0,7),(1,2),(1,4),(2,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2}
0010 => ([(0,2),(0,3),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,5),(8,5),(8,6)],9)
=> ([(0,5),(0,8),(1,4),(1,6),(2,6),(2,8),(3,4),(3,5),(3,8),(4,7),(5,7),(6,7),(7,8)],9)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2}
0011 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,6),(0,7),(1,4),(1,5),(2,5),(2,7),(3,4),(3,6),(4,8),(5,8),(6,8),(7,8)],9)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2}
0100 => ([(0,2),(0,3),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,5),(8,5),(8,6)],9)
=> ([(0,5),(0,8),(1,4),(1,6),(2,6),(2,8),(3,4),(3,5),(3,8),(4,7),(5,7),(6,7),(7,8)],9)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2}
0101 => ([(0,1),(0,2),(1,6),(1,7),(2,6),(2,7),(4,3),(5,3),(6,4),(6,5),(7,4),(7,5)],8)
=> ([(0,4),(0,5),(1,2),(1,3),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2}
0110 => ([(0,2),(0,3),(1,5),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,6),(8,5)],9)
=> ([(0,5),(0,6),(1,7),(1,8),(2,5),(2,6),(2,8),(3,6),(3,7),(3,8),(4,5),(4,7),(4,8)],9)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2}
0111 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,3),(0,7),(1,2),(1,4),(2,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2}
1000 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,3),(0,7),(1,2),(1,4),(2,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2}
1001 => ([(0,2),(0,3),(1,5),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,6),(8,5)],9)
=> ([(0,5),(0,6),(1,7),(1,8),(2,5),(2,6),(2,8),(3,6),(3,7),(3,8),(4,5),(4,7),(4,8)],9)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2}
1010 => ([(0,1),(0,2),(1,6),(1,7),(2,6),(2,7),(4,3),(5,3),(6,4),(6,5),(7,4),(7,5)],8)
=> ([(0,4),(0,5),(1,2),(1,3),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2}
1011 => ([(0,2),(0,3),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,5),(8,5),(8,6)],9)
=> ([(0,5),(0,8),(1,4),(1,6),(2,6),(2,8),(3,4),(3,5),(3,8),(4,7),(5,7),(6,7),(7,8)],9)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2}
1100 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,6),(0,7),(1,4),(1,5),(2,5),(2,7),(3,4),(3,6),(4,8),(5,8),(6,8),(7,8)],9)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2}
1101 => ([(0,2),(0,3),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,5),(8,5),(8,6)],9)
=> ([(0,5),(0,8),(1,4),(1,6),(2,6),(2,8),(3,4),(3,5),(3,8),(4,7),(5,7),(6,7),(7,8)],9)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2}
1110 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,3),(0,7),(1,2),(1,4),(2,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2}
1111 => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> 1
00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> 1
00001 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ([(0,3),(0,7),(1,2),(1,6),(2,8),(3,9),(4,5),(4,8),(4,9),(5,6),(5,7),(6,8),(7,9)],10)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
00010 => ([(0,3),(0,4),(1,2),(1,11),(2,8),(3,9),(3,10),(4,1),(4,9),(4,10),(6,7),(7,5),(8,5),(9,6),(10,6),(10,11),(11,7),(11,8)],12)
=> ([(0,7),(0,11),(1,5),(1,8),(2,6),(2,8),(3,4),(3,7),(3,11),(4,5),(4,9),(5,10),(6,10),(6,11),(7,9),(8,10),(9,10),(9,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
00011 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ([(0,5),(0,9),(1,4),(1,9),(2,6),(2,8),(3,7),(3,8),(4,6),(4,10),(5,7),(5,10),(6,11),(7,11),(8,11),(9,10),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
00100 => ([(0,2),(0,3),(1,5),(1,6),(2,10),(2,11),(3,1),(3,10),(3,11),(5,8),(6,7),(7,4),(8,4),(9,7),(9,8),(10,6),(10,9),(11,5),(11,9)],12)
=> ([(0,7),(0,11),(1,5),(1,6),(2,3),(2,4),(2,11),(3,6),(3,9),(4,5),(4,8),(5,10),(6,10),(7,8),(7,9),(8,10),(8,11),(9,10),(9,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
00101 => ([(0,2),(0,3),(1,8),(2,10),(2,11),(3,1),(3,10),(3,11),(5,6),(6,4),(7,4),(8,7),(9,6),(9,7),(10,5),(10,9),(11,5),(11,8),(11,9)],12)
=> ([(0,5),(0,6),(1,7),(1,10),(2,4),(2,10),(3,6),(3,8),(3,11),(4,5),(4,11),(5,9),(6,9),(7,8),(7,11),(8,9),(8,10),(9,11),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
00110 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ([(0,11),(0,12),(1,8),(1,12),(2,6),(2,7),(3,4),(3,11),(3,12),(4,5),(4,6),(5,9),(5,11),(6,9),(7,8),(7,9),(8,10),(9,10),(10,11),(10,12)],13)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
00111 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ([(0,5),(0,9),(1,4),(1,9),(2,6),(2,8),(3,7),(3,8),(4,6),(4,10),(5,7),(5,10),(6,11),(7,11),(8,11),(9,10),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
01000 => ([(0,3),(0,4),(1,2),(1,11),(2,8),(3,9),(3,10),(4,1),(4,9),(4,10),(6,7),(7,5),(8,5),(9,6),(10,6),(10,11),(11,7),(11,8)],12)
=> ([(0,7),(0,11),(1,5),(1,8),(2,6),(2,8),(3,4),(3,7),(3,11),(4,5),(4,9),(5,10),(6,10),(6,11),(7,9),(8,10),(9,10),(9,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
01001 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
=> ([(0,7),(0,11),(1,5),(1,6),(2,3),(2,10),(2,11),(3,5),(3,8),(4,6),(4,8),(4,9),(5,10),(6,10),(7,8),(7,9),(8,11),(9,10),(9,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
01010 => ([(0,1),(0,2),(1,8),(1,9),(2,8),(2,9),(4,3),(5,3),(6,4),(6,5),(7,4),(7,5),(8,6),(8,7),(9,6),(9,7)],10)
=> ([(0,4),(0,5),(1,2),(1,3),(2,6),(2,7),(3,6),(3,7),(4,8),(4,9),(5,8),(5,9),(6,8),(6,9),(7,8),(7,9)],10)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
01011 => ([(0,2),(0,3),(1,8),(2,10),(2,11),(3,1),(3,10),(3,11),(5,6),(6,4),(7,4),(8,7),(9,6),(9,7),(10,5),(10,9),(11,5),(11,8),(11,9)],12)
=> ([(0,5),(0,6),(1,7),(1,10),(2,4),(2,10),(3,6),(3,8),(3,11),(4,5),(4,11),(5,9),(6,9),(7,8),(7,11),(8,9),(8,10),(9,11),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
01100 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ([(0,11),(0,12),(1,8),(1,12),(2,6),(2,7),(3,4),(3,11),(3,12),(4,5),(4,6),(5,9),(5,11),(6,9),(7,8),(7,9),(8,10),(9,10),(10,11),(10,12)],13)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
01101 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
=> ([(0,7),(0,11),(1,5),(1,6),(2,3),(2,10),(2,11),(3,5),(3,8),(4,6),(4,8),(4,9),(5,10),(6,10),(7,8),(7,9),(8,11),(9,10),(9,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
01110 => ([(0,3),(0,4),(1,2),(1,10),(1,11),(2,8),(2,9),(3,6),(3,7),(4,1),(4,6),(4,7),(6,11),(7,10),(8,5),(9,5),(10,8),(11,9)],12)
=> ([(0,9),(0,11),(1,7),(1,8),(2,5),(2,9),(2,11),(3,4),(3,9),(3,11),(4,7),(4,10),(5,8),(5,10),(6,7),(6,8),(6,10),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
01111 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ([(0,3),(0,7),(1,2),(1,6),(2,8),(3,9),(4,5),(4,8),(4,9),(5,6),(5,7),(6,8),(7,9)],10)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ([(0,3),(0,7),(1,2),(1,6),(2,8),(3,9),(4,5),(4,8),(4,9),(5,6),(5,7),(6,8),(7,9)],10)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
10001 => ([(0,3),(0,4),(1,2),(1,10),(1,11),(2,8),(2,9),(3,6),(3,7),(4,1),(4,6),(4,7),(6,11),(7,10),(8,5),(9,5),(10,8),(11,9)],12)
=> ([(0,9),(0,11),(1,7),(1,8),(2,5),(2,9),(2,11),(3,4),(3,9),(3,11),(4,7),(4,10),(5,8),(5,10),(6,7),(6,8),(6,10),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
10010 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
=> ([(0,7),(0,11),(1,5),(1,6),(2,3),(2,10),(2,11),(3,5),(3,8),(4,6),(4,8),(4,9),(5,10),(6,10),(7,8),(7,9),(8,11),(9,10),(9,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
10011 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ([(0,11),(0,12),(1,8),(1,12),(2,6),(2,7),(3,4),(3,11),(3,12),(4,5),(4,6),(5,9),(5,11),(6,9),(7,8),(7,9),(8,10),(9,10),(10,11),(10,12)],13)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
10100 => ([(0,2),(0,3),(1,8),(2,10),(2,11),(3,1),(3,10),(3,11),(5,6),(6,4),(7,4),(8,7),(9,6),(9,7),(10,5),(10,9),(11,5),(11,8),(11,9)],12)
=> ([(0,5),(0,6),(1,7),(1,10),(2,4),(2,10),(3,6),(3,8),(3,11),(4,5),(4,11),(5,9),(6,9),(7,8),(7,11),(8,9),(8,10),(9,11),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
10101 => ([(0,1),(0,2),(1,8),(1,9),(2,8),(2,9),(4,3),(5,3),(6,4),(6,5),(7,4),(7,5),(8,6),(8,7),(9,6),(9,7)],10)
=> ([(0,4),(0,5),(1,2),(1,3),(2,6),(2,7),(3,6),(3,7),(4,8),(4,9),(5,8),(5,9),(6,8),(6,9),(7,8),(7,9)],10)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
10110 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
=> ([(0,7),(0,11),(1,5),(1,6),(2,3),(2,10),(2,11),(3,5),(3,8),(4,6),(4,8),(4,9),(5,10),(6,10),(7,8),(7,9),(8,11),(9,10),(9,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
10111 => ([(0,3),(0,4),(1,2),(1,11),(2,8),(3,9),(3,10),(4,1),(4,9),(4,10),(6,7),(7,5),(8,5),(9,6),(10,6),(10,11),(11,7),(11,8)],12)
=> ([(0,7),(0,11),(1,5),(1,8),(2,6),(2,8),(3,4),(3,7),(3,11),(4,5),(4,9),(5,10),(6,10),(6,11),(7,9),(8,10),(9,10),(9,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
11000 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ([(0,5),(0,9),(1,4),(1,9),(2,6),(2,8),(3,7),(3,8),(4,6),(4,10),(5,7),(5,10),(6,11),(7,11),(8,11),(9,10),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
11001 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ([(0,11),(0,12),(1,8),(1,12),(2,6),(2,7),(3,4),(3,11),(3,12),(4,5),(4,6),(5,9),(5,11),(6,9),(7,8),(7,9),(8,10),(9,10),(10,11),(10,12)],13)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
11010 => ([(0,2),(0,3),(1,8),(2,10),(2,11),(3,1),(3,10),(3,11),(5,6),(6,4),(7,4),(8,7),(9,6),(9,7),(10,5),(10,9),(11,5),(11,8),(11,9)],12)
=> ([(0,5),(0,6),(1,7),(1,10),(2,4),(2,10),(3,6),(3,8),(3,11),(4,5),(4,11),(5,9),(6,9),(7,8),(7,11),(8,9),(8,10),(9,11),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
11011 => ([(0,2),(0,3),(1,5),(1,6),(2,10),(2,11),(3,1),(3,10),(3,11),(5,8),(6,7),(7,4),(8,4),(9,7),(9,8),(10,6),(10,9),(11,5),(11,9)],12)
=> ([(0,7),(0,11),(1,5),(1,6),(2,3),(2,4),(2,11),(3,6),(3,9),(4,5),(4,8),(5,10),(6,10),(7,8),(7,9),(8,10),(8,11),(9,10),(9,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
11100 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ([(0,5),(0,9),(1,4),(1,9),(2,6),(2,8),(3,7),(3,8),(4,6),(4,10),(5,7),(5,10),(6,11),(7,11),(8,11),(9,10),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
11101 => ([(0,3),(0,4),(1,2),(1,11),(2,8),(3,9),(3,10),(4,1),(4,9),(4,10),(6,7),(7,5),(8,5),(9,6),(10,6),(10,11),(11,7),(11,8)],12)
=> ([(0,7),(0,11),(1,5),(1,8),(2,6),(2,8),(3,4),(3,7),(3,11),(4,5),(4,9),(5,10),(6,10),(6,11),(7,9),(8,10),(9,10),(9,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
11110 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ([(0,3),(0,7),(1,2),(1,6),(2,8),(3,9),(4,5),(4,8),(4,9),(5,6),(5,7),(6,8),(7,9)],10)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> 1
000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
=> 1
000001 => ([(0,2),(0,6),(1,8),(2,7),(3,5),(3,9),(4,3),(4,11),(5,1),(5,10),(6,4),(6,7),(7,11),(9,10),(10,8),(11,9)],12)
=> ([(0,3),(0,11),(1,2),(1,8),(2,9),(3,10),(4,5),(4,6),(4,8),(5,7),(5,9),(6,7),(6,10),(7,11),(8,9),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3}
000010 => ([(0,4),(0,5),(1,3),(1,12),(2,11),(3,2),(3,14),(4,10),(4,13),(5,1),(5,10),(5,13),(7,8),(8,9),(9,6),(10,7),(11,6),(12,8),(12,14),(13,7),(13,12),(14,9),(14,11)],15)
=> ([(0,9),(0,14),(1,7),(1,10),(2,8),(2,10),(3,4),(3,9),(3,14),(4,5),(4,11),(5,7),(5,13),(6,8),(6,13),(6,14),(7,12),(8,12),(9,11),(10,12),(11,13),(11,14),(12,13)],15)
=> ? ∊ {1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3}
000011 => ([(0,5),(0,6),(1,4),(1,14),(2,11),(3,10),(4,3),(4,12),(5,1),(5,13),(6,2),(6,13),(8,9),(9,7),(10,7),(11,8),(12,9),(12,10),(13,11),(13,14),(14,8),(14,12)],15)
=> ([(0,7),(0,11),(1,6),(1,10),(2,8),(2,10),(3,9),(3,11),(4,8),(4,9),(4,14),(5,6),(5,7),(5,14),(6,12),(7,13),(8,12),(9,13),(10,12),(11,13),(12,14),(13,14)],15)
=> ? ∊ {1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3}
000100 => ([(0,3),(0,4),(1,10),(2,1),(2,6),(2,12),(3,14),(3,15),(4,2),(4,14),(4,15),(6,7),(7,8),(8,5),(9,5),(10,9),(11,7),(11,13),(12,10),(12,13),(13,8),(13,9),(14,6),(14,11),(15,11),(15,12)],16)
=> ([(0,7),(0,15),(1,5),(1,14),(2,6),(2,8),(3,4),(3,13),(3,15),(4,6),(4,10),(5,12),(5,13),(6,11),(7,8),(7,9),(8,11),(9,11),(9,12),(9,15),(10,11),(10,12),(10,13),(12,14),(13,14),(14,15)],16)
=> ? ∊ {1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3}
000101 => ([(0,3),(0,4),(1,2),(1,14),(2,6),(3,13),(3,15),(4,1),(4,13),(4,15),(6,9),(7,8),(8,10),(9,5),(10,5),(11,8),(11,12),(12,9),(12,10),(13,7),(13,11),(14,6),(14,12),(15,7),(15,11),(15,14)],16)
=> ([(0,5),(0,7),(1,6),(1,8),(2,9),(2,14),(3,4),(3,8),(3,13),(4,10),(4,15),(5,6),(5,11),(6,12),(7,11),(7,14),(8,12),(9,10),(9,15),(10,13),(10,14),(11,12),(11,15),(12,13),(13,15),(14,15)],16)
=> ? ∊ {1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3}
000110 => ([(0,4),(0,5),(1,11),(2,1),(2,13),(3,7),(3,14),(4,2),(4,12),(4,16),(5,3),(5,12),(5,16),(7,8),(8,9),(9,6),(10,6),(11,10),(12,7),(13,11),(13,15),(14,8),(14,15),(15,9),(15,10),(16,13),(16,14)],17)
=> ([(0,15),(0,16),(1,7),(1,10),(2,8),(2,9),(3,4),(3,5),(3,6),(4,15),(4,16),(5,11),(5,15),(6,8),(6,11),(7,14),(7,16),(8,13),(9,10),(9,13),(10,14),(11,12),(11,13),(12,14),(12,15),(12,16),(13,14)],17)
=> ? ∊ {1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3}
111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
=> 1
Description
The independence gap of a graph.
This is the difference between the independence number [[St000093]] and the minimal size of a maximally independent set of a graph.
In particular, this statistic is $0$ for well covered graphs
Matching statistic: St000272
Values
0 => ([(0,1)],2)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 1 = 0 + 1
1 => ([(0,1)],2)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 1 = 0 + 1
00 => ([(0,2),(2,1)],3)
=> ([(0,2),(1,2)],3)
=> ([(0,2),(1,2)],3)
=> 1 = 0 + 1
01 => ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> 2 = 1 + 1
10 => ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> 2 = 1 + 1
11 => ([(0,2),(2,1)],3)
=> ([(0,2),(1,2)],3)
=> ([(0,2),(1,2)],3)
=> 1 = 0 + 1
000 => ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(1,2),(2,3)],4)
=> ([(0,3),(1,2),(2,3)],4)
=> 1 = 0 + 1
001 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,5),(3,4),(4,5)],6)
=> 2 = 1 + 1
010 => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6)
=> 2 = 1 + 1
011 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,5),(3,4),(4,5)],6)
=> 2 = 1 + 1
100 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,5),(3,4),(4,5)],6)
=> 2 = 1 + 1
101 => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6)
=> 2 = 1 + 1
110 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,5),(3,4),(4,5)],6)
=> 2 = 1 + 1
111 => ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(1,2),(2,3)],4)
=> ([(0,3),(1,2),(2,3)],4)
=> 1 = 0 + 1
0000 => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> 2 = 1 + 1
0001 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,3),(0,7),(1,2),(1,4),(2,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ([(0,3),(0,5),(0,6),(0,7),(1,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6),(6,7)],8)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2} + 1
0010 => ([(0,2),(0,3),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,5),(8,5),(8,6)],9)
=> ([(0,5),(0,8),(1,4),(1,6),(2,6),(2,8),(3,4),(3,5),(3,8),(4,7),(5,7),(6,7),(7,8)],9)
=> ([(0,2),(0,3),(0,4),(0,8),(1,5),(1,6),(1,7),(1,8),(2,3),(2,4),(2,5),(2,6),(3,4),(3,7),(3,8),(4,6),(4,7),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2} + 1
0011 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,6),(0,7),(1,4),(1,5),(2,5),(2,7),(3,4),(3,6),(4,8),(5,8),(6,8),(7,8)],9)
=> ([(0,5),(0,6),(0,7),(0,8),(1,2),(1,3),(1,4),(1,7),(1,8),(2,3),(2,4),(2,5),(2,6),(3,4),(3,6),(3,8),(4,5),(4,7),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2} + 1
0100 => ([(0,2),(0,3),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,5),(8,5),(8,6)],9)
=> ([(0,5),(0,8),(1,4),(1,6),(2,6),(2,8),(3,4),(3,5),(3,8),(4,7),(5,7),(6,7),(7,8)],9)
=> ([(0,2),(0,3),(0,4),(0,8),(1,5),(1,6),(1,7),(1,8),(2,3),(2,4),(2,5),(2,6),(3,4),(3,7),(3,8),(4,6),(4,7),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2} + 1
0101 => ([(0,1),(0,2),(1,6),(1,7),(2,6),(2,7),(4,3),(5,3),(6,4),(6,5),(7,4),(7,5)],8)
=> ([(0,4),(0,5),(1,2),(1,3),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
=> ([(0,1),(0,6),(0,7),(1,6),(1,7),(2,3),(2,4),(2,5),(2,7),(3,4),(3,5),(3,7),(4,5),(4,6),(5,6),(6,7)],8)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2} + 1
0110 => ([(0,2),(0,3),(1,5),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,6),(8,5)],9)
=> ([(0,5),(0,6),(1,7),(1,8),(2,5),(2,6),(2,8),(3,6),(3,7),(3,8),(4,5),(4,7),(4,8)],9)
=> ([(0,4),(0,5),(0,6),(0,8),(1,2),(1,3),(1,4),(1,7),(1,8),(2,3),(2,6),(2,7),(2,8),(3,5),(3,7),(3,8),(4,5),(4,6),(4,8),(5,6),(5,7),(6,7),(7,8)],9)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2} + 1
0111 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,3),(0,7),(1,2),(1,4),(2,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ([(0,3),(0,5),(0,6),(0,7),(1,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6),(6,7)],8)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2} + 1
1000 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,3),(0,7),(1,2),(1,4),(2,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ([(0,3),(0,5),(0,6),(0,7),(1,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6),(6,7)],8)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2} + 1
1001 => ([(0,2),(0,3),(1,5),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,6),(8,5)],9)
=> ([(0,5),(0,6),(1,7),(1,8),(2,5),(2,6),(2,8),(3,6),(3,7),(3,8),(4,5),(4,7),(4,8)],9)
=> ([(0,4),(0,5),(0,6),(0,8),(1,2),(1,3),(1,4),(1,7),(1,8),(2,3),(2,6),(2,7),(2,8),(3,5),(3,7),(3,8),(4,5),(4,6),(4,8),(5,6),(5,7),(6,7),(7,8)],9)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2} + 1
1010 => ([(0,1),(0,2),(1,6),(1,7),(2,6),(2,7),(4,3),(5,3),(6,4),(6,5),(7,4),(7,5)],8)
=> ([(0,4),(0,5),(1,2),(1,3),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
=> ([(0,1),(0,6),(0,7),(1,6),(1,7),(2,3),(2,4),(2,5),(2,7),(3,4),(3,5),(3,7),(4,5),(4,6),(5,6),(6,7)],8)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2} + 1
1011 => ([(0,2),(0,3),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,5),(8,5),(8,6)],9)
=> ([(0,5),(0,8),(1,4),(1,6),(2,6),(2,8),(3,4),(3,5),(3,8),(4,7),(5,7),(6,7),(7,8)],9)
=> ([(0,2),(0,3),(0,4),(0,8),(1,5),(1,6),(1,7),(1,8),(2,3),(2,4),(2,5),(2,6),(3,4),(3,7),(3,8),(4,6),(4,7),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2} + 1
1100 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,6),(0,7),(1,4),(1,5),(2,5),(2,7),(3,4),(3,6),(4,8),(5,8),(6,8),(7,8)],9)
=> ([(0,5),(0,6),(0,7),(0,8),(1,2),(1,3),(1,4),(1,7),(1,8),(2,3),(2,4),(2,5),(2,6),(3,4),(3,6),(3,8),(4,5),(4,7),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2} + 1
1101 => ([(0,2),(0,3),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,5),(8,5),(8,6)],9)
=> ([(0,5),(0,8),(1,4),(1,6),(2,6),(2,8),(3,4),(3,5),(3,8),(4,7),(5,7),(6,7),(7,8)],9)
=> ([(0,2),(0,3),(0,4),(0,8),(1,5),(1,6),(1,7),(1,8),(2,3),(2,4),(2,5),(2,6),(3,4),(3,7),(3,8),(4,6),(4,7),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2} + 1
1110 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,3),(0,7),(1,2),(1,4),(2,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ([(0,3),(0,5),(0,6),(0,7),(1,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6),(6,7)],8)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2} + 1
1111 => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> 2 = 1 + 1
00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> ([(0,1),(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 3 = 2 + 1
00001 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ([(0,3),(0,7),(1,2),(1,6),(2,8),(3,9),(4,5),(4,8),(4,9),(5,6),(5,7),(6,8),(7,9)],10)
=> ([(0,1),(0,3),(0,5),(0,6),(0,7),(0,9),(1,2),(1,5),(1,6),(1,7),(1,8),(2,3),(2,4),(2,6),(2,8),(2,9),(3,4),(3,7),(3,8),(3,9),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,7),(6,8),(7,9),(8,9)],10)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
00010 => ([(0,3),(0,4),(1,2),(1,11),(2,8),(3,9),(3,10),(4,1),(4,9),(4,10),(6,7),(7,5),(8,5),(9,6),(10,6),(10,11),(11,7),(11,8)],12)
=> ([(0,7),(0,11),(1,5),(1,8),(2,6),(2,8),(3,4),(3,7),(3,11),(4,5),(4,9),(5,10),(6,10),(6,11),(7,9),(8,10),(9,10),(9,11)],12)
=> ([(0,3),(0,4),(0,5),(0,6),(0,9),(0,10),(0,11),(1,2),(1,4),(1,5),(1,7),(1,8),(1,10),(1,11),(2,6),(2,7),(2,8),(2,9),(2,10),(2,11),(3,4),(3,5),(3,6),(3,7),(3,8),(3,9),(3,11),(4,5),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,9),(5,10),(6,9),(6,10),(6,11),(7,8),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
00011 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ([(0,5),(0,9),(1,4),(1,9),(2,6),(2,8),(3,7),(3,8),(4,6),(4,10),(5,7),(5,10),(6,11),(7,11),(8,11),(9,10),(10,11)],12)
=> ([(0,3),(0,6),(0,7),(0,8),(0,9),(0,10),(0,11),(1,2),(1,4),(1,5),(1,8),(1,9),(1,10),(1,11),(2,3),(2,4),(2,5),(2,6),(2,7),(2,8),(2,9),(3,4),(3,5),(3,6),(3,7),(3,10),(3,11),(4,5),(4,7),(4,8),(4,9),(4,11),(5,6),(5,8),(5,9),(5,10),(6,7),(6,8),(6,10),(6,11),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
00100 => ([(0,2),(0,3),(1,5),(1,6),(2,10),(2,11),(3,1),(3,10),(3,11),(5,8),(6,7),(7,4),(8,4),(9,7),(9,8),(10,6),(10,9),(11,5),(11,9)],12)
=> ([(0,7),(0,11),(1,5),(1,6),(2,3),(2,4),(2,11),(3,6),(3,9),(4,5),(4,8),(5,10),(6,10),(7,8),(7,9),(8,10),(8,11),(9,10),(9,11)],12)
=> ([(0,3),(0,4),(0,5),(0,6),(0,8),(0,9),(0,11),(1,2),(1,5),(1,6),(1,7),(1,9),(1,10),(1,11),(2,5),(2,6),(2,7),(2,8),(2,10),(2,11),(3,4),(3,7),(3,8),(3,9),(3,10),(3,11),(4,5),(4,6),(4,7),(4,8),(4,9),(4,11),(5,6),(5,7),(5,8),(5,10),(6,7),(6,9),(6,10),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
00101 => ([(0,2),(0,3),(1,8),(2,10),(2,11),(3,1),(3,10),(3,11),(5,6),(6,4),(7,4),(8,7),(9,6),(9,7),(10,5),(10,9),(11,5),(11,8),(11,9)],12)
=> ([(0,5),(0,6),(1,7),(1,10),(2,4),(2,10),(3,6),(3,8),(3,11),(4,5),(4,11),(5,9),(6,9),(7,8),(7,11),(8,9),(8,10),(9,11),(10,11)],12)
=> ([(0,3),(0,7),(0,8),(0,9),(0,10),(0,11),(1,2),(1,4),(1,5),(1,6),(1,7),(1,8),(1,11),(2,4),(2,5),(2,6),(2,9),(2,10),(2,11),(3,5),(3,7),(3,8),(3,9),(3,10),(3,11),(4,5),(4,6),(4,7),(4,8),(4,9),(4,11),(5,6),(5,7),(5,10),(5,11),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(8,9),(8,10),(9,10),(9,11),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
00110 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ([(0,11),(0,12),(1,8),(1,12),(2,6),(2,7),(3,4),(3,11),(3,12),(4,5),(4,6),(5,9),(5,11),(6,9),(7,8),(7,9),(8,10),(9,10),(10,11),(10,12)],13)
=> ([(0,4),(0,5),(0,6),(0,7),(0,9),(0,10),(0,11),(0,12),(1,2),(1,3),(1,4),(1,6),(1,7),(1,8),(1,9),(1,12),(2,3),(2,6),(2,7),(2,8),(2,9),(2,11),(2,12),(3,5),(3,8),(3,9),(3,10),(3,11),(3,12),(4,5),(4,6),(4,7),(4,8),(4,10),(4,11),(4,12),(5,6),(5,7),(5,8),(5,10),(5,11),(5,12),(6,7),(6,9),(6,10),(6,11),(7,8),(7,10),(7,11),(8,9),(8,10),(8,12),(9,10),(9,11),(9,12),(10,11),(10,12),(11,12)],13)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
00111 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ([(0,5),(0,9),(1,4),(1,9),(2,6),(2,8),(3,7),(3,8),(4,6),(4,10),(5,7),(5,10),(6,11),(7,11),(8,11),(9,10),(10,11)],12)
=> ([(0,3),(0,6),(0,7),(0,8),(0,9),(0,10),(0,11),(1,2),(1,4),(1,5),(1,8),(1,9),(1,10),(1,11),(2,3),(2,4),(2,5),(2,6),(2,7),(2,8),(2,9),(3,4),(3,5),(3,6),(3,7),(3,10),(3,11),(4,5),(4,7),(4,8),(4,9),(4,11),(5,6),(5,8),(5,9),(5,10),(6,7),(6,8),(6,10),(6,11),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
01000 => ([(0,3),(0,4),(1,2),(1,11),(2,8),(3,9),(3,10),(4,1),(4,9),(4,10),(6,7),(7,5),(8,5),(9,6),(10,6),(10,11),(11,7),(11,8)],12)
=> ([(0,7),(0,11),(1,5),(1,8),(2,6),(2,8),(3,4),(3,7),(3,11),(4,5),(4,9),(5,10),(6,10),(6,11),(7,9),(8,10),(9,10),(9,11)],12)
=> ([(0,3),(0,4),(0,5),(0,6),(0,9),(0,10),(0,11),(1,2),(1,4),(1,5),(1,7),(1,8),(1,10),(1,11),(2,6),(2,7),(2,8),(2,9),(2,10),(2,11),(3,4),(3,5),(3,6),(3,7),(3,8),(3,9),(3,11),(4,5),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,9),(5,10),(6,9),(6,10),(6,11),(7,8),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
01001 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
=> ([(0,7),(0,11),(1,5),(1,6),(2,3),(2,10),(2,11),(3,5),(3,8),(4,6),(4,8),(4,9),(5,10),(6,10),(7,8),(7,9),(8,11),(9,10),(9,11)],12)
=> ([(0,2),(0,4),(0,5),(0,7),(0,8),(0,9),(0,11),(1,3),(1,6),(1,7),(1,8),(1,9),(1,10),(1,11),(2,3),(2,4),(2,5),(2,8),(2,10),(2,11),(3,6),(3,7),(3,9),(3,10),(3,11),(4,5),(4,6),(4,7),(4,8),(4,9),(4,11),(5,6),(5,7),(5,8),(5,10),(5,11),(6,7),(6,9),(6,10),(6,11),(7,9),(7,10),(8,9),(8,10),(8,11),(9,10),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
01010 => ([(0,1),(0,2),(1,8),(1,9),(2,8),(2,9),(4,3),(5,3),(6,4),(6,5),(7,4),(7,5),(8,6),(8,7),(9,6),(9,7)],10)
=> ([(0,4),(0,5),(1,2),(1,3),(2,6),(2,7),(3,6),(3,7),(4,8),(4,9),(5,8),(5,9),(6,8),(6,9),(7,8),(7,9)],10)
=> ([(0,1),(0,4),(0,5),(0,8),(0,9),(1,4),(1,5),(1,8),(1,9),(2,3),(2,6),(2,7),(2,8),(2,9),(3,6),(3,7),(3,8),(3,9),(4,5),(4,6),(4,7),(4,9),(5,6),(5,7),(5,9),(6,7),(6,8),(7,8),(8,9)],10)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
01011 => ([(0,2),(0,3),(1,8),(2,10),(2,11),(3,1),(3,10),(3,11),(5,6),(6,4),(7,4),(8,7),(9,6),(9,7),(10,5),(10,9),(11,5),(11,8),(11,9)],12)
=> ([(0,5),(0,6),(1,7),(1,10),(2,4),(2,10),(3,6),(3,8),(3,11),(4,5),(4,11),(5,9),(6,9),(7,8),(7,11),(8,9),(8,10),(9,11),(10,11)],12)
=> ([(0,3),(0,7),(0,8),(0,9),(0,10),(0,11),(1,2),(1,4),(1,5),(1,6),(1,7),(1,8),(1,11),(2,4),(2,5),(2,6),(2,9),(2,10),(2,11),(3,5),(3,7),(3,8),(3,9),(3,10),(3,11),(4,5),(4,6),(4,7),(4,8),(4,9),(4,11),(5,6),(5,7),(5,10),(5,11),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(8,9),(8,10),(9,10),(9,11),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
01100 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ([(0,11),(0,12),(1,8),(1,12),(2,6),(2,7),(3,4),(3,11),(3,12),(4,5),(4,6),(5,9),(5,11),(6,9),(7,8),(7,9),(8,10),(9,10),(10,11),(10,12)],13)
=> ([(0,4),(0,5),(0,6),(0,7),(0,9),(0,10),(0,11),(0,12),(1,2),(1,3),(1,4),(1,6),(1,7),(1,8),(1,9),(1,12),(2,3),(2,6),(2,7),(2,8),(2,9),(2,11),(2,12),(3,5),(3,8),(3,9),(3,10),(3,11),(3,12),(4,5),(4,6),(4,7),(4,8),(4,10),(4,11),(4,12),(5,6),(5,7),(5,8),(5,10),(5,11),(5,12),(6,7),(6,9),(6,10),(6,11),(7,8),(7,10),(7,11),(8,9),(8,10),(8,12),(9,10),(9,11),(9,12),(10,11),(10,12),(11,12)],13)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
01101 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
=> ([(0,7),(0,11),(1,5),(1,6),(2,3),(2,10),(2,11),(3,5),(3,8),(4,6),(4,8),(4,9),(5,10),(6,10),(7,8),(7,9),(8,11),(9,10),(9,11)],12)
=> ([(0,2),(0,4),(0,5),(0,7),(0,8),(0,9),(0,11),(1,3),(1,6),(1,7),(1,8),(1,9),(1,10),(1,11),(2,3),(2,4),(2,5),(2,8),(2,10),(2,11),(3,6),(3,7),(3,9),(3,10),(3,11),(4,5),(4,6),(4,7),(4,8),(4,9),(4,11),(5,6),(5,7),(5,8),(5,10),(5,11),(6,7),(6,9),(6,10),(6,11),(7,9),(7,10),(8,9),(8,10),(8,11),(9,10),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
01110 => ([(0,3),(0,4),(1,2),(1,10),(1,11),(2,8),(2,9),(3,6),(3,7),(4,1),(4,6),(4,7),(6,11),(7,10),(8,5),(9,5),(10,8),(11,9)],12)
=> ([(0,9),(0,11),(1,7),(1,8),(2,5),(2,9),(2,11),(3,4),(3,9),(3,11),(4,7),(4,10),(5,8),(5,10),(6,7),(6,8),(6,10),(10,11)],12)
=> ([(0,2),(0,3),(0,4),(0,7),(0,8),(0,9),(0,11),(1,5),(1,6),(1,7),(1,8),(1,9),(1,10),(1,11),(2,3),(2,4),(2,5),(2,6),(2,7),(2,10),(2,11),(3,4),(3,6),(3,7),(3,9),(3,10),(3,11),(4,5),(4,7),(4,8),(4,10),(4,11),(5,6),(5,8),(5,9),(5,10),(5,11),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,11),(8,9),(8,10),(9,10),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
01111 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ([(0,3),(0,7),(1,2),(1,6),(2,8),(3,9),(4,5),(4,8),(4,9),(5,6),(5,7),(6,8),(7,9)],10)
=> ([(0,1),(0,3),(0,5),(0,6),(0,7),(0,9),(1,2),(1,5),(1,6),(1,7),(1,8),(2,3),(2,4),(2,6),(2,8),(2,9),(3,4),(3,7),(3,8),(3,9),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,7),(6,8),(7,9),(8,9)],10)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ([(0,3),(0,7),(1,2),(1,6),(2,8),(3,9),(4,5),(4,8),(4,9),(5,6),(5,7),(6,8),(7,9)],10)
=> ([(0,1),(0,3),(0,5),(0,6),(0,7),(0,9),(1,2),(1,5),(1,6),(1,7),(1,8),(2,3),(2,4),(2,6),(2,8),(2,9),(3,4),(3,7),(3,8),(3,9),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,7),(6,8),(7,9),(8,9)],10)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
10001 => ([(0,3),(0,4),(1,2),(1,10),(1,11),(2,8),(2,9),(3,6),(3,7),(4,1),(4,6),(4,7),(6,11),(7,10),(8,5),(9,5),(10,8),(11,9)],12)
=> ([(0,9),(0,11),(1,7),(1,8),(2,5),(2,9),(2,11),(3,4),(3,9),(3,11),(4,7),(4,10),(5,8),(5,10),(6,7),(6,8),(6,10),(10,11)],12)
=> ([(0,2),(0,3),(0,4),(0,7),(0,8),(0,9),(0,11),(1,5),(1,6),(1,7),(1,8),(1,9),(1,10),(1,11),(2,3),(2,4),(2,5),(2,6),(2,7),(2,10),(2,11),(3,4),(3,6),(3,7),(3,9),(3,10),(3,11),(4,5),(4,7),(4,8),(4,10),(4,11),(5,6),(5,8),(5,9),(5,10),(5,11),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,11),(8,9),(8,10),(9,10),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
10010 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
=> ([(0,7),(0,11),(1,5),(1,6),(2,3),(2,10),(2,11),(3,5),(3,8),(4,6),(4,8),(4,9),(5,10),(6,10),(7,8),(7,9),(8,11),(9,10),(9,11)],12)
=> ([(0,2),(0,4),(0,5),(0,7),(0,8),(0,9),(0,11),(1,3),(1,6),(1,7),(1,8),(1,9),(1,10),(1,11),(2,3),(2,4),(2,5),(2,8),(2,10),(2,11),(3,6),(3,7),(3,9),(3,10),(3,11),(4,5),(4,6),(4,7),(4,8),(4,9),(4,11),(5,6),(5,7),(5,8),(5,10),(5,11),(6,7),(6,9),(6,10),(6,11),(7,9),(7,10),(8,9),(8,10),(8,11),(9,10),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
10011 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ([(0,11),(0,12),(1,8),(1,12),(2,6),(2,7),(3,4),(3,11),(3,12),(4,5),(4,6),(5,9),(5,11),(6,9),(7,8),(7,9),(8,10),(9,10),(10,11),(10,12)],13)
=> ([(0,4),(0,5),(0,6),(0,7),(0,9),(0,10),(0,11),(0,12),(1,2),(1,3),(1,4),(1,6),(1,7),(1,8),(1,9),(1,12),(2,3),(2,6),(2,7),(2,8),(2,9),(2,11),(2,12),(3,5),(3,8),(3,9),(3,10),(3,11),(3,12),(4,5),(4,6),(4,7),(4,8),(4,10),(4,11),(4,12),(5,6),(5,7),(5,8),(5,10),(5,11),(5,12),(6,7),(6,9),(6,10),(6,11),(7,8),(7,10),(7,11),(8,9),(8,10),(8,12),(9,10),(9,11),(9,12),(10,11),(10,12),(11,12)],13)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
10100 => ([(0,2),(0,3),(1,8),(2,10),(2,11),(3,1),(3,10),(3,11),(5,6),(6,4),(7,4),(8,7),(9,6),(9,7),(10,5),(10,9),(11,5),(11,8),(11,9)],12)
=> ([(0,5),(0,6),(1,7),(1,10),(2,4),(2,10),(3,6),(3,8),(3,11),(4,5),(4,11),(5,9),(6,9),(7,8),(7,11),(8,9),(8,10),(9,11),(10,11)],12)
=> ([(0,3),(0,7),(0,8),(0,9),(0,10),(0,11),(1,2),(1,4),(1,5),(1,6),(1,7),(1,8),(1,11),(2,4),(2,5),(2,6),(2,9),(2,10),(2,11),(3,5),(3,7),(3,8),(3,9),(3,10),(3,11),(4,5),(4,6),(4,7),(4,8),(4,9),(4,11),(5,6),(5,7),(5,10),(5,11),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(8,9),(8,10),(9,10),(9,11),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
10101 => ([(0,1),(0,2),(1,8),(1,9),(2,8),(2,9),(4,3),(5,3),(6,4),(6,5),(7,4),(7,5),(8,6),(8,7),(9,6),(9,7)],10)
=> ([(0,4),(0,5),(1,2),(1,3),(2,6),(2,7),(3,6),(3,7),(4,8),(4,9),(5,8),(5,9),(6,8),(6,9),(7,8),(7,9)],10)
=> ([(0,1),(0,4),(0,5),(0,8),(0,9),(1,4),(1,5),(1,8),(1,9),(2,3),(2,6),(2,7),(2,8),(2,9),(3,6),(3,7),(3,8),(3,9),(4,5),(4,6),(4,7),(4,9),(5,6),(5,7),(5,9),(6,7),(6,8),(7,8),(8,9)],10)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
10110 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
=> ([(0,7),(0,11),(1,5),(1,6),(2,3),(2,10),(2,11),(3,5),(3,8),(4,6),(4,8),(4,9),(5,10),(6,10),(7,8),(7,9),(8,11),(9,10),(9,11)],12)
=> ([(0,2),(0,4),(0,5),(0,7),(0,8),(0,9),(0,11),(1,3),(1,6),(1,7),(1,8),(1,9),(1,10),(1,11),(2,3),(2,4),(2,5),(2,8),(2,10),(2,11),(3,6),(3,7),(3,9),(3,10),(3,11),(4,5),(4,6),(4,7),(4,8),(4,9),(4,11),(5,6),(5,7),(5,8),(5,10),(5,11),(6,7),(6,9),(6,10),(6,11),(7,9),(7,10),(8,9),(8,10),(8,11),(9,10),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
10111 => ([(0,3),(0,4),(1,2),(1,11),(2,8),(3,9),(3,10),(4,1),(4,9),(4,10),(6,7),(7,5),(8,5),(9,6),(10,6),(10,11),(11,7),(11,8)],12)
=> ([(0,7),(0,11),(1,5),(1,8),(2,6),(2,8),(3,4),(3,7),(3,11),(4,5),(4,9),(5,10),(6,10),(6,11),(7,9),(8,10),(9,10),(9,11)],12)
=> ([(0,3),(0,4),(0,5),(0,6),(0,9),(0,10),(0,11),(1,2),(1,4),(1,5),(1,7),(1,8),(1,10),(1,11),(2,6),(2,7),(2,8),(2,9),(2,10),(2,11),(3,4),(3,5),(3,6),(3,7),(3,8),(3,9),(3,11),(4,5),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,9),(5,10),(6,9),(6,10),(6,11),(7,8),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
11000 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ([(0,5),(0,9),(1,4),(1,9),(2,6),(2,8),(3,7),(3,8),(4,6),(4,10),(5,7),(5,10),(6,11),(7,11),(8,11),(9,10),(10,11)],12)
=> ([(0,3),(0,6),(0,7),(0,8),(0,9),(0,10),(0,11),(1,2),(1,4),(1,5),(1,8),(1,9),(1,10),(1,11),(2,3),(2,4),(2,5),(2,6),(2,7),(2,8),(2,9),(3,4),(3,5),(3,6),(3,7),(3,10),(3,11),(4,5),(4,7),(4,8),(4,9),(4,11),(5,6),(5,8),(5,9),(5,10),(6,7),(6,8),(6,10),(6,11),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
11001 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ([(0,11),(0,12),(1,8),(1,12),(2,6),(2,7),(3,4),(3,11),(3,12),(4,5),(4,6),(5,9),(5,11),(6,9),(7,8),(7,9),(8,10),(9,10),(10,11),(10,12)],13)
=> ([(0,4),(0,5),(0,6),(0,7),(0,9),(0,10),(0,11),(0,12),(1,2),(1,3),(1,4),(1,6),(1,7),(1,8),(1,9),(1,12),(2,3),(2,6),(2,7),(2,8),(2,9),(2,11),(2,12),(3,5),(3,8),(3,9),(3,10),(3,11),(3,12),(4,5),(4,6),(4,7),(4,8),(4,10),(4,11),(4,12),(5,6),(5,7),(5,8),(5,10),(5,11),(5,12),(6,7),(6,9),(6,10),(6,11),(7,8),(7,10),(7,11),(8,9),(8,10),(8,12),(9,10),(9,11),(9,12),(10,11),(10,12),(11,12)],13)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
11010 => ([(0,2),(0,3),(1,8),(2,10),(2,11),(3,1),(3,10),(3,11),(5,6),(6,4),(7,4),(8,7),(9,6),(9,7),(10,5),(10,9),(11,5),(11,8),(11,9)],12)
=> ([(0,5),(0,6),(1,7),(1,10),(2,4),(2,10),(3,6),(3,8),(3,11),(4,5),(4,11),(5,9),(6,9),(7,8),(7,11),(8,9),(8,10),(9,11),(10,11)],12)
=> ([(0,3),(0,7),(0,8),(0,9),(0,10),(0,11),(1,2),(1,4),(1,5),(1,6),(1,7),(1,8),(1,11),(2,4),(2,5),(2,6),(2,9),(2,10),(2,11),(3,5),(3,7),(3,8),(3,9),(3,10),(3,11),(4,5),(4,6),(4,7),(4,8),(4,9),(4,11),(5,6),(5,7),(5,10),(5,11),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(8,9),(8,10),(9,10),(9,11),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
11011 => ([(0,2),(0,3),(1,5),(1,6),(2,10),(2,11),(3,1),(3,10),(3,11),(5,8),(6,7),(7,4),(8,4),(9,7),(9,8),(10,6),(10,9),(11,5),(11,9)],12)
=> ([(0,7),(0,11),(1,5),(1,6),(2,3),(2,4),(2,11),(3,6),(3,9),(4,5),(4,8),(5,10),(6,10),(7,8),(7,9),(8,10),(8,11),(9,10),(9,11)],12)
=> ([(0,3),(0,4),(0,5),(0,6),(0,8),(0,9),(0,11),(1,2),(1,5),(1,6),(1,7),(1,9),(1,10),(1,11),(2,5),(2,6),(2,7),(2,8),(2,10),(2,11),(3,4),(3,7),(3,8),(3,9),(3,10),(3,11),(4,5),(4,6),(4,7),(4,8),(4,9),(4,11),(5,6),(5,7),(5,8),(5,10),(6,7),(6,9),(6,10),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
11100 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ([(0,5),(0,9),(1,4),(1,9),(2,6),(2,8),(3,7),(3,8),(4,6),(4,10),(5,7),(5,10),(6,11),(7,11),(8,11),(9,10),(10,11)],12)
=> ([(0,3),(0,6),(0,7),(0,8),(0,9),(0,10),(0,11),(1,2),(1,4),(1,5),(1,8),(1,9),(1,10),(1,11),(2,3),(2,4),(2,5),(2,6),(2,7),(2,8),(2,9),(3,4),(3,5),(3,6),(3,7),(3,10),(3,11),(4,5),(4,7),(4,8),(4,9),(4,11),(5,6),(5,8),(5,9),(5,10),(6,7),(6,8),(6,10),(6,11),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
11101 => ([(0,3),(0,4),(1,2),(1,11),(2,8),(3,9),(3,10),(4,1),(4,9),(4,10),(6,7),(7,5),(8,5),(9,6),(10,6),(10,11),(11,7),(11,8)],12)
=> ([(0,7),(0,11),(1,5),(1,8),(2,6),(2,8),(3,4),(3,7),(3,11),(4,5),(4,9),(5,10),(6,10),(6,11),(7,9),(8,10),(9,10),(9,11)],12)
=> ([(0,3),(0,4),(0,5),(0,6),(0,9),(0,10),(0,11),(1,2),(1,4),(1,5),(1,7),(1,8),(1,10),(1,11),(2,6),(2,7),(2,8),(2,9),(2,10),(2,11),(3,4),(3,5),(3,6),(3,7),(3,8),(3,9),(3,11),(4,5),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,9),(5,10),(6,9),(6,10),(6,11),(7,8),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
11110 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ([(0,3),(0,7),(1,2),(1,6),(2,8),(3,9),(4,5),(4,8),(4,9),(5,6),(5,7),(6,8),(7,9)],10)
=> ([(0,1),(0,3),(0,5),(0,6),(0,7),(0,9),(1,2),(1,5),(1,6),(1,7),(1,8),(2,3),(2,4),(2,6),(2,8),(2,9),(3,4),(3,7),(3,8),(3,9),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,7),(6,8),(7,9),(8,9)],10)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> ([(0,1),(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 3 = 2 + 1
000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
=> ([(0,1),(0,3),(0,4),(0,6),(1,2),(1,4),(1,5),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 4 = 3 + 1
000001 => ([(0,2),(0,6),(1,8),(2,7),(3,5),(3,9),(4,3),(4,11),(5,1),(5,10),(6,4),(6,7),(7,11),(9,10),(10,8),(11,9)],12)
=> ([(0,3),(0,11),(1,2),(1,8),(2,9),(3,10),(4,5),(4,6),(4,8),(5,7),(5,9),(6,7),(6,10),(7,11),(8,9),(10,11)],12)
=> ([(0,2),(0,3),(0,5),(0,6),(0,7),(0,9),(0,10),(0,11),(1,2),(1,3),(1,4),(1,6),(1,7),(1,8),(1,10),(1,11),(2,4),(2,5),(2,6),(2,8),(2,9),(2,10),(3,4),(3,5),(3,7),(3,8),(3,9),(3,11),(4,7),(4,8),(4,9),(4,10),(4,11),(5,6),(5,8),(5,9),(5,10),(5,11),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11),(8,10),(8,11),(9,10),(9,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3} + 1
000010 => ([(0,4),(0,5),(1,3),(1,12),(2,11),(3,2),(3,14),(4,10),(4,13),(5,1),(5,10),(5,13),(7,8),(8,9),(9,6),(10,7),(11,6),(12,8),(12,14),(13,7),(13,12),(14,9),(14,11)],15)
=> ([(0,9),(0,14),(1,7),(1,10),(2,8),(2,10),(3,4),(3,9),(3,14),(4,5),(4,11),(5,7),(5,13),(6,8),(6,13),(6,14),(7,12),(8,12),(9,11),(10,12),(11,13),(11,14),(12,13)],15)
=> ([(0,3),(0,5),(0,6),(0,8),(0,9),(0,10),(0,11),(0,12),(0,13),(0,14),(1,2),(1,4),(1,7),(1,8),(1,9),(1,10),(1,11),(1,12),(1,13),(1,14),(2,3),(2,4),(2,6),(2,7),(2,8),(2,9),(2,10),(2,13),(2,14),(3,4),(3,5),(3,6),(3,7),(3,11),(3,12),(3,13),(3,14),(4,5),(4,6),(4,7),(4,8),(4,9),(4,10),(4,13),(4,14),(5,6),(5,7),(5,8),(5,10),(5,11),(5,12),(5,13),(5,14),(6,8),(6,9),(6,11),(6,12),(6,13),(6,14),(7,8),(7,9),(7,10),(7,12),(7,13),(7,14),(8,9),(8,10),(8,11),(8,12),(9,10),(9,11),(9,12),(9,13),(10,11),(10,12),(10,14),(11,12),(11,13),(11,14),(12,13),(12,14),(13,14)],15)
=> ? ∊ {1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3} + 1
000011 => ([(0,5),(0,6),(1,4),(1,14),(2,11),(3,10),(4,3),(4,12),(5,1),(5,13),(6,2),(6,13),(8,9),(9,7),(10,7),(11,8),(12,9),(12,10),(13,11),(13,14),(14,8),(14,12)],15)
=> ([(0,7),(0,11),(1,6),(1,10),(2,8),(2,10),(3,9),(3,11),(4,8),(4,9),(4,14),(5,6),(5,7),(5,14),(6,12),(7,13),(8,12),(9,13),(10,12),(11,13),(12,14),(13,14)],15)
=> ([(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,11),(0,12),(0,13),(0,14),(1,2),(1,4),(1,7),(1,8),(1,9),(1,10),(1,11),(1,12),(1,13),(1,14),(2,3),(2,5),(2,6),(2,9),(2,10),(2,11),(2,12),(2,13),(2,14),(3,4),(3,5),(3,6),(3,7),(3,8),(3,9),(3,10),(3,11),(3,12),(4,5),(4,6),(4,7),(4,8),(4,9),(4,10),(4,13),(4,14),(5,6),(5,7),(5,8),(5,10),(5,11),(5,12),(5,14),(6,7),(6,8),(6,9),(6,11),(6,12),(6,13),(7,8),(7,9),(7,11),(7,13),(7,14),(8,10),(8,12),(8,13),(8,14),(9,10),(9,11),(9,12),(9,13),(9,14),(10,11),(10,12),(10,13),(10,14),(11,12),(11,13),(11,14),(12,13),(12,14),(13,14)],15)
=> ? ∊ {1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3} + 1
000100 => ([(0,3),(0,4),(1,10),(2,1),(2,6),(2,12),(3,14),(3,15),(4,2),(4,14),(4,15),(6,7),(7,8),(8,5),(9,5),(10,9),(11,7),(11,13),(12,10),(12,13),(13,8),(13,9),(14,6),(14,11),(15,11),(15,12)],16)
=> ([(0,7),(0,15),(1,5),(1,14),(2,6),(2,8),(3,4),(3,13),(3,15),(4,6),(4,10),(5,12),(5,13),(6,11),(7,8),(7,9),(8,11),(9,11),(9,12),(9,15),(10,11),(10,12),(10,13),(12,14),(13,14),(14,15)],16)
=> ([(0,1),(0,3),(0,4),(0,5),(0,7),(0,8),(0,9),(0,11),(0,13),(0,14),(0,15),(1,4),(1,5),(1,6),(1,7),(1,10),(1,11),(1,12),(1,13),(1,14),(1,15),(2,3),(2,5),(2,6),(2,8),(2,9),(2,10),(2,11),(2,12),(2,13),(2,14),(2,15),(3,6),(3,7),(3,8),(3,9),(3,10),(3,12),(3,13),(3,14),(3,15),(4,5),(4,7),(4,8),(4,9),(4,10),(4,11),(4,13),(4,14),(4,15),(5,7),(5,8),(5,9),(5,11),(5,12),(5,13),(5,15),(6,7),(6,8),(6,9),(6,10),(6,11),(6,12),(6,13),(6,14),(7,9),(7,11),(7,12),(7,13),(7,14),(7,15),(8,9),(8,10),(8,11),(8,12),(8,14),(8,15),(9,10),(9,12),(9,14),(9,15),(10,11),(10,12),(10,13),(10,14),(10,15),(11,12),(11,13),(11,15),(12,13),(12,14),(13,14),(13,15),(14,15)],16)
=> ? ∊ {1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3} + 1
000101 => ([(0,3),(0,4),(1,2),(1,14),(2,6),(3,13),(3,15),(4,1),(4,13),(4,15),(6,9),(7,8),(8,10),(9,5),(10,5),(11,8),(11,12),(12,9),(12,10),(13,7),(13,11),(14,6),(14,12),(15,7),(15,11),(15,14)],16)
=> ([(0,5),(0,7),(1,6),(1,8),(2,9),(2,14),(3,4),(3,8),(3,13),(4,10),(4,15),(5,6),(5,11),(6,12),(7,11),(7,14),(8,12),(9,10),(9,15),(10,13),(10,14),(11,12),(11,15),(12,13),(13,15),(14,15)],16)
=> ([(0,4),(0,5),(0,8),(0,9),(0,10),(0,11),(0,12),(0,13),(0,14),(0,15),(1,2),(1,3),(1,6),(1,7),(1,8),(1,9),(1,11),(1,12),(1,13),(1,14),(1,15),(2,3),(2,5),(2,6),(2,7),(2,9),(2,10),(2,11),(2,12),(2,14),(2,15),(3,4),(3,6),(3,7),(3,10),(3,11),(3,12),(3,13),(3,14),(3,15),(4,5),(4,8),(4,9),(4,10),(4,11),(4,12),(4,13),(4,14),(4,15),(5,6),(5,7),(5,8),(5,9),(5,10),(5,13),(5,14),(5,15),(6,7),(6,8),(6,9),(6,10),(6,11),(6,12),(6,14),(6,15),(7,8),(7,9),(7,11),(7,12),(7,13),(7,14),(7,15),(8,9),(8,10),(8,11),(8,12),(8,13),(8,15),(9,10),(9,11),(9,13),(9,15),(10,12),(10,13),(10,14),(10,15),(11,12),(11,13),(11,14),(12,13),(12,14),(13,14),(13,15),(14,15)],16)
=> ? ∊ {1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3} + 1
000110 => ([(0,4),(0,5),(1,11),(2,1),(2,13),(3,7),(3,14),(4,2),(4,12),(4,16),(5,3),(5,12),(5,16),(7,8),(8,9),(9,6),(10,6),(11,10),(12,7),(13,11),(13,15),(14,8),(14,15),(15,9),(15,10),(16,13),(16,14)],17)
=> ([(0,15),(0,16),(1,7),(1,10),(2,8),(2,9),(3,4),(3,5),(3,6),(4,15),(4,16),(5,11),(5,15),(6,8),(6,11),(7,14),(7,16),(8,13),(9,10),(9,13),(10,14),(11,12),(11,13),(12,14),(12,15),(12,16),(13,14)],17)
=> ([(0,3),(0,6),(0,7),(0,8),(0,9),(0,10),(0,11),(0,12),(0,13),(0,14),(0,15),(0,16),(1,2),(1,4),(1,5),(1,6),(1,7),(1,8),(1,9),(1,12),(1,13),(1,14),(1,15),(1,16),(2,4),(2,5),(2,7),(2,8),(2,10),(2,11),(2,12),(2,13),(2,14),(2,15),(2,16),(3,4),(3,5),(3,6),(3,9),(3,10),(3,11),(3,12),(3,13),(3,14),(3,15),(3,16),(4,5),(4,6),(4,7),(4,8),(4,9),(4,11),(4,13),(4,15),(4,16),(5,7),(5,8),(5,9),(5,10),(5,11),(5,13),(5,15),(5,16),(6,7),(6,8),(6,9),(6,10),(6,11),(6,12),(6,13),(6,14),(6,16),(7,8),(7,9),(7,10),(7,12),(7,13),(7,14),(7,15),(8,10),(8,11),(8,12),(8,13),(8,14),(8,15),(9,10),(9,11),(9,12),(9,13),(9,14),(9,16),(10,11),(10,12),(10,14),(10,15),(10,16),(11,12),(11,14),(11,15),(11,16),(12,14),(12,15),(12,16),(13,14),(13,15),(13,16),(14,15),(14,16),(15,16)],17)
=> ? ∊ {1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3} + 1
111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
=> ([(0,1),(0,3),(0,4),(0,6),(1,2),(1,4),(1,5),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 4 = 3 + 1
Description
The treewidth of a graph.
A graph has treewidth zero if and only if it has no edges. A connected graph has treewidth at most one if and only if it is a tree. A connected graph has treewidth at most two if and only if it is a series-parallel graph.
Matching statistic: St000536
Values
0 => ([(0,1)],2)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 1 = 0 + 1
1 => ([(0,1)],2)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 1 = 0 + 1
00 => ([(0,2),(2,1)],3)
=> ([(0,2),(1,2)],3)
=> ([(0,2),(1,2)],3)
=> 1 = 0 + 1
01 => ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> 2 = 1 + 1
10 => ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> 2 = 1 + 1
11 => ([(0,2),(2,1)],3)
=> ([(0,2),(1,2)],3)
=> ([(0,2),(1,2)],3)
=> 1 = 0 + 1
000 => ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(1,2),(2,3)],4)
=> ([(0,3),(1,2),(2,3)],4)
=> 1 = 0 + 1
001 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,5),(3,4),(4,5)],6)
=> 2 = 1 + 1
010 => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6)
=> 2 = 1 + 1
011 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,5),(3,4),(4,5)],6)
=> 2 = 1 + 1
100 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,5),(3,4),(4,5)],6)
=> 2 = 1 + 1
101 => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6)
=> 2 = 1 + 1
110 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,5),(3,4),(4,5)],6)
=> 2 = 1 + 1
111 => ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(1,2),(2,3)],4)
=> ([(0,3),(1,2),(2,3)],4)
=> 1 = 0 + 1
0000 => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> 2 = 1 + 1
0001 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,3),(0,7),(1,2),(1,4),(2,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ([(0,3),(0,5),(0,6),(0,7),(1,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6),(6,7)],8)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2} + 1
0010 => ([(0,2),(0,3),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,5),(8,5),(8,6)],9)
=> ([(0,5),(0,8),(1,4),(1,6),(2,6),(2,8),(3,4),(3,5),(3,8),(4,7),(5,7),(6,7),(7,8)],9)
=> ([(0,2),(0,3),(0,4),(0,8),(1,5),(1,6),(1,7),(1,8),(2,3),(2,4),(2,5),(2,6),(3,4),(3,7),(3,8),(4,6),(4,7),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2} + 1
0011 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,6),(0,7),(1,4),(1,5),(2,5),(2,7),(3,4),(3,6),(4,8),(5,8),(6,8),(7,8)],9)
=> ([(0,5),(0,6),(0,7),(0,8),(1,2),(1,3),(1,4),(1,7),(1,8),(2,3),(2,4),(2,5),(2,6),(3,4),(3,6),(3,8),(4,5),(4,7),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2} + 1
0100 => ([(0,2),(0,3),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,5),(8,5),(8,6)],9)
=> ([(0,5),(0,8),(1,4),(1,6),(2,6),(2,8),(3,4),(3,5),(3,8),(4,7),(5,7),(6,7),(7,8)],9)
=> ([(0,2),(0,3),(0,4),(0,8),(1,5),(1,6),(1,7),(1,8),(2,3),(2,4),(2,5),(2,6),(3,4),(3,7),(3,8),(4,6),(4,7),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2} + 1
0101 => ([(0,1),(0,2),(1,6),(1,7),(2,6),(2,7),(4,3),(5,3),(6,4),(6,5),(7,4),(7,5)],8)
=> ([(0,4),(0,5),(1,2),(1,3),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
=> ([(0,1),(0,6),(0,7),(1,6),(1,7),(2,3),(2,4),(2,5),(2,7),(3,4),(3,5),(3,7),(4,5),(4,6),(5,6),(6,7)],8)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2} + 1
0110 => ([(0,2),(0,3),(1,5),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,6),(8,5)],9)
=> ([(0,5),(0,6),(1,7),(1,8),(2,5),(2,6),(2,8),(3,6),(3,7),(3,8),(4,5),(4,7),(4,8)],9)
=> ([(0,4),(0,5),(0,6),(0,8),(1,2),(1,3),(1,4),(1,7),(1,8),(2,3),(2,6),(2,7),(2,8),(3,5),(3,7),(3,8),(4,5),(4,6),(4,8),(5,6),(5,7),(6,7),(7,8)],9)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2} + 1
0111 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,3),(0,7),(1,2),(1,4),(2,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ([(0,3),(0,5),(0,6),(0,7),(1,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6),(6,7)],8)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2} + 1
1000 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,3),(0,7),(1,2),(1,4),(2,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ([(0,3),(0,5),(0,6),(0,7),(1,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6),(6,7)],8)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2} + 1
1001 => ([(0,2),(0,3),(1,5),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,6),(8,5)],9)
=> ([(0,5),(0,6),(1,7),(1,8),(2,5),(2,6),(2,8),(3,6),(3,7),(3,8),(4,5),(4,7),(4,8)],9)
=> ([(0,4),(0,5),(0,6),(0,8),(1,2),(1,3),(1,4),(1,7),(1,8),(2,3),(2,6),(2,7),(2,8),(3,5),(3,7),(3,8),(4,5),(4,6),(4,8),(5,6),(5,7),(6,7),(7,8)],9)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2} + 1
1010 => ([(0,1),(0,2),(1,6),(1,7),(2,6),(2,7),(4,3),(5,3),(6,4),(6,5),(7,4),(7,5)],8)
=> ([(0,4),(0,5),(1,2),(1,3),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
=> ([(0,1),(0,6),(0,7),(1,6),(1,7),(2,3),(2,4),(2,5),(2,7),(3,4),(3,5),(3,7),(4,5),(4,6),(5,6),(6,7)],8)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2} + 1
1011 => ([(0,2),(0,3),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,5),(8,5),(8,6)],9)
=> ([(0,5),(0,8),(1,4),(1,6),(2,6),(2,8),(3,4),(3,5),(3,8),(4,7),(5,7),(6,7),(7,8)],9)
=> ([(0,2),(0,3),(0,4),(0,8),(1,5),(1,6),(1,7),(1,8),(2,3),(2,4),(2,5),(2,6),(3,4),(3,7),(3,8),(4,6),(4,7),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2} + 1
1100 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,6),(0,7),(1,4),(1,5),(2,5),(2,7),(3,4),(3,6),(4,8),(5,8),(6,8),(7,8)],9)
=> ([(0,5),(0,6),(0,7),(0,8),(1,2),(1,3),(1,4),(1,7),(1,8),(2,3),(2,4),(2,5),(2,6),(3,4),(3,6),(3,8),(4,5),(4,7),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2} + 1
1101 => ([(0,2),(0,3),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,5),(8,5),(8,6)],9)
=> ([(0,5),(0,8),(1,4),(1,6),(2,6),(2,8),(3,4),(3,5),(3,8),(4,7),(5,7),(6,7),(7,8)],9)
=> ([(0,2),(0,3),(0,4),(0,8),(1,5),(1,6),(1,7),(1,8),(2,3),(2,4),(2,5),(2,6),(3,4),(3,7),(3,8),(4,6),(4,7),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2} + 1
1110 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,3),(0,7),(1,2),(1,4),(2,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ([(0,3),(0,5),(0,6),(0,7),(1,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6),(6,7)],8)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2} + 1
1111 => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> 2 = 1 + 1
00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> ([(0,1),(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 3 = 2 + 1
00001 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ([(0,3),(0,7),(1,2),(1,6),(2,8),(3,9),(4,5),(4,8),(4,9),(5,6),(5,7),(6,8),(7,9)],10)
=> ([(0,1),(0,3),(0,5),(0,6),(0,7),(0,9),(1,2),(1,5),(1,6),(1,7),(1,8),(2,3),(2,4),(2,6),(2,8),(2,9),(3,4),(3,7),(3,8),(3,9),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,7),(6,8),(7,9),(8,9)],10)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
00010 => ([(0,3),(0,4),(1,2),(1,11),(2,8),(3,9),(3,10),(4,1),(4,9),(4,10),(6,7),(7,5),(8,5),(9,6),(10,6),(10,11),(11,7),(11,8)],12)
=> ([(0,7),(0,11),(1,5),(1,8),(2,6),(2,8),(3,4),(3,7),(3,11),(4,5),(4,9),(5,10),(6,10),(6,11),(7,9),(8,10),(9,10),(9,11)],12)
=> ([(0,3),(0,4),(0,5),(0,6),(0,9),(0,10),(0,11),(1,2),(1,4),(1,5),(1,7),(1,8),(1,10),(1,11),(2,6),(2,7),(2,8),(2,9),(2,10),(2,11),(3,4),(3,5),(3,6),(3,7),(3,8),(3,9),(3,11),(4,5),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,9),(5,10),(6,9),(6,10),(6,11),(7,8),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
00011 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ([(0,5),(0,9),(1,4),(1,9),(2,6),(2,8),(3,7),(3,8),(4,6),(4,10),(5,7),(5,10),(6,11),(7,11),(8,11),(9,10),(10,11)],12)
=> ([(0,3),(0,6),(0,7),(0,8),(0,9),(0,10),(0,11),(1,2),(1,4),(1,5),(1,8),(1,9),(1,10),(1,11),(2,3),(2,4),(2,5),(2,6),(2,7),(2,8),(2,9),(3,4),(3,5),(3,6),(3,7),(3,10),(3,11),(4,5),(4,7),(4,8),(4,9),(4,11),(5,6),(5,8),(5,9),(5,10),(6,7),(6,8),(6,10),(6,11),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
00100 => ([(0,2),(0,3),(1,5),(1,6),(2,10),(2,11),(3,1),(3,10),(3,11),(5,8),(6,7),(7,4),(8,4),(9,7),(9,8),(10,6),(10,9),(11,5),(11,9)],12)
=> ([(0,7),(0,11),(1,5),(1,6),(2,3),(2,4),(2,11),(3,6),(3,9),(4,5),(4,8),(5,10),(6,10),(7,8),(7,9),(8,10),(8,11),(9,10),(9,11)],12)
=> ([(0,3),(0,4),(0,5),(0,6),(0,8),(0,9),(0,11),(1,2),(1,5),(1,6),(1,7),(1,9),(1,10),(1,11),(2,5),(2,6),(2,7),(2,8),(2,10),(2,11),(3,4),(3,7),(3,8),(3,9),(3,10),(3,11),(4,5),(4,6),(4,7),(4,8),(4,9),(4,11),(5,6),(5,7),(5,8),(5,10),(6,7),(6,9),(6,10),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
00101 => ([(0,2),(0,3),(1,8),(2,10),(2,11),(3,1),(3,10),(3,11),(5,6),(6,4),(7,4),(8,7),(9,6),(9,7),(10,5),(10,9),(11,5),(11,8),(11,9)],12)
=> ([(0,5),(0,6),(1,7),(1,10),(2,4),(2,10),(3,6),(3,8),(3,11),(4,5),(4,11),(5,9),(6,9),(7,8),(7,11),(8,9),(8,10),(9,11),(10,11)],12)
=> ([(0,3),(0,7),(0,8),(0,9),(0,10),(0,11),(1,2),(1,4),(1,5),(1,6),(1,7),(1,8),(1,11),(2,4),(2,5),(2,6),(2,9),(2,10),(2,11),(3,5),(3,7),(3,8),(3,9),(3,10),(3,11),(4,5),(4,6),(4,7),(4,8),(4,9),(4,11),(5,6),(5,7),(5,10),(5,11),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(8,9),(8,10),(9,10),(9,11),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
00110 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ([(0,11),(0,12),(1,8),(1,12),(2,6),(2,7),(3,4),(3,11),(3,12),(4,5),(4,6),(5,9),(5,11),(6,9),(7,8),(7,9),(8,10),(9,10),(10,11),(10,12)],13)
=> ([(0,4),(0,5),(0,6),(0,7),(0,9),(0,10),(0,11),(0,12),(1,2),(1,3),(1,4),(1,6),(1,7),(1,8),(1,9),(1,12),(2,3),(2,6),(2,7),(2,8),(2,9),(2,11),(2,12),(3,5),(3,8),(3,9),(3,10),(3,11),(3,12),(4,5),(4,6),(4,7),(4,8),(4,10),(4,11),(4,12),(5,6),(5,7),(5,8),(5,10),(5,11),(5,12),(6,7),(6,9),(6,10),(6,11),(7,8),(7,10),(7,11),(8,9),(8,10),(8,12),(9,10),(9,11),(9,12),(10,11),(10,12),(11,12)],13)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
00111 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ([(0,5),(0,9),(1,4),(1,9),(2,6),(2,8),(3,7),(3,8),(4,6),(4,10),(5,7),(5,10),(6,11),(7,11),(8,11),(9,10),(10,11)],12)
=> ([(0,3),(0,6),(0,7),(0,8),(0,9),(0,10),(0,11),(1,2),(1,4),(1,5),(1,8),(1,9),(1,10),(1,11),(2,3),(2,4),(2,5),(2,6),(2,7),(2,8),(2,9),(3,4),(3,5),(3,6),(3,7),(3,10),(3,11),(4,5),(4,7),(4,8),(4,9),(4,11),(5,6),(5,8),(5,9),(5,10),(6,7),(6,8),(6,10),(6,11),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
01000 => ([(0,3),(0,4),(1,2),(1,11),(2,8),(3,9),(3,10),(4,1),(4,9),(4,10),(6,7),(7,5),(8,5),(9,6),(10,6),(10,11),(11,7),(11,8)],12)
=> ([(0,7),(0,11),(1,5),(1,8),(2,6),(2,8),(3,4),(3,7),(3,11),(4,5),(4,9),(5,10),(6,10),(6,11),(7,9),(8,10),(9,10),(9,11)],12)
=> ([(0,3),(0,4),(0,5),(0,6),(0,9),(0,10),(0,11),(1,2),(1,4),(1,5),(1,7),(1,8),(1,10),(1,11),(2,6),(2,7),(2,8),(2,9),(2,10),(2,11),(3,4),(3,5),(3,6),(3,7),(3,8),(3,9),(3,11),(4,5),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,9),(5,10),(6,9),(6,10),(6,11),(7,8),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
01001 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
=> ([(0,7),(0,11),(1,5),(1,6),(2,3),(2,10),(2,11),(3,5),(3,8),(4,6),(4,8),(4,9),(5,10),(6,10),(7,8),(7,9),(8,11),(9,10),(9,11)],12)
=> ([(0,2),(0,4),(0,5),(0,7),(0,8),(0,9),(0,11),(1,3),(1,6),(1,7),(1,8),(1,9),(1,10),(1,11),(2,3),(2,4),(2,5),(2,8),(2,10),(2,11),(3,6),(3,7),(3,9),(3,10),(3,11),(4,5),(4,6),(4,7),(4,8),(4,9),(4,11),(5,6),(5,7),(5,8),(5,10),(5,11),(6,7),(6,9),(6,10),(6,11),(7,9),(7,10),(8,9),(8,10),(8,11),(9,10),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
01010 => ([(0,1),(0,2),(1,8),(1,9),(2,8),(2,9),(4,3),(5,3),(6,4),(6,5),(7,4),(7,5),(8,6),(8,7),(9,6),(9,7)],10)
=> ([(0,4),(0,5),(1,2),(1,3),(2,6),(2,7),(3,6),(3,7),(4,8),(4,9),(5,8),(5,9),(6,8),(6,9),(7,8),(7,9)],10)
=> ([(0,1),(0,4),(0,5),(0,8),(0,9),(1,4),(1,5),(1,8),(1,9),(2,3),(2,6),(2,7),(2,8),(2,9),(3,6),(3,7),(3,8),(3,9),(4,5),(4,6),(4,7),(4,9),(5,6),(5,7),(5,9),(6,7),(6,8),(7,8),(8,9)],10)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
01011 => ([(0,2),(0,3),(1,8),(2,10),(2,11),(3,1),(3,10),(3,11),(5,6),(6,4),(7,4),(8,7),(9,6),(9,7),(10,5),(10,9),(11,5),(11,8),(11,9)],12)
=> ([(0,5),(0,6),(1,7),(1,10),(2,4),(2,10),(3,6),(3,8),(3,11),(4,5),(4,11),(5,9),(6,9),(7,8),(7,11),(8,9),(8,10),(9,11),(10,11)],12)
=> ([(0,3),(0,7),(0,8),(0,9),(0,10),(0,11),(1,2),(1,4),(1,5),(1,6),(1,7),(1,8),(1,11),(2,4),(2,5),(2,6),(2,9),(2,10),(2,11),(3,5),(3,7),(3,8),(3,9),(3,10),(3,11),(4,5),(4,6),(4,7),(4,8),(4,9),(4,11),(5,6),(5,7),(5,10),(5,11),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(8,9),(8,10),(9,10),(9,11),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
01100 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ([(0,11),(0,12),(1,8),(1,12),(2,6),(2,7),(3,4),(3,11),(3,12),(4,5),(4,6),(5,9),(5,11),(6,9),(7,8),(7,9),(8,10),(9,10),(10,11),(10,12)],13)
=> ([(0,4),(0,5),(0,6),(0,7),(0,9),(0,10),(0,11),(0,12),(1,2),(1,3),(1,4),(1,6),(1,7),(1,8),(1,9),(1,12),(2,3),(2,6),(2,7),(2,8),(2,9),(2,11),(2,12),(3,5),(3,8),(3,9),(3,10),(3,11),(3,12),(4,5),(4,6),(4,7),(4,8),(4,10),(4,11),(4,12),(5,6),(5,7),(5,8),(5,10),(5,11),(5,12),(6,7),(6,9),(6,10),(6,11),(7,8),(7,10),(7,11),(8,9),(8,10),(8,12),(9,10),(9,11),(9,12),(10,11),(10,12),(11,12)],13)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
01101 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
=> ([(0,7),(0,11),(1,5),(1,6),(2,3),(2,10),(2,11),(3,5),(3,8),(4,6),(4,8),(4,9),(5,10),(6,10),(7,8),(7,9),(8,11),(9,10),(9,11)],12)
=> ([(0,2),(0,4),(0,5),(0,7),(0,8),(0,9),(0,11),(1,3),(1,6),(1,7),(1,8),(1,9),(1,10),(1,11),(2,3),(2,4),(2,5),(2,8),(2,10),(2,11),(3,6),(3,7),(3,9),(3,10),(3,11),(4,5),(4,6),(4,7),(4,8),(4,9),(4,11),(5,6),(5,7),(5,8),(5,10),(5,11),(6,7),(6,9),(6,10),(6,11),(7,9),(7,10),(8,9),(8,10),(8,11),(9,10),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
01110 => ([(0,3),(0,4),(1,2),(1,10),(1,11),(2,8),(2,9),(3,6),(3,7),(4,1),(4,6),(4,7),(6,11),(7,10),(8,5),(9,5),(10,8),(11,9)],12)
=> ([(0,9),(0,11),(1,7),(1,8),(2,5),(2,9),(2,11),(3,4),(3,9),(3,11),(4,7),(4,10),(5,8),(5,10),(6,7),(6,8),(6,10),(10,11)],12)
=> ([(0,2),(0,3),(0,4),(0,7),(0,8),(0,9),(0,11),(1,5),(1,6),(1,7),(1,8),(1,9),(1,10),(1,11),(2,3),(2,4),(2,5),(2,6),(2,7),(2,10),(2,11),(3,4),(3,6),(3,7),(3,9),(3,10),(3,11),(4,5),(4,7),(4,8),(4,10),(4,11),(5,6),(5,8),(5,9),(5,10),(5,11),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,11),(8,9),(8,10),(9,10),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
01111 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ([(0,3),(0,7),(1,2),(1,6),(2,8),(3,9),(4,5),(4,8),(4,9),(5,6),(5,7),(6,8),(7,9)],10)
=> ([(0,1),(0,3),(0,5),(0,6),(0,7),(0,9),(1,2),(1,5),(1,6),(1,7),(1,8),(2,3),(2,4),(2,6),(2,8),(2,9),(3,4),(3,7),(3,8),(3,9),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,7),(6,8),(7,9),(8,9)],10)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ([(0,3),(0,7),(1,2),(1,6),(2,8),(3,9),(4,5),(4,8),(4,9),(5,6),(5,7),(6,8),(7,9)],10)
=> ([(0,1),(0,3),(0,5),(0,6),(0,7),(0,9),(1,2),(1,5),(1,6),(1,7),(1,8),(2,3),(2,4),(2,6),(2,8),(2,9),(3,4),(3,7),(3,8),(3,9),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,7),(6,8),(7,9),(8,9)],10)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
10001 => ([(0,3),(0,4),(1,2),(1,10),(1,11),(2,8),(2,9),(3,6),(3,7),(4,1),(4,6),(4,7),(6,11),(7,10),(8,5),(9,5),(10,8),(11,9)],12)
=> ([(0,9),(0,11),(1,7),(1,8),(2,5),(2,9),(2,11),(3,4),(3,9),(3,11),(4,7),(4,10),(5,8),(5,10),(6,7),(6,8),(6,10),(10,11)],12)
=> ([(0,2),(0,3),(0,4),(0,7),(0,8),(0,9),(0,11),(1,5),(1,6),(1,7),(1,8),(1,9),(1,10),(1,11),(2,3),(2,4),(2,5),(2,6),(2,7),(2,10),(2,11),(3,4),(3,6),(3,7),(3,9),(3,10),(3,11),(4,5),(4,7),(4,8),(4,10),(4,11),(5,6),(5,8),(5,9),(5,10),(5,11),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,11),(8,9),(8,10),(9,10),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
10010 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
=> ([(0,7),(0,11),(1,5),(1,6),(2,3),(2,10),(2,11),(3,5),(3,8),(4,6),(4,8),(4,9),(5,10),(6,10),(7,8),(7,9),(8,11),(9,10),(9,11)],12)
=> ([(0,2),(0,4),(0,5),(0,7),(0,8),(0,9),(0,11),(1,3),(1,6),(1,7),(1,8),(1,9),(1,10),(1,11),(2,3),(2,4),(2,5),(2,8),(2,10),(2,11),(3,6),(3,7),(3,9),(3,10),(3,11),(4,5),(4,6),(4,7),(4,8),(4,9),(4,11),(5,6),(5,7),(5,8),(5,10),(5,11),(6,7),(6,9),(6,10),(6,11),(7,9),(7,10),(8,9),(8,10),(8,11),(9,10),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
10011 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ([(0,11),(0,12),(1,8),(1,12),(2,6),(2,7),(3,4),(3,11),(3,12),(4,5),(4,6),(5,9),(5,11),(6,9),(7,8),(7,9),(8,10),(9,10),(10,11),(10,12)],13)
=> ([(0,4),(0,5),(0,6),(0,7),(0,9),(0,10),(0,11),(0,12),(1,2),(1,3),(1,4),(1,6),(1,7),(1,8),(1,9),(1,12),(2,3),(2,6),(2,7),(2,8),(2,9),(2,11),(2,12),(3,5),(3,8),(3,9),(3,10),(3,11),(3,12),(4,5),(4,6),(4,7),(4,8),(4,10),(4,11),(4,12),(5,6),(5,7),(5,8),(5,10),(5,11),(5,12),(6,7),(6,9),(6,10),(6,11),(7,8),(7,10),(7,11),(8,9),(8,10),(8,12),(9,10),(9,11),(9,12),(10,11),(10,12),(11,12)],13)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
10100 => ([(0,2),(0,3),(1,8),(2,10),(2,11),(3,1),(3,10),(3,11),(5,6),(6,4),(7,4),(8,7),(9,6),(9,7),(10,5),(10,9),(11,5),(11,8),(11,9)],12)
=> ([(0,5),(0,6),(1,7),(1,10),(2,4),(2,10),(3,6),(3,8),(3,11),(4,5),(4,11),(5,9),(6,9),(7,8),(7,11),(8,9),(8,10),(9,11),(10,11)],12)
=> ([(0,3),(0,7),(0,8),(0,9),(0,10),(0,11),(1,2),(1,4),(1,5),(1,6),(1,7),(1,8),(1,11),(2,4),(2,5),(2,6),(2,9),(2,10),(2,11),(3,5),(3,7),(3,8),(3,9),(3,10),(3,11),(4,5),(4,6),(4,7),(4,8),(4,9),(4,11),(5,6),(5,7),(5,10),(5,11),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(8,9),(8,10),(9,10),(9,11),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
10101 => ([(0,1),(0,2),(1,8),(1,9),(2,8),(2,9),(4,3),(5,3),(6,4),(6,5),(7,4),(7,5),(8,6),(8,7),(9,6),(9,7)],10)
=> ([(0,4),(0,5),(1,2),(1,3),(2,6),(2,7),(3,6),(3,7),(4,8),(4,9),(5,8),(5,9),(6,8),(6,9),(7,8),(7,9)],10)
=> ([(0,1),(0,4),(0,5),(0,8),(0,9),(1,4),(1,5),(1,8),(1,9),(2,3),(2,6),(2,7),(2,8),(2,9),(3,6),(3,7),(3,8),(3,9),(4,5),(4,6),(4,7),(4,9),(5,6),(5,7),(5,9),(6,7),(6,8),(7,8),(8,9)],10)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
10110 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
=> ([(0,7),(0,11),(1,5),(1,6),(2,3),(2,10),(2,11),(3,5),(3,8),(4,6),(4,8),(4,9),(5,10),(6,10),(7,8),(7,9),(8,11),(9,10),(9,11)],12)
=> ([(0,2),(0,4),(0,5),(0,7),(0,8),(0,9),(0,11),(1,3),(1,6),(1,7),(1,8),(1,9),(1,10),(1,11),(2,3),(2,4),(2,5),(2,8),(2,10),(2,11),(3,6),(3,7),(3,9),(3,10),(3,11),(4,5),(4,6),(4,7),(4,8),(4,9),(4,11),(5,6),(5,7),(5,8),(5,10),(5,11),(6,7),(6,9),(6,10),(6,11),(7,9),(7,10),(8,9),(8,10),(8,11),(9,10),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
10111 => ([(0,3),(0,4),(1,2),(1,11),(2,8),(3,9),(3,10),(4,1),(4,9),(4,10),(6,7),(7,5),(8,5),(9,6),(10,6),(10,11),(11,7),(11,8)],12)
=> ([(0,7),(0,11),(1,5),(1,8),(2,6),(2,8),(3,4),(3,7),(3,11),(4,5),(4,9),(5,10),(6,10),(6,11),(7,9),(8,10),(9,10),(9,11)],12)
=> ([(0,3),(0,4),(0,5),(0,6),(0,9),(0,10),(0,11),(1,2),(1,4),(1,5),(1,7),(1,8),(1,10),(1,11),(2,6),(2,7),(2,8),(2,9),(2,10),(2,11),(3,4),(3,5),(3,6),(3,7),(3,8),(3,9),(3,11),(4,5),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,9),(5,10),(6,9),(6,10),(6,11),(7,8),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
11000 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ([(0,5),(0,9),(1,4),(1,9),(2,6),(2,8),(3,7),(3,8),(4,6),(4,10),(5,7),(5,10),(6,11),(7,11),(8,11),(9,10),(10,11)],12)
=> ([(0,3),(0,6),(0,7),(0,8),(0,9),(0,10),(0,11),(1,2),(1,4),(1,5),(1,8),(1,9),(1,10),(1,11),(2,3),(2,4),(2,5),(2,6),(2,7),(2,8),(2,9),(3,4),(3,5),(3,6),(3,7),(3,10),(3,11),(4,5),(4,7),(4,8),(4,9),(4,11),(5,6),(5,8),(5,9),(5,10),(6,7),(6,8),(6,10),(6,11),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
11001 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ([(0,11),(0,12),(1,8),(1,12),(2,6),(2,7),(3,4),(3,11),(3,12),(4,5),(4,6),(5,9),(5,11),(6,9),(7,8),(7,9),(8,10),(9,10),(10,11),(10,12)],13)
=> ([(0,4),(0,5),(0,6),(0,7),(0,9),(0,10),(0,11),(0,12),(1,2),(1,3),(1,4),(1,6),(1,7),(1,8),(1,9),(1,12),(2,3),(2,6),(2,7),(2,8),(2,9),(2,11),(2,12),(3,5),(3,8),(3,9),(3,10),(3,11),(3,12),(4,5),(4,6),(4,7),(4,8),(4,10),(4,11),(4,12),(5,6),(5,7),(5,8),(5,10),(5,11),(5,12),(6,7),(6,9),(6,10),(6,11),(7,8),(7,10),(7,11),(8,9),(8,10),(8,12),(9,10),(9,11),(9,12),(10,11),(10,12),(11,12)],13)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
11010 => ([(0,2),(0,3),(1,8),(2,10),(2,11),(3,1),(3,10),(3,11),(5,6),(6,4),(7,4),(8,7),(9,6),(9,7),(10,5),(10,9),(11,5),(11,8),(11,9)],12)
=> ([(0,5),(0,6),(1,7),(1,10),(2,4),(2,10),(3,6),(3,8),(3,11),(4,5),(4,11),(5,9),(6,9),(7,8),(7,11),(8,9),(8,10),(9,11),(10,11)],12)
=> ([(0,3),(0,7),(0,8),(0,9),(0,10),(0,11),(1,2),(1,4),(1,5),(1,6),(1,7),(1,8),(1,11),(2,4),(2,5),(2,6),(2,9),(2,10),(2,11),(3,5),(3,7),(3,8),(3,9),(3,10),(3,11),(4,5),(4,6),(4,7),(4,8),(4,9),(4,11),(5,6),(5,7),(5,10),(5,11),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(8,9),(8,10),(9,10),(9,11),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
11011 => ([(0,2),(0,3),(1,5),(1,6),(2,10),(2,11),(3,1),(3,10),(3,11),(5,8),(6,7),(7,4),(8,4),(9,7),(9,8),(10,6),(10,9),(11,5),(11,9)],12)
=> ([(0,7),(0,11),(1,5),(1,6),(2,3),(2,4),(2,11),(3,6),(3,9),(4,5),(4,8),(5,10),(6,10),(7,8),(7,9),(8,10),(8,11),(9,10),(9,11)],12)
=> ([(0,3),(0,4),(0,5),(0,6),(0,8),(0,9),(0,11),(1,2),(1,5),(1,6),(1,7),(1,9),(1,10),(1,11),(2,5),(2,6),(2,7),(2,8),(2,10),(2,11),(3,4),(3,7),(3,8),(3,9),(3,10),(3,11),(4,5),(4,6),(4,7),(4,8),(4,9),(4,11),(5,6),(5,7),(5,8),(5,10),(6,7),(6,9),(6,10),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
11100 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ([(0,5),(0,9),(1,4),(1,9),(2,6),(2,8),(3,7),(3,8),(4,6),(4,10),(5,7),(5,10),(6,11),(7,11),(8,11),(9,10),(10,11)],12)
=> ([(0,3),(0,6),(0,7),(0,8),(0,9),(0,10),(0,11),(1,2),(1,4),(1,5),(1,8),(1,9),(1,10),(1,11),(2,3),(2,4),(2,5),(2,6),(2,7),(2,8),(2,9),(3,4),(3,5),(3,6),(3,7),(3,10),(3,11),(4,5),(4,7),(4,8),(4,9),(4,11),(5,6),(5,8),(5,9),(5,10),(6,7),(6,8),(6,10),(6,11),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
11101 => ([(0,3),(0,4),(1,2),(1,11),(2,8),(3,9),(3,10),(4,1),(4,9),(4,10),(6,7),(7,5),(8,5),(9,6),(10,6),(10,11),(11,7),(11,8)],12)
=> ([(0,7),(0,11),(1,5),(1,8),(2,6),(2,8),(3,4),(3,7),(3,11),(4,5),(4,9),(5,10),(6,10),(6,11),(7,9),(8,10),(9,10),(9,11)],12)
=> ([(0,3),(0,4),(0,5),(0,6),(0,9),(0,10),(0,11),(1,2),(1,4),(1,5),(1,7),(1,8),(1,10),(1,11),(2,6),(2,7),(2,8),(2,9),(2,10),(2,11),(3,4),(3,5),(3,6),(3,7),(3,8),(3,9),(3,11),(4,5),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,9),(5,10),(6,9),(6,10),(6,11),(7,8),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
11110 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ([(0,3),(0,7),(1,2),(1,6),(2,8),(3,9),(4,5),(4,8),(4,9),(5,6),(5,7),(6,8),(7,9)],10)
=> ([(0,1),(0,3),(0,5),(0,6),(0,7),(0,9),(1,2),(1,5),(1,6),(1,7),(1,8),(2,3),(2,4),(2,6),(2,8),(2,9),(3,4),(3,7),(3,8),(3,9),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,7),(6,8),(7,9),(8,9)],10)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> ([(0,1),(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 3 = 2 + 1
000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
=> ([(0,1),(0,3),(0,4),(0,6),(1,2),(1,4),(1,5),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 4 = 3 + 1
000001 => ([(0,2),(0,6),(1,8),(2,7),(3,5),(3,9),(4,3),(4,11),(5,1),(5,10),(6,4),(6,7),(7,11),(9,10),(10,8),(11,9)],12)
=> ([(0,3),(0,11),(1,2),(1,8),(2,9),(3,10),(4,5),(4,6),(4,8),(5,7),(5,9),(6,7),(6,10),(7,11),(8,9),(10,11)],12)
=> ([(0,2),(0,3),(0,5),(0,6),(0,7),(0,9),(0,10),(0,11),(1,2),(1,3),(1,4),(1,6),(1,7),(1,8),(1,10),(1,11),(2,4),(2,5),(2,6),(2,8),(2,9),(2,10),(3,4),(3,5),(3,7),(3,8),(3,9),(3,11),(4,7),(4,8),(4,9),(4,10),(4,11),(5,6),(5,8),(5,9),(5,10),(5,11),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11),(8,10),(8,11),(9,10),(9,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3} + 1
000010 => ([(0,4),(0,5),(1,3),(1,12),(2,11),(3,2),(3,14),(4,10),(4,13),(5,1),(5,10),(5,13),(7,8),(8,9),(9,6),(10,7),(11,6),(12,8),(12,14),(13,7),(13,12),(14,9),(14,11)],15)
=> ([(0,9),(0,14),(1,7),(1,10),(2,8),(2,10),(3,4),(3,9),(3,14),(4,5),(4,11),(5,7),(5,13),(6,8),(6,13),(6,14),(7,12),(8,12),(9,11),(10,12),(11,13),(11,14),(12,13)],15)
=> ([(0,3),(0,5),(0,6),(0,8),(0,9),(0,10),(0,11),(0,12),(0,13),(0,14),(1,2),(1,4),(1,7),(1,8),(1,9),(1,10),(1,11),(1,12),(1,13),(1,14),(2,3),(2,4),(2,6),(2,7),(2,8),(2,9),(2,10),(2,13),(2,14),(3,4),(3,5),(3,6),(3,7),(3,11),(3,12),(3,13),(3,14),(4,5),(4,6),(4,7),(4,8),(4,9),(4,10),(4,13),(4,14),(5,6),(5,7),(5,8),(5,10),(5,11),(5,12),(5,13),(5,14),(6,8),(6,9),(6,11),(6,12),(6,13),(6,14),(7,8),(7,9),(7,10),(7,12),(7,13),(7,14),(8,9),(8,10),(8,11),(8,12),(9,10),(9,11),(9,12),(9,13),(10,11),(10,12),(10,14),(11,12),(11,13),(11,14),(12,13),(12,14),(13,14)],15)
=> ? ∊ {1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3} + 1
000011 => ([(0,5),(0,6),(1,4),(1,14),(2,11),(3,10),(4,3),(4,12),(5,1),(5,13),(6,2),(6,13),(8,9),(9,7),(10,7),(11,8),(12,9),(12,10),(13,11),(13,14),(14,8),(14,12)],15)
=> ([(0,7),(0,11),(1,6),(1,10),(2,8),(2,10),(3,9),(3,11),(4,8),(4,9),(4,14),(5,6),(5,7),(5,14),(6,12),(7,13),(8,12),(9,13),(10,12),(11,13),(12,14),(13,14)],15)
=> ([(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,11),(0,12),(0,13),(0,14),(1,2),(1,4),(1,7),(1,8),(1,9),(1,10),(1,11),(1,12),(1,13),(1,14),(2,3),(2,5),(2,6),(2,9),(2,10),(2,11),(2,12),(2,13),(2,14),(3,4),(3,5),(3,6),(3,7),(3,8),(3,9),(3,10),(3,11),(3,12),(4,5),(4,6),(4,7),(4,8),(4,9),(4,10),(4,13),(4,14),(5,6),(5,7),(5,8),(5,10),(5,11),(5,12),(5,14),(6,7),(6,8),(6,9),(6,11),(6,12),(6,13),(7,8),(7,9),(7,11),(7,13),(7,14),(8,10),(8,12),(8,13),(8,14),(9,10),(9,11),(9,12),(9,13),(9,14),(10,11),(10,12),(10,13),(10,14),(11,12),(11,13),(11,14),(12,13),(12,14),(13,14)],15)
=> ? ∊ {1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3} + 1
000100 => ([(0,3),(0,4),(1,10),(2,1),(2,6),(2,12),(3,14),(3,15),(4,2),(4,14),(4,15),(6,7),(7,8),(8,5),(9,5),(10,9),(11,7),(11,13),(12,10),(12,13),(13,8),(13,9),(14,6),(14,11),(15,11),(15,12)],16)
=> ([(0,7),(0,15),(1,5),(1,14),(2,6),(2,8),(3,4),(3,13),(3,15),(4,6),(4,10),(5,12),(5,13),(6,11),(7,8),(7,9),(8,11),(9,11),(9,12),(9,15),(10,11),(10,12),(10,13),(12,14),(13,14),(14,15)],16)
=> ([(0,1),(0,3),(0,4),(0,5),(0,7),(0,8),(0,9),(0,11),(0,13),(0,14),(0,15),(1,4),(1,5),(1,6),(1,7),(1,10),(1,11),(1,12),(1,13),(1,14),(1,15),(2,3),(2,5),(2,6),(2,8),(2,9),(2,10),(2,11),(2,12),(2,13),(2,14),(2,15),(3,6),(3,7),(3,8),(3,9),(3,10),(3,12),(3,13),(3,14),(3,15),(4,5),(4,7),(4,8),(4,9),(4,10),(4,11),(4,13),(4,14),(4,15),(5,7),(5,8),(5,9),(5,11),(5,12),(5,13),(5,15),(6,7),(6,8),(6,9),(6,10),(6,11),(6,12),(6,13),(6,14),(7,9),(7,11),(7,12),(7,13),(7,14),(7,15),(8,9),(8,10),(8,11),(8,12),(8,14),(8,15),(9,10),(9,12),(9,14),(9,15),(10,11),(10,12),(10,13),(10,14),(10,15),(11,12),(11,13),(11,15),(12,13),(12,14),(13,14),(13,15),(14,15)],16)
=> ? ∊ {1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3} + 1
000101 => ([(0,3),(0,4),(1,2),(1,14),(2,6),(3,13),(3,15),(4,1),(4,13),(4,15),(6,9),(7,8),(8,10),(9,5),(10,5),(11,8),(11,12),(12,9),(12,10),(13,7),(13,11),(14,6),(14,12),(15,7),(15,11),(15,14)],16)
=> ([(0,5),(0,7),(1,6),(1,8),(2,9),(2,14),(3,4),(3,8),(3,13),(4,10),(4,15),(5,6),(5,11),(6,12),(7,11),(7,14),(8,12),(9,10),(9,15),(10,13),(10,14),(11,12),(11,15),(12,13),(13,15),(14,15)],16)
=> ([(0,4),(0,5),(0,8),(0,9),(0,10),(0,11),(0,12),(0,13),(0,14),(0,15),(1,2),(1,3),(1,6),(1,7),(1,8),(1,9),(1,11),(1,12),(1,13),(1,14),(1,15),(2,3),(2,5),(2,6),(2,7),(2,9),(2,10),(2,11),(2,12),(2,14),(2,15),(3,4),(3,6),(3,7),(3,10),(3,11),(3,12),(3,13),(3,14),(3,15),(4,5),(4,8),(4,9),(4,10),(4,11),(4,12),(4,13),(4,14),(4,15),(5,6),(5,7),(5,8),(5,9),(5,10),(5,13),(5,14),(5,15),(6,7),(6,8),(6,9),(6,10),(6,11),(6,12),(6,14),(6,15),(7,8),(7,9),(7,11),(7,12),(7,13),(7,14),(7,15),(8,9),(8,10),(8,11),(8,12),(8,13),(8,15),(9,10),(9,11),(9,13),(9,15),(10,12),(10,13),(10,14),(10,15),(11,12),(11,13),(11,14),(12,13),(12,14),(13,14),(13,15),(14,15)],16)
=> ? ∊ {1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3} + 1
000110 => ([(0,4),(0,5),(1,11),(2,1),(2,13),(3,7),(3,14),(4,2),(4,12),(4,16),(5,3),(5,12),(5,16),(7,8),(8,9),(9,6),(10,6),(11,10),(12,7),(13,11),(13,15),(14,8),(14,15),(15,9),(15,10),(16,13),(16,14)],17)
=> ([(0,15),(0,16),(1,7),(1,10),(2,8),(2,9),(3,4),(3,5),(3,6),(4,15),(4,16),(5,11),(5,15),(6,8),(6,11),(7,14),(7,16),(8,13),(9,10),(9,13),(10,14),(11,12),(11,13),(12,14),(12,15),(12,16),(13,14)],17)
=> ([(0,3),(0,6),(0,7),(0,8),(0,9),(0,10),(0,11),(0,12),(0,13),(0,14),(0,15),(0,16),(1,2),(1,4),(1,5),(1,6),(1,7),(1,8),(1,9),(1,12),(1,13),(1,14),(1,15),(1,16),(2,4),(2,5),(2,7),(2,8),(2,10),(2,11),(2,12),(2,13),(2,14),(2,15),(2,16),(3,4),(3,5),(3,6),(3,9),(3,10),(3,11),(3,12),(3,13),(3,14),(3,15),(3,16),(4,5),(4,6),(4,7),(4,8),(4,9),(4,11),(4,13),(4,15),(4,16),(5,7),(5,8),(5,9),(5,10),(5,11),(5,13),(5,15),(5,16),(6,7),(6,8),(6,9),(6,10),(6,11),(6,12),(6,13),(6,14),(6,16),(7,8),(7,9),(7,10),(7,12),(7,13),(7,14),(7,15),(8,10),(8,11),(8,12),(8,13),(8,14),(8,15),(9,10),(9,11),(9,12),(9,13),(9,14),(9,16),(10,11),(10,12),(10,14),(10,15),(10,16),(11,12),(11,14),(11,15),(11,16),(12,14),(12,15),(12,16),(13,14),(13,15),(13,16),(14,15),(14,16),(15,16)],17)
=> ? ∊ {1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3} + 1
111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
=> ([(0,1),(0,3),(0,4),(0,6),(1,2),(1,4),(1,5),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 4 = 3 + 1
Description
The pathwidth of a graph.
Matching statistic: St000778
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Values
0 => ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 1 = 0 + 1
1 => ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 1 = 0 + 1
00 => ([(0,2),(2,1)],3)
=> ([(0,2),(1,2)],3)
=> ([(1,2)],3)
=> 1 = 0 + 1
01 => ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,3),(1,2)],4)
=> 2 = 1 + 1
10 => ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,3),(1,2)],4)
=> 2 = 1 + 1
11 => ([(0,2),(2,1)],3)
=> ([(0,2),(1,2)],3)
=> ([(1,2)],3)
=> 1 = 0 + 1
000 => ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(1,2),(2,3)],4)
=> ([(0,3),(1,2),(2,3)],4)
=> 1 = 0 + 1
001 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,5),(3,4),(4,5)],6)
=> 2 = 1 + 1
010 => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6)
=> 2 = 1 + 1
011 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,5),(3,4),(4,5)],6)
=> 2 = 1 + 1
100 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,5),(3,4),(4,5)],6)
=> 2 = 1 + 1
101 => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6)
=> 2 = 1 + 1
110 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,5),(3,4),(4,5)],6)
=> 2 = 1 + 1
111 => ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(1,2),(2,3)],4)
=> ([(0,3),(1,2),(2,3)],4)
=> 1 = 0 + 1
0000 => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> 2 = 1 + 1
0001 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,3),(0,7),(1,2),(1,4),(2,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ([(0,3),(0,5),(0,6),(0,7),(1,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6),(6,7)],8)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2} + 1
0010 => ([(0,2),(0,3),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,5),(8,5),(8,6)],9)
=> ([(0,5),(0,8),(1,4),(1,6),(2,6),(2,8),(3,4),(3,5),(3,8),(4,7),(5,7),(6,7),(7,8)],9)
=> ([(0,2),(0,3),(0,4),(0,8),(1,5),(1,6),(1,7),(1,8),(2,3),(2,4),(2,5),(2,6),(3,4),(3,7),(3,8),(4,6),(4,7),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2} + 1
0011 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,6),(0,7),(1,4),(1,5),(2,5),(2,7),(3,4),(3,6),(4,8),(5,8),(6,8),(7,8)],9)
=> ([(0,5),(0,6),(0,7),(0,8),(1,2),(1,3),(1,4),(1,7),(1,8),(2,3),(2,4),(2,5),(2,6),(3,4),(3,6),(3,8),(4,5),(4,7),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2} + 1
0100 => ([(0,2),(0,3),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,5),(8,5),(8,6)],9)
=> ([(0,5),(0,8),(1,4),(1,6),(2,6),(2,8),(3,4),(3,5),(3,8),(4,7),(5,7),(6,7),(7,8)],9)
=> ([(0,2),(0,3),(0,4),(0,8),(1,5),(1,6),(1,7),(1,8),(2,3),(2,4),(2,5),(2,6),(3,4),(3,7),(3,8),(4,6),(4,7),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2} + 1
0101 => ([(0,1),(0,2),(1,6),(1,7),(2,6),(2,7),(4,3),(5,3),(6,4),(6,5),(7,4),(7,5)],8)
=> ([(0,4),(0,5),(1,2),(1,3),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
=> ([(0,1),(0,6),(0,7),(1,6),(1,7),(2,3),(2,4),(2,5),(2,7),(3,4),(3,5),(3,7),(4,5),(4,6),(5,6),(6,7)],8)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2} + 1
0110 => ([(0,2),(0,3),(1,5),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,6),(8,5)],9)
=> ([(0,5),(0,6),(1,7),(1,8),(2,5),(2,6),(2,8),(3,6),(3,7),(3,8),(4,5),(4,7),(4,8)],9)
=> ([(0,4),(0,5),(0,6),(0,8),(1,2),(1,3),(1,4),(1,7),(1,8),(2,3),(2,6),(2,7),(2,8),(3,5),(3,7),(3,8),(4,5),(4,6),(4,8),(5,6),(5,7),(6,7),(7,8)],9)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2} + 1
0111 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,3),(0,7),(1,2),(1,4),(2,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ([(0,3),(0,5),(0,6),(0,7),(1,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6),(6,7)],8)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2} + 1
1000 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,3),(0,7),(1,2),(1,4),(2,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ([(0,3),(0,5),(0,6),(0,7),(1,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6),(6,7)],8)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2} + 1
1001 => ([(0,2),(0,3),(1,5),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,6),(8,5)],9)
=> ([(0,5),(0,6),(1,7),(1,8),(2,5),(2,6),(2,8),(3,6),(3,7),(3,8),(4,5),(4,7),(4,8)],9)
=> ([(0,4),(0,5),(0,6),(0,8),(1,2),(1,3),(1,4),(1,7),(1,8),(2,3),(2,6),(2,7),(2,8),(3,5),(3,7),(3,8),(4,5),(4,6),(4,8),(5,6),(5,7),(6,7),(7,8)],9)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2} + 1
1010 => ([(0,1),(0,2),(1,6),(1,7),(2,6),(2,7),(4,3),(5,3),(6,4),(6,5),(7,4),(7,5)],8)
=> ([(0,4),(0,5),(1,2),(1,3),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
=> ([(0,1),(0,6),(0,7),(1,6),(1,7),(2,3),(2,4),(2,5),(2,7),(3,4),(3,5),(3,7),(4,5),(4,6),(5,6),(6,7)],8)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2} + 1
1011 => ([(0,2),(0,3),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,5),(8,5),(8,6)],9)
=> ([(0,5),(0,8),(1,4),(1,6),(2,6),(2,8),(3,4),(3,5),(3,8),(4,7),(5,7),(6,7),(7,8)],9)
=> ([(0,2),(0,3),(0,4),(0,8),(1,5),(1,6),(1,7),(1,8),(2,3),(2,4),(2,5),(2,6),(3,4),(3,7),(3,8),(4,6),(4,7),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2} + 1
1100 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,6),(0,7),(1,4),(1,5),(2,5),(2,7),(3,4),(3,6),(4,8),(5,8),(6,8),(7,8)],9)
=> ([(0,5),(0,6),(0,7),(0,8),(1,2),(1,3),(1,4),(1,7),(1,8),(2,3),(2,4),(2,5),(2,6),(3,4),(3,6),(3,8),(4,5),(4,7),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2} + 1
1101 => ([(0,2),(0,3),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,5),(8,5),(8,6)],9)
=> ([(0,5),(0,8),(1,4),(1,6),(2,6),(2,8),(3,4),(3,5),(3,8),(4,7),(5,7),(6,7),(7,8)],9)
=> ([(0,2),(0,3),(0,4),(0,8),(1,5),(1,6),(1,7),(1,8),(2,3),(2,4),(2,5),(2,6),(3,4),(3,7),(3,8),(4,6),(4,7),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2} + 1
1110 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,3),(0,7),(1,2),(1,4),(2,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ([(0,3),(0,5),(0,6),(0,7),(1,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6),(6,7)],8)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2} + 1
1111 => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> 2 = 1 + 1
00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> ([(0,1),(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 2 = 1 + 1
00001 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ([(0,3),(0,7),(1,2),(1,6),(2,8),(3,9),(4,5),(4,8),(4,9),(5,6),(5,7),(6,8),(7,9)],10)
=> ([(0,1),(0,3),(0,5),(0,6),(0,7),(0,9),(1,2),(1,5),(1,6),(1,7),(1,8),(2,3),(2,4),(2,6),(2,8),(2,9),(3,4),(3,7),(3,8),(3,9),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,7),(6,8),(7,9),(8,9)],10)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
00010 => ([(0,3),(0,4),(1,2),(1,11),(2,8),(3,9),(3,10),(4,1),(4,9),(4,10),(6,7),(7,5),(8,5),(9,6),(10,6),(10,11),(11,7),(11,8)],12)
=> ([(0,7),(0,11),(1,5),(1,8),(2,6),(2,8),(3,4),(3,7),(3,11),(4,5),(4,9),(5,10),(6,10),(6,11),(7,9),(8,10),(9,10),(9,11)],12)
=> ([(0,3),(0,4),(0,5),(0,6),(0,9),(0,10),(0,11),(1,2),(1,4),(1,5),(1,7),(1,8),(1,10),(1,11),(2,6),(2,7),(2,8),(2,9),(2,10),(2,11),(3,4),(3,5),(3,6),(3,7),(3,8),(3,9),(3,11),(4,5),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,9),(5,10),(6,9),(6,10),(6,11),(7,8),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
00011 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ([(0,5),(0,9),(1,4),(1,9),(2,6),(2,8),(3,7),(3,8),(4,6),(4,10),(5,7),(5,10),(6,11),(7,11),(8,11),(9,10),(10,11)],12)
=> ([(0,3),(0,6),(0,7),(0,8),(0,9),(0,10),(0,11),(1,2),(1,4),(1,5),(1,8),(1,9),(1,10),(1,11),(2,3),(2,4),(2,5),(2,6),(2,7),(2,8),(2,9),(3,4),(3,5),(3,6),(3,7),(3,10),(3,11),(4,5),(4,7),(4,8),(4,9),(4,11),(5,6),(5,8),(5,9),(5,10),(6,7),(6,8),(6,10),(6,11),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
00100 => ([(0,2),(0,3),(1,5),(1,6),(2,10),(2,11),(3,1),(3,10),(3,11),(5,8),(6,7),(7,4),(8,4),(9,7),(9,8),(10,6),(10,9),(11,5),(11,9)],12)
=> ([(0,7),(0,11),(1,5),(1,6),(2,3),(2,4),(2,11),(3,6),(3,9),(4,5),(4,8),(5,10),(6,10),(7,8),(7,9),(8,10),(8,11),(9,10),(9,11)],12)
=> ([(0,3),(0,4),(0,5),(0,6),(0,8),(0,9),(0,11),(1,2),(1,5),(1,6),(1,7),(1,9),(1,10),(1,11),(2,5),(2,6),(2,7),(2,8),(2,10),(2,11),(3,4),(3,7),(3,8),(3,9),(3,10),(3,11),(4,5),(4,6),(4,7),(4,8),(4,9),(4,11),(5,6),(5,7),(5,8),(5,10),(6,7),(6,9),(6,10),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
00101 => ([(0,2),(0,3),(1,8),(2,10),(2,11),(3,1),(3,10),(3,11),(5,6),(6,4),(7,4),(8,7),(9,6),(9,7),(10,5),(10,9),(11,5),(11,8),(11,9)],12)
=> ([(0,5),(0,6),(1,7),(1,10),(2,4),(2,10),(3,6),(3,8),(3,11),(4,5),(4,11),(5,9),(6,9),(7,8),(7,11),(8,9),(8,10),(9,11),(10,11)],12)
=> ([(0,3),(0,7),(0,8),(0,9),(0,10),(0,11),(1,2),(1,4),(1,5),(1,6),(1,7),(1,8),(1,11),(2,4),(2,5),(2,6),(2,9),(2,10),(2,11),(3,5),(3,7),(3,8),(3,9),(3,10),(3,11),(4,5),(4,6),(4,7),(4,8),(4,9),(4,11),(5,6),(5,7),(5,10),(5,11),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(8,9),(8,10),(9,10),(9,11),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
00110 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ([(0,11),(0,12),(1,8),(1,12),(2,6),(2,7),(3,4),(3,11),(3,12),(4,5),(4,6),(5,9),(5,11),(6,9),(7,8),(7,9),(8,10),(9,10),(10,11),(10,12)],13)
=> ([(0,4),(0,5),(0,6),(0,7),(0,9),(0,10),(0,11),(0,12),(1,2),(1,3),(1,4),(1,6),(1,7),(1,8),(1,9),(1,12),(2,3),(2,6),(2,7),(2,8),(2,9),(2,11),(2,12),(3,5),(3,8),(3,9),(3,10),(3,11),(3,12),(4,5),(4,6),(4,7),(4,8),(4,10),(4,11),(4,12),(5,6),(5,7),(5,8),(5,10),(5,11),(5,12),(6,7),(6,9),(6,10),(6,11),(7,8),(7,10),(7,11),(8,9),(8,10),(8,12),(9,10),(9,11),(9,12),(10,11),(10,12),(11,12)],13)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
00111 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ([(0,5),(0,9),(1,4),(1,9),(2,6),(2,8),(3,7),(3,8),(4,6),(4,10),(5,7),(5,10),(6,11),(7,11),(8,11),(9,10),(10,11)],12)
=> ([(0,3),(0,6),(0,7),(0,8),(0,9),(0,10),(0,11),(1,2),(1,4),(1,5),(1,8),(1,9),(1,10),(1,11),(2,3),(2,4),(2,5),(2,6),(2,7),(2,8),(2,9),(3,4),(3,5),(3,6),(3,7),(3,10),(3,11),(4,5),(4,7),(4,8),(4,9),(4,11),(5,6),(5,8),(5,9),(5,10),(6,7),(6,8),(6,10),(6,11),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
01000 => ([(0,3),(0,4),(1,2),(1,11),(2,8),(3,9),(3,10),(4,1),(4,9),(4,10),(6,7),(7,5),(8,5),(9,6),(10,6),(10,11),(11,7),(11,8)],12)
=> ([(0,7),(0,11),(1,5),(1,8),(2,6),(2,8),(3,4),(3,7),(3,11),(4,5),(4,9),(5,10),(6,10),(6,11),(7,9),(8,10),(9,10),(9,11)],12)
=> ([(0,3),(0,4),(0,5),(0,6),(0,9),(0,10),(0,11),(1,2),(1,4),(1,5),(1,7),(1,8),(1,10),(1,11),(2,6),(2,7),(2,8),(2,9),(2,10),(2,11),(3,4),(3,5),(3,6),(3,7),(3,8),(3,9),(3,11),(4,5),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,9),(5,10),(6,9),(6,10),(6,11),(7,8),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
01001 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
=> ([(0,7),(0,11),(1,5),(1,6),(2,3),(2,10),(2,11),(3,5),(3,8),(4,6),(4,8),(4,9),(5,10),(6,10),(7,8),(7,9),(8,11),(9,10),(9,11)],12)
=> ([(0,2),(0,4),(0,5),(0,7),(0,8),(0,9),(0,11),(1,3),(1,6),(1,7),(1,8),(1,9),(1,10),(1,11),(2,3),(2,4),(2,5),(2,8),(2,10),(2,11),(3,6),(3,7),(3,9),(3,10),(3,11),(4,5),(4,6),(4,7),(4,8),(4,9),(4,11),(5,6),(5,7),(5,8),(5,10),(5,11),(6,7),(6,9),(6,10),(6,11),(7,9),(7,10),(8,9),(8,10),(8,11),(9,10),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
01010 => ([(0,1),(0,2),(1,8),(1,9),(2,8),(2,9),(4,3),(5,3),(6,4),(6,5),(7,4),(7,5),(8,6),(8,7),(9,6),(9,7)],10)
=> ([(0,4),(0,5),(1,2),(1,3),(2,6),(2,7),(3,6),(3,7),(4,8),(4,9),(5,8),(5,9),(6,8),(6,9),(7,8),(7,9)],10)
=> ([(0,1),(0,4),(0,5),(0,8),(0,9),(1,4),(1,5),(1,8),(1,9),(2,3),(2,6),(2,7),(2,8),(2,9),(3,6),(3,7),(3,8),(3,9),(4,5),(4,6),(4,7),(4,9),(5,6),(5,7),(5,9),(6,7),(6,8),(7,8),(8,9)],10)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
01011 => ([(0,2),(0,3),(1,8),(2,10),(2,11),(3,1),(3,10),(3,11),(5,6),(6,4),(7,4),(8,7),(9,6),(9,7),(10,5),(10,9),(11,5),(11,8),(11,9)],12)
=> ([(0,5),(0,6),(1,7),(1,10),(2,4),(2,10),(3,6),(3,8),(3,11),(4,5),(4,11),(5,9),(6,9),(7,8),(7,11),(8,9),(8,10),(9,11),(10,11)],12)
=> ([(0,3),(0,7),(0,8),(0,9),(0,10),(0,11),(1,2),(1,4),(1,5),(1,6),(1,7),(1,8),(1,11),(2,4),(2,5),(2,6),(2,9),(2,10),(2,11),(3,5),(3,7),(3,8),(3,9),(3,10),(3,11),(4,5),(4,6),(4,7),(4,8),(4,9),(4,11),(5,6),(5,7),(5,10),(5,11),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(8,9),(8,10),(9,10),(9,11),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
01100 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ([(0,11),(0,12),(1,8),(1,12),(2,6),(2,7),(3,4),(3,11),(3,12),(4,5),(4,6),(5,9),(5,11),(6,9),(7,8),(7,9),(8,10),(9,10),(10,11),(10,12)],13)
=> ([(0,4),(0,5),(0,6),(0,7),(0,9),(0,10),(0,11),(0,12),(1,2),(1,3),(1,4),(1,6),(1,7),(1,8),(1,9),(1,12),(2,3),(2,6),(2,7),(2,8),(2,9),(2,11),(2,12),(3,5),(3,8),(3,9),(3,10),(3,11),(3,12),(4,5),(4,6),(4,7),(4,8),(4,10),(4,11),(4,12),(5,6),(5,7),(5,8),(5,10),(5,11),(5,12),(6,7),(6,9),(6,10),(6,11),(7,8),(7,10),(7,11),(8,9),(8,10),(8,12),(9,10),(9,11),(9,12),(10,11),(10,12),(11,12)],13)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
01101 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
=> ([(0,7),(0,11),(1,5),(1,6),(2,3),(2,10),(2,11),(3,5),(3,8),(4,6),(4,8),(4,9),(5,10),(6,10),(7,8),(7,9),(8,11),(9,10),(9,11)],12)
=> ([(0,2),(0,4),(0,5),(0,7),(0,8),(0,9),(0,11),(1,3),(1,6),(1,7),(1,8),(1,9),(1,10),(1,11),(2,3),(2,4),(2,5),(2,8),(2,10),(2,11),(3,6),(3,7),(3,9),(3,10),(3,11),(4,5),(4,6),(4,7),(4,8),(4,9),(4,11),(5,6),(5,7),(5,8),(5,10),(5,11),(6,7),(6,9),(6,10),(6,11),(7,9),(7,10),(8,9),(8,10),(8,11),(9,10),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
01110 => ([(0,3),(0,4),(1,2),(1,10),(1,11),(2,8),(2,9),(3,6),(3,7),(4,1),(4,6),(4,7),(6,11),(7,10),(8,5),(9,5),(10,8),(11,9)],12)
=> ([(0,9),(0,11),(1,7),(1,8),(2,5),(2,9),(2,11),(3,4),(3,9),(3,11),(4,7),(4,10),(5,8),(5,10),(6,7),(6,8),(6,10),(10,11)],12)
=> ([(0,2),(0,3),(0,4),(0,7),(0,8),(0,9),(0,11),(1,5),(1,6),(1,7),(1,8),(1,9),(1,10),(1,11),(2,3),(2,4),(2,5),(2,6),(2,7),(2,10),(2,11),(3,4),(3,6),(3,7),(3,9),(3,10),(3,11),(4,5),(4,7),(4,8),(4,10),(4,11),(5,6),(5,8),(5,9),(5,10),(5,11),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,11),(8,9),(8,10),(9,10),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
01111 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ([(0,3),(0,7),(1,2),(1,6),(2,8),(3,9),(4,5),(4,8),(4,9),(5,6),(5,7),(6,8),(7,9)],10)
=> ([(0,1),(0,3),(0,5),(0,6),(0,7),(0,9),(1,2),(1,5),(1,6),(1,7),(1,8),(2,3),(2,4),(2,6),(2,8),(2,9),(3,4),(3,7),(3,8),(3,9),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,7),(6,8),(7,9),(8,9)],10)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ([(0,3),(0,7),(1,2),(1,6),(2,8),(3,9),(4,5),(4,8),(4,9),(5,6),(5,7),(6,8),(7,9)],10)
=> ([(0,1),(0,3),(0,5),(0,6),(0,7),(0,9),(1,2),(1,5),(1,6),(1,7),(1,8),(2,3),(2,4),(2,6),(2,8),(2,9),(3,4),(3,7),(3,8),(3,9),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,7),(6,8),(7,9),(8,9)],10)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
10001 => ([(0,3),(0,4),(1,2),(1,10),(1,11),(2,8),(2,9),(3,6),(3,7),(4,1),(4,6),(4,7),(6,11),(7,10),(8,5),(9,5),(10,8),(11,9)],12)
=> ([(0,9),(0,11),(1,7),(1,8),(2,5),(2,9),(2,11),(3,4),(3,9),(3,11),(4,7),(4,10),(5,8),(5,10),(6,7),(6,8),(6,10),(10,11)],12)
=> ([(0,2),(0,3),(0,4),(0,7),(0,8),(0,9),(0,11),(1,5),(1,6),(1,7),(1,8),(1,9),(1,10),(1,11),(2,3),(2,4),(2,5),(2,6),(2,7),(2,10),(2,11),(3,4),(3,6),(3,7),(3,9),(3,10),(3,11),(4,5),(4,7),(4,8),(4,10),(4,11),(5,6),(5,8),(5,9),(5,10),(5,11),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,11),(8,9),(8,10),(9,10),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
10010 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
=> ([(0,7),(0,11),(1,5),(1,6),(2,3),(2,10),(2,11),(3,5),(3,8),(4,6),(4,8),(4,9),(5,10),(6,10),(7,8),(7,9),(8,11),(9,10),(9,11)],12)
=> ([(0,2),(0,4),(0,5),(0,7),(0,8),(0,9),(0,11),(1,3),(1,6),(1,7),(1,8),(1,9),(1,10),(1,11),(2,3),(2,4),(2,5),(2,8),(2,10),(2,11),(3,6),(3,7),(3,9),(3,10),(3,11),(4,5),(4,6),(4,7),(4,8),(4,9),(4,11),(5,6),(5,7),(5,8),(5,10),(5,11),(6,7),(6,9),(6,10),(6,11),(7,9),(7,10),(8,9),(8,10),(8,11),(9,10),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
10011 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ([(0,11),(0,12),(1,8),(1,12),(2,6),(2,7),(3,4),(3,11),(3,12),(4,5),(4,6),(5,9),(5,11),(6,9),(7,8),(7,9),(8,10),(9,10),(10,11),(10,12)],13)
=> ([(0,4),(0,5),(0,6),(0,7),(0,9),(0,10),(0,11),(0,12),(1,2),(1,3),(1,4),(1,6),(1,7),(1,8),(1,9),(1,12),(2,3),(2,6),(2,7),(2,8),(2,9),(2,11),(2,12),(3,5),(3,8),(3,9),(3,10),(3,11),(3,12),(4,5),(4,6),(4,7),(4,8),(4,10),(4,11),(4,12),(5,6),(5,7),(5,8),(5,10),(5,11),(5,12),(6,7),(6,9),(6,10),(6,11),(7,8),(7,10),(7,11),(8,9),(8,10),(8,12),(9,10),(9,11),(9,12),(10,11),(10,12),(11,12)],13)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
10100 => ([(0,2),(0,3),(1,8),(2,10),(2,11),(3,1),(3,10),(3,11),(5,6),(6,4),(7,4),(8,7),(9,6),(9,7),(10,5),(10,9),(11,5),(11,8),(11,9)],12)
=> ([(0,5),(0,6),(1,7),(1,10),(2,4),(2,10),(3,6),(3,8),(3,11),(4,5),(4,11),(5,9),(6,9),(7,8),(7,11),(8,9),(8,10),(9,11),(10,11)],12)
=> ([(0,3),(0,7),(0,8),(0,9),(0,10),(0,11),(1,2),(1,4),(1,5),(1,6),(1,7),(1,8),(1,11),(2,4),(2,5),(2,6),(2,9),(2,10),(2,11),(3,5),(3,7),(3,8),(3,9),(3,10),(3,11),(4,5),(4,6),(4,7),(4,8),(4,9),(4,11),(5,6),(5,7),(5,10),(5,11),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(8,9),(8,10),(9,10),(9,11),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
10101 => ([(0,1),(0,2),(1,8),(1,9),(2,8),(2,9),(4,3),(5,3),(6,4),(6,5),(7,4),(7,5),(8,6),(8,7),(9,6),(9,7)],10)
=> ([(0,4),(0,5),(1,2),(1,3),(2,6),(2,7),(3,6),(3,7),(4,8),(4,9),(5,8),(5,9),(6,8),(6,9),(7,8),(7,9)],10)
=> ([(0,1),(0,4),(0,5),(0,8),(0,9),(1,4),(1,5),(1,8),(1,9),(2,3),(2,6),(2,7),(2,8),(2,9),(3,6),(3,7),(3,8),(3,9),(4,5),(4,6),(4,7),(4,9),(5,6),(5,7),(5,9),(6,7),(6,8),(7,8),(8,9)],10)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
10110 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
=> ([(0,7),(0,11),(1,5),(1,6),(2,3),(2,10),(2,11),(3,5),(3,8),(4,6),(4,8),(4,9),(5,10),(6,10),(7,8),(7,9),(8,11),(9,10),(9,11)],12)
=> ([(0,2),(0,4),(0,5),(0,7),(0,8),(0,9),(0,11),(1,3),(1,6),(1,7),(1,8),(1,9),(1,10),(1,11),(2,3),(2,4),(2,5),(2,8),(2,10),(2,11),(3,6),(3,7),(3,9),(3,10),(3,11),(4,5),(4,6),(4,7),(4,8),(4,9),(4,11),(5,6),(5,7),(5,8),(5,10),(5,11),(6,7),(6,9),(6,10),(6,11),(7,9),(7,10),(8,9),(8,10),(8,11),(9,10),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
10111 => ([(0,3),(0,4),(1,2),(1,11),(2,8),(3,9),(3,10),(4,1),(4,9),(4,10),(6,7),(7,5),(8,5),(9,6),(10,6),(10,11),(11,7),(11,8)],12)
=> ([(0,7),(0,11),(1,5),(1,8),(2,6),(2,8),(3,4),(3,7),(3,11),(4,5),(4,9),(5,10),(6,10),(6,11),(7,9),(8,10),(9,10),(9,11)],12)
=> ([(0,3),(0,4),(0,5),(0,6),(0,9),(0,10),(0,11),(1,2),(1,4),(1,5),(1,7),(1,8),(1,10),(1,11),(2,6),(2,7),(2,8),(2,9),(2,10),(2,11),(3,4),(3,5),(3,6),(3,7),(3,8),(3,9),(3,11),(4,5),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,9),(5,10),(6,9),(6,10),(6,11),(7,8),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
11000 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ([(0,5),(0,9),(1,4),(1,9),(2,6),(2,8),(3,7),(3,8),(4,6),(4,10),(5,7),(5,10),(6,11),(7,11),(8,11),(9,10),(10,11)],12)
=> ([(0,3),(0,6),(0,7),(0,8),(0,9),(0,10),(0,11),(1,2),(1,4),(1,5),(1,8),(1,9),(1,10),(1,11),(2,3),(2,4),(2,5),(2,6),(2,7),(2,8),(2,9),(3,4),(3,5),(3,6),(3,7),(3,10),(3,11),(4,5),(4,7),(4,8),(4,9),(4,11),(5,6),(5,8),(5,9),(5,10),(6,7),(6,8),(6,10),(6,11),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
11001 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ([(0,11),(0,12),(1,8),(1,12),(2,6),(2,7),(3,4),(3,11),(3,12),(4,5),(4,6),(5,9),(5,11),(6,9),(7,8),(7,9),(8,10),(9,10),(10,11),(10,12)],13)
=> ([(0,4),(0,5),(0,6),(0,7),(0,9),(0,10),(0,11),(0,12),(1,2),(1,3),(1,4),(1,6),(1,7),(1,8),(1,9),(1,12),(2,3),(2,6),(2,7),(2,8),(2,9),(2,11),(2,12),(3,5),(3,8),(3,9),(3,10),(3,11),(3,12),(4,5),(4,6),(4,7),(4,8),(4,10),(4,11),(4,12),(5,6),(5,7),(5,8),(5,10),(5,11),(5,12),(6,7),(6,9),(6,10),(6,11),(7,8),(7,10),(7,11),(8,9),(8,10),(8,12),(9,10),(9,11),(9,12),(10,11),(10,12),(11,12)],13)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
11010 => ([(0,2),(0,3),(1,8),(2,10),(2,11),(3,1),(3,10),(3,11),(5,6),(6,4),(7,4),(8,7),(9,6),(9,7),(10,5),(10,9),(11,5),(11,8),(11,9)],12)
=> ([(0,5),(0,6),(1,7),(1,10),(2,4),(2,10),(3,6),(3,8),(3,11),(4,5),(4,11),(5,9),(6,9),(7,8),(7,11),(8,9),(8,10),(9,11),(10,11)],12)
=> ([(0,3),(0,7),(0,8),(0,9),(0,10),(0,11),(1,2),(1,4),(1,5),(1,6),(1,7),(1,8),(1,11),(2,4),(2,5),(2,6),(2,9),(2,10),(2,11),(3,5),(3,7),(3,8),(3,9),(3,10),(3,11),(4,5),(4,6),(4,7),(4,8),(4,9),(4,11),(5,6),(5,7),(5,10),(5,11),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(8,9),(8,10),(9,10),(9,11),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
11011 => ([(0,2),(0,3),(1,5),(1,6),(2,10),(2,11),(3,1),(3,10),(3,11),(5,8),(6,7),(7,4),(8,4),(9,7),(9,8),(10,6),(10,9),(11,5),(11,9)],12)
=> ([(0,7),(0,11),(1,5),(1,6),(2,3),(2,4),(2,11),(3,6),(3,9),(4,5),(4,8),(5,10),(6,10),(7,8),(7,9),(8,10),(8,11),(9,10),(9,11)],12)
=> ([(0,3),(0,4),(0,5),(0,6),(0,8),(0,9),(0,11),(1,2),(1,5),(1,6),(1,7),(1,9),(1,10),(1,11),(2,5),(2,6),(2,7),(2,8),(2,10),(2,11),(3,4),(3,7),(3,8),(3,9),(3,10),(3,11),(4,5),(4,6),(4,7),(4,8),(4,9),(4,11),(5,6),(5,7),(5,8),(5,10),(6,7),(6,9),(6,10),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
11100 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ([(0,5),(0,9),(1,4),(1,9),(2,6),(2,8),(3,7),(3,8),(4,6),(4,10),(5,7),(5,10),(6,11),(7,11),(8,11),(9,10),(10,11)],12)
=> ([(0,3),(0,6),(0,7),(0,8),(0,9),(0,10),(0,11),(1,2),(1,4),(1,5),(1,8),(1,9),(1,10),(1,11),(2,3),(2,4),(2,5),(2,6),(2,7),(2,8),(2,9),(3,4),(3,5),(3,6),(3,7),(3,10),(3,11),(4,5),(4,7),(4,8),(4,9),(4,11),(5,6),(5,8),(5,9),(5,10),(6,7),(6,8),(6,10),(6,11),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
11101 => ([(0,3),(0,4),(1,2),(1,11),(2,8),(3,9),(3,10),(4,1),(4,9),(4,10),(6,7),(7,5),(8,5),(9,6),(10,6),(10,11),(11,7),(11,8)],12)
=> ([(0,7),(0,11),(1,5),(1,8),(2,6),(2,8),(3,4),(3,7),(3,11),(4,5),(4,9),(5,10),(6,10),(6,11),(7,9),(8,10),(9,10),(9,11)],12)
=> ([(0,3),(0,4),(0,5),(0,6),(0,9),(0,10),(0,11),(1,2),(1,4),(1,5),(1,7),(1,8),(1,10),(1,11),(2,6),(2,7),(2,8),(2,9),(2,10),(2,11),(3,4),(3,5),(3,6),(3,7),(3,8),(3,9),(3,11),(4,5),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,9),(5,10),(6,9),(6,10),(6,11),(7,8),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
11110 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ([(0,3),(0,7),(1,2),(1,6),(2,8),(3,9),(4,5),(4,8),(4,9),(5,6),(5,7),(6,8),(7,9)],10)
=> ([(0,1),(0,3),(0,5),(0,6),(0,7),(0,9),(1,2),(1,5),(1,6),(1,7),(1,8),(2,3),(2,4),(2,6),(2,8),(2,9),(3,4),(3,7),(3,8),(3,9),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,7),(6,8),(7,9),(8,9)],10)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> ([(0,1),(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 2 = 1 + 1
000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
=> ([(0,1),(0,3),(0,4),(0,6),(1,2),(1,4),(1,5),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 2 + 1
000001 => ([(0,2),(0,6),(1,8),(2,7),(3,5),(3,9),(4,3),(4,11),(5,1),(5,10),(6,4),(6,7),(7,11),(9,10),(10,8),(11,9)],12)
=> ([(0,3),(0,11),(1,2),(1,8),(2,9),(3,10),(4,5),(4,6),(4,8),(5,7),(5,9),(6,7),(6,10),(7,11),(8,9),(10,11)],12)
=> ([(0,2),(0,3),(0,5),(0,6),(0,7),(0,9),(0,10),(0,11),(1,2),(1,3),(1,4),(1,6),(1,7),(1,8),(1,10),(1,11),(2,4),(2,5),(2,6),(2,8),(2,9),(2,10),(3,4),(3,5),(3,7),(3,8),(3,9),(3,11),(4,7),(4,8),(4,9),(4,10),(4,11),(5,6),(5,8),(5,9),(5,10),(5,11),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11),(8,10),(8,11),(9,10),(9,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3} + 1
000010 => ([(0,4),(0,5),(1,3),(1,12),(2,11),(3,2),(3,14),(4,10),(4,13),(5,1),(5,10),(5,13),(7,8),(8,9),(9,6),(10,7),(11,6),(12,8),(12,14),(13,7),(13,12),(14,9),(14,11)],15)
=> ([(0,9),(0,14),(1,7),(1,10),(2,8),(2,10),(3,4),(3,9),(3,14),(4,5),(4,11),(5,7),(5,13),(6,8),(6,13),(6,14),(7,12),(8,12),(9,11),(10,12),(11,13),(11,14),(12,13)],15)
=> ([(0,3),(0,5),(0,6),(0,8),(0,9),(0,10),(0,11),(0,12),(0,13),(0,14),(1,2),(1,4),(1,7),(1,8),(1,9),(1,10),(1,11),(1,12),(1,13),(1,14),(2,3),(2,4),(2,6),(2,7),(2,8),(2,9),(2,10),(2,13),(2,14),(3,4),(3,5),(3,6),(3,7),(3,11),(3,12),(3,13),(3,14),(4,5),(4,6),(4,7),(4,8),(4,9),(4,10),(4,13),(4,14),(5,6),(5,7),(5,8),(5,10),(5,11),(5,12),(5,13),(5,14),(6,8),(6,9),(6,11),(6,12),(6,13),(6,14),(7,8),(7,9),(7,10),(7,12),(7,13),(7,14),(8,9),(8,10),(8,11),(8,12),(9,10),(9,11),(9,12),(9,13),(10,11),(10,12),(10,14),(11,12),(11,13),(11,14),(12,13),(12,14),(13,14)],15)
=> ? ∊ {1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3} + 1
000011 => ([(0,5),(0,6),(1,4),(1,14),(2,11),(3,10),(4,3),(4,12),(5,1),(5,13),(6,2),(6,13),(8,9),(9,7),(10,7),(11,8),(12,9),(12,10),(13,11),(13,14),(14,8),(14,12)],15)
=> ([(0,7),(0,11),(1,6),(1,10),(2,8),(2,10),(3,9),(3,11),(4,8),(4,9),(4,14),(5,6),(5,7),(5,14),(6,12),(7,13),(8,12),(9,13),(10,12),(11,13),(12,14),(13,14)],15)
=> ([(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,11),(0,12),(0,13),(0,14),(1,2),(1,4),(1,7),(1,8),(1,9),(1,10),(1,11),(1,12),(1,13),(1,14),(2,3),(2,5),(2,6),(2,9),(2,10),(2,11),(2,12),(2,13),(2,14),(3,4),(3,5),(3,6),(3,7),(3,8),(3,9),(3,10),(3,11),(3,12),(4,5),(4,6),(4,7),(4,8),(4,9),(4,10),(4,13),(4,14),(5,6),(5,7),(5,8),(5,10),(5,11),(5,12),(5,14),(6,7),(6,8),(6,9),(6,11),(6,12),(6,13),(7,8),(7,9),(7,11),(7,13),(7,14),(8,10),(8,12),(8,13),(8,14),(9,10),(9,11),(9,12),(9,13),(9,14),(10,11),(10,12),(10,13),(10,14),(11,12),(11,13),(11,14),(12,13),(12,14),(13,14)],15)
=> ? ∊ {1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3} + 1
000100 => ([(0,3),(0,4),(1,10),(2,1),(2,6),(2,12),(3,14),(3,15),(4,2),(4,14),(4,15),(6,7),(7,8),(8,5),(9,5),(10,9),(11,7),(11,13),(12,10),(12,13),(13,8),(13,9),(14,6),(14,11),(15,11),(15,12)],16)
=> ([(0,7),(0,15),(1,5),(1,14),(2,6),(2,8),(3,4),(3,13),(3,15),(4,6),(4,10),(5,12),(5,13),(6,11),(7,8),(7,9),(8,11),(9,11),(9,12),(9,15),(10,11),(10,12),(10,13),(12,14),(13,14),(14,15)],16)
=> ([(0,1),(0,3),(0,4),(0,5),(0,7),(0,8),(0,9),(0,11),(0,13),(0,14),(0,15),(1,4),(1,5),(1,6),(1,7),(1,10),(1,11),(1,12),(1,13),(1,14),(1,15),(2,3),(2,5),(2,6),(2,8),(2,9),(2,10),(2,11),(2,12),(2,13),(2,14),(2,15),(3,6),(3,7),(3,8),(3,9),(3,10),(3,12),(3,13),(3,14),(3,15),(4,5),(4,7),(4,8),(4,9),(4,10),(4,11),(4,13),(4,14),(4,15),(5,7),(5,8),(5,9),(5,11),(5,12),(5,13),(5,15),(6,7),(6,8),(6,9),(6,10),(6,11),(6,12),(6,13),(6,14),(7,9),(7,11),(7,12),(7,13),(7,14),(7,15),(8,9),(8,10),(8,11),(8,12),(8,14),(8,15),(9,10),(9,12),(9,14),(9,15),(10,11),(10,12),(10,13),(10,14),(10,15),(11,12),(11,13),(11,15),(12,13),(12,14),(13,14),(13,15),(14,15)],16)
=> ? ∊ {1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3} + 1
000101 => ([(0,3),(0,4),(1,2),(1,14),(2,6),(3,13),(3,15),(4,1),(4,13),(4,15),(6,9),(7,8),(8,10),(9,5),(10,5),(11,8),(11,12),(12,9),(12,10),(13,7),(13,11),(14,6),(14,12),(15,7),(15,11),(15,14)],16)
=> ([(0,5),(0,7),(1,6),(1,8),(2,9),(2,14),(3,4),(3,8),(3,13),(4,10),(4,15),(5,6),(5,11),(6,12),(7,11),(7,14),(8,12),(9,10),(9,15),(10,13),(10,14),(11,12),(11,15),(12,13),(13,15),(14,15)],16)
=> ([(0,4),(0,5),(0,8),(0,9),(0,10),(0,11),(0,12),(0,13),(0,14),(0,15),(1,2),(1,3),(1,6),(1,7),(1,8),(1,9),(1,11),(1,12),(1,13),(1,14),(1,15),(2,3),(2,5),(2,6),(2,7),(2,9),(2,10),(2,11),(2,12),(2,14),(2,15),(3,4),(3,6),(3,7),(3,10),(3,11),(3,12),(3,13),(3,14),(3,15),(4,5),(4,8),(4,9),(4,10),(4,11),(4,12),(4,13),(4,14),(4,15),(5,6),(5,7),(5,8),(5,9),(5,10),(5,13),(5,14),(5,15),(6,7),(6,8),(6,9),(6,10),(6,11),(6,12),(6,14),(6,15),(7,8),(7,9),(7,11),(7,12),(7,13),(7,14),(7,15),(8,9),(8,10),(8,11),(8,12),(8,13),(8,15),(9,10),(9,11),(9,13),(9,15),(10,12),(10,13),(10,14),(10,15),(11,12),(11,13),(11,14),(12,13),(12,14),(13,14),(13,15),(14,15)],16)
=> ? ∊ {1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3} + 1
000110 => ([(0,4),(0,5),(1,11),(2,1),(2,13),(3,7),(3,14),(4,2),(4,12),(4,16),(5,3),(5,12),(5,16),(7,8),(8,9),(9,6),(10,6),(11,10),(12,7),(13,11),(13,15),(14,8),(14,15),(15,9),(15,10),(16,13),(16,14)],17)
=> ([(0,15),(0,16),(1,7),(1,10),(2,8),(2,9),(3,4),(3,5),(3,6),(4,15),(4,16),(5,11),(5,15),(6,8),(6,11),(7,14),(7,16),(8,13),(9,10),(9,13),(10,14),(11,12),(11,13),(12,14),(12,15),(12,16),(13,14)],17)
=> ([(0,3),(0,6),(0,7),(0,8),(0,9),(0,10),(0,11),(0,12),(0,13),(0,14),(0,15),(0,16),(1,2),(1,4),(1,5),(1,6),(1,7),(1,8),(1,9),(1,12),(1,13),(1,14),(1,15),(1,16),(2,4),(2,5),(2,7),(2,8),(2,10),(2,11),(2,12),(2,13),(2,14),(2,15),(2,16),(3,4),(3,5),(3,6),(3,9),(3,10),(3,11),(3,12),(3,13),(3,14),(3,15),(3,16),(4,5),(4,6),(4,7),(4,8),(4,9),(4,11),(4,13),(4,15),(4,16),(5,7),(5,8),(5,9),(5,10),(5,11),(5,13),(5,15),(5,16),(6,7),(6,8),(6,9),(6,10),(6,11),(6,12),(6,13),(6,14),(6,16),(7,8),(7,9),(7,10),(7,12),(7,13),(7,14),(7,15),(8,10),(8,11),(8,12),(8,13),(8,14),(8,15),(9,10),(9,11),(9,12),(9,13),(9,14),(9,16),(10,11),(10,12),(10,14),(10,15),(10,16),(11,12),(11,14),(11,15),(11,16),(12,14),(12,15),(12,16),(13,14),(13,15),(13,16),(14,15),(14,16),(15,16)],17)
=> ? ∊ {1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3} + 1
111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
=> ([(0,1),(0,3),(0,4),(0,6),(1,2),(1,4),(1,5),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 2 + 1
Description
The metric dimension of a graph.
This is the length of the shortest vector of vertices, such that every vertex is uniquely determined by the vector of distances from these vertices.
Matching statistic: St001792
Values
0 => ([(0,1)],2)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 1 = 0 + 1
1 => ([(0,1)],2)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 1 = 0 + 1
00 => ([(0,2),(2,1)],3)
=> ([(0,2),(1,2)],3)
=> ([(0,2),(1,2)],3)
=> 1 = 0 + 1
01 => ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> 2 = 1 + 1
10 => ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> 2 = 1 + 1
11 => ([(0,2),(2,1)],3)
=> ([(0,2),(1,2)],3)
=> ([(0,2),(1,2)],3)
=> 1 = 0 + 1
000 => ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(1,2),(2,3)],4)
=> ([(0,3),(1,2),(2,3)],4)
=> 1 = 0 + 1
001 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,5),(3,4),(4,5)],6)
=> 2 = 1 + 1
010 => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6)
=> 2 = 1 + 1
011 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,5),(3,4),(4,5)],6)
=> 2 = 1 + 1
100 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,5),(3,4),(4,5)],6)
=> 2 = 1 + 1
101 => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6)
=> 2 = 1 + 1
110 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,5),(3,4),(4,5)],6)
=> 2 = 1 + 1
111 => ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(1,2),(2,3)],4)
=> ([(0,3),(1,2),(2,3)],4)
=> 1 = 0 + 1
0000 => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> 2 = 1 + 1
0001 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,3),(0,7),(1,2),(1,4),(2,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ([(0,3),(0,5),(0,6),(0,7),(1,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6),(6,7)],8)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2} + 1
0010 => ([(0,2),(0,3),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,5),(8,5),(8,6)],9)
=> ([(0,5),(0,8),(1,4),(1,6),(2,6),(2,8),(3,4),(3,5),(3,8),(4,7),(5,7),(6,7),(7,8)],9)
=> ([(0,2),(0,3),(0,4),(0,8),(1,5),(1,6),(1,7),(1,8),(2,3),(2,4),(2,5),(2,6),(3,4),(3,7),(3,8),(4,6),(4,7),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2} + 1
0011 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,6),(0,7),(1,4),(1,5),(2,5),(2,7),(3,4),(3,6),(4,8),(5,8),(6,8),(7,8)],9)
=> ([(0,5),(0,6),(0,7),(0,8),(1,2),(1,3),(1,4),(1,7),(1,8),(2,3),(2,4),(2,5),(2,6),(3,4),(3,6),(3,8),(4,5),(4,7),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2} + 1
0100 => ([(0,2),(0,3),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,5),(8,5),(8,6)],9)
=> ([(0,5),(0,8),(1,4),(1,6),(2,6),(2,8),(3,4),(3,5),(3,8),(4,7),(5,7),(6,7),(7,8)],9)
=> ([(0,2),(0,3),(0,4),(0,8),(1,5),(1,6),(1,7),(1,8),(2,3),(2,4),(2,5),(2,6),(3,4),(3,7),(3,8),(4,6),(4,7),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2} + 1
0101 => ([(0,1),(0,2),(1,6),(1,7),(2,6),(2,7),(4,3),(5,3),(6,4),(6,5),(7,4),(7,5)],8)
=> ([(0,4),(0,5),(1,2),(1,3),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
=> ([(0,1),(0,6),(0,7),(1,6),(1,7),(2,3),(2,4),(2,5),(2,7),(3,4),(3,5),(3,7),(4,5),(4,6),(5,6),(6,7)],8)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2} + 1
0110 => ([(0,2),(0,3),(1,5),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,6),(8,5)],9)
=> ([(0,5),(0,6),(1,7),(1,8),(2,5),(2,6),(2,8),(3,6),(3,7),(3,8),(4,5),(4,7),(4,8)],9)
=> ([(0,4),(0,5),(0,6),(0,8),(1,2),(1,3),(1,4),(1,7),(1,8),(2,3),(2,6),(2,7),(2,8),(3,5),(3,7),(3,8),(4,5),(4,6),(4,8),(5,6),(5,7),(6,7),(7,8)],9)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2} + 1
0111 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,3),(0,7),(1,2),(1,4),(2,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ([(0,3),(0,5),(0,6),(0,7),(1,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6),(6,7)],8)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2} + 1
1000 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,3),(0,7),(1,2),(1,4),(2,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ([(0,3),(0,5),(0,6),(0,7),(1,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6),(6,7)],8)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2} + 1
1001 => ([(0,2),(0,3),(1,5),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,6),(8,5)],9)
=> ([(0,5),(0,6),(1,7),(1,8),(2,5),(2,6),(2,8),(3,6),(3,7),(3,8),(4,5),(4,7),(4,8)],9)
=> ([(0,4),(0,5),(0,6),(0,8),(1,2),(1,3),(1,4),(1,7),(1,8),(2,3),(2,6),(2,7),(2,8),(3,5),(3,7),(3,8),(4,5),(4,6),(4,8),(5,6),(5,7),(6,7),(7,8)],9)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2} + 1
1010 => ([(0,1),(0,2),(1,6),(1,7),(2,6),(2,7),(4,3),(5,3),(6,4),(6,5),(7,4),(7,5)],8)
=> ([(0,4),(0,5),(1,2),(1,3),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
=> ([(0,1),(0,6),(0,7),(1,6),(1,7),(2,3),(2,4),(2,5),(2,7),(3,4),(3,5),(3,7),(4,5),(4,6),(5,6),(6,7)],8)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2} + 1
1011 => ([(0,2),(0,3),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,5),(8,5),(8,6)],9)
=> ([(0,5),(0,8),(1,4),(1,6),(2,6),(2,8),(3,4),(3,5),(3,8),(4,7),(5,7),(6,7),(7,8)],9)
=> ([(0,2),(0,3),(0,4),(0,8),(1,5),(1,6),(1,7),(1,8),(2,3),(2,4),(2,5),(2,6),(3,4),(3,7),(3,8),(4,6),(4,7),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2} + 1
1100 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,6),(0,7),(1,4),(1,5),(2,5),(2,7),(3,4),(3,6),(4,8),(5,8),(6,8),(7,8)],9)
=> ([(0,5),(0,6),(0,7),(0,8),(1,2),(1,3),(1,4),(1,7),(1,8),(2,3),(2,4),(2,5),(2,6),(3,4),(3,6),(3,8),(4,5),(4,7),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2} + 1
1101 => ([(0,2),(0,3),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,5),(8,5),(8,6)],9)
=> ([(0,5),(0,8),(1,4),(1,6),(2,6),(2,8),(3,4),(3,5),(3,8),(4,7),(5,7),(6,7),(7,8)],9)
=> ([(0,2),(0,3),(0,4),(0,8),(1,5),(1,6),(1,7),(1,8),(2,3),(2,4),(2,5),(2,6),(3,4),(3,7),(3,8),(4,6),(4,7),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2} + 1
1110 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,3),(0,7),(1,2),(1,4),(2,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ([(0,3),(0,5),(0,6),(0,7),(1,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6),(6,7)],8)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2} + 1
1111 => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> 2 = 1 + 1
00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> ([(0,1),(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 2 = 1 + 1
00001 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ([(0,3),(0,7),(1,2),(1,6),(2,8),(3,9),(4,5),(4,8),(4,9),(5,6),(5,7),(6,8),(7,9)],10)
=> ([(0,1),(0,3),(0,5),(0,6),(0,7),(0,9),(1,2),(1,5),(1,6),(1,7),(1,8),(2,3),(2,4),(2,6),(2,8),(2,9),(3,4),(3,7),(3,8),(3,9),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,7),(6,8),(7,9),(8,9)],10)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
00010 => ([(0,3),(0,4),(1,2),(1,11),(2,8),(3,9),(3,10),(4,1),(4,9),(4,10),(6,7),(7,5),(8,5),(9,6),(10,6),(10,11),(11,7),(11,8)],12)
=> ([(0,7),(0,11),(1,5),(1,8),(2,6),(2,8),(3,4),(3,7),(3,11),(4,5),(4,9),(5,10),(6,10),(6,11),(7,9),(8,10),(9,10),(9,11)],12)
=> ([(0,3),(0,4),(0,5),(0,6),(0,9),(0,10),(0,11),(1,2),(1,4),(1,5),(1,7),(1,8),(1,10),(1,11),(2,6),(2,7),(2,8),(2,9),(2,10),(2,11),(3,4),(3,5),(3,6),(3,7),(3,8),(3,9),(3,11),(4,5),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,9),(5,10),(6,9),(6,10),(6,11),(7,8),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
00011 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ([(0,5),(0,9),(1,4),(1,9),(2,6),(2,8),(3,7),(3,8),(4,6),(4,10),(5,7),(5,10),(6,11),(7,11),(8,11),(9,10),(10,11)],12)
=> ([(0,3),(0,6),(0,7),(0,8),(0,9),(0,10),(0,11),(1,2),(1,4),(1,5),(1,8),(1,9),(1,10),(1,11),(2,3),(2,4),(2,5),(2,6),(2,7),(2,8),(2,9),(3,4),(3,5),(3,6),(3,7),(3,10),(3,11),(4,5),(4,7),(4,8),(4,9),(4,11),(5,6),(5,8),(5,9),(5,10),(6,7),(6,8),(6,10),(6,11),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
00100 => ([(0,2),(0,3),(1,5),(1,6),(2,10),(2,11),(3,1),(3,10),(3,11),(5,8),(6,7),(7,4),(8,4),(9,7),(9,8),(10,6),(10,9),(11,5),(11,9)],12)
=> ([(0,7),(0,11),(1,5),(1,6),(2,3),(2,4),(2,11),(3,6),(3,9),(4,5),(4,8),(5,10),(6,10),(7,8),(7,9),(8,10),(8,11),(9,10),(9,11)],12)
=> ([(0,3),(0,4),(0,5),(0,6),(0,8),(0,9),(0,11),(1,2),(1,5),(1,6),(1,7),(1,9),(1,10),(1,11),(2,5),(2,6),(2,7),(2,8),(2,10),(2,11),(3,4),(3,7),(3,8),(3,9),(3,10),(3,11),(4,5),(4,6),(4,7),(4,8),(4,9),(4,11),(5,6),(5,7),(5,8),(5,10),(6,7),(6,9),(6,10),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
00101 => ([(0,2),(0,3),(1,8),(2,10),(2,11),(3,1),(3,10),(3,11),(5,6),(6,4),(7,4),(8,7),(9,6),(9,7),(10,5),(10,9),(11,5),(11,8),(11,9)],12)
=> ([(0,5),(0,6),(1,7),(1,10),(2,4),(2,10),(3,6),(3,8),(3,11),(4,5),(4,11),(5,9),(6,9),(7,8),(7,11),(8,9),(8,10),(9,11),(10,11)],12)
=> ([(0,3),(0,7),(0,8),(0,9),(0,10),(0,11),(1,2),(1,4),(1,5),(1,6),(1,7),(1,8),(1,11),(2,4),(2,5),(2,6),(2,9),(2,10),(2,11),(3,5),(3,7),(3,8),(3,9),(3,10),(3,11),(4,5),(4,6),(4,7),(4,8),(4,9),(4,11),(5,6),(5,7),(5,10),(5,11),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(8,9),(8,10),(9,10),(9,11),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
00110 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ([(0,11),(0,12),(1,8),(1,12),(2,6),(2,7),(3,4),(3,11),(3,12),(4,5),(4,6),(5,9),(5,11),(6,9),(7,8),(7,9),(8,10),(9,10),(10,11),(10,12)],13)
=> ([(0,4),(0,5),(0,6),(0,7),(0,9),(0,10),(0,11),(0,12),(1,2),(1,3),(1,4),(1,6),(1,7),(1,8),(1,9),(1,12),(2,3),(2,6),(2,7),(2,8),(2,9),(2,11),(2,12),(3,5),(3,8),(3,9),(3,10),(3,11),(3,12),(4,5),(4,6),(4,7),(4,8),(4,10),(4,11),(4,12),(5,6),(5,7),(5,8),(5,10),(5,11),(5,12),(6,7),(6,9),(6,10),(6,11),(7,8),(7,10),(7,11),(8,9),(8,10),(8,12),(9,10),(9,11),(9,12),(10,11),(10,12),(11,12)],13)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
00111 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ([(0,5),(0,9),(1,4),(1,9),(2,6),(2,8),(3,7),(3,8),(4,6),(4,10),(5,7),(5,10),(6,11),(7,11),(8,11),(9,10),(10,11)],12)
=> ([(0,3),(0,6),(0,7),(0,8),(0,9),(0,10),(0,11),(1,2),(1,4),(1,5),(1,8),(1,9),(1,10),(1,11),(2,3),(2,4),(2,5),(2,6),(2,7),(2,8),(2,9),(3,4),(3,5),(3,6),(3,7),(3,10),(3,11),(4,5),(4,7),(4,8),(4,9),(4,11),(5,6),(5,8),(5,9),(5,10),(6,7),(6,8),(6,10),(6,11),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
01000 => ([(0,3),(0,4),(1,2),(1,11),(2,8),(3,9),(3,10),(4,1),(4,9),(4,10),(6,7),(7,5),(8,5),(9,6),(10,6),(10,11),(11,7),(11,8)],12)
=> ([(0,7),(0,11),(1,5),(1,8),(2,6),(2,8),(3,4),(3,7),(3,11),(4,5),(4,9),(5,10),(6,10),(6,11),(7,9),(8,10),(9,10),(9,11)],12)
=> ([(0,3),(0,4),(0,5),(0,6),(0,9),(0,10),(0,11),(1,2),(1,4),(1,5),(1,7),(1,8),(1,10),(1,11),(2,6),(2,7),(2,8),(2,9),(2,10),(2,11),(3,4),(3,5),(3,6),(3,7),(3,8),(3,9),(3,11),(4,5),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,9),(5,10),(6,9),(6,10),(6,11),(7,8),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
01001 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
=> ([(0,7),(0,11),(1,5),(1,6),(2,3),(2,10),(2,11),(3,5),(3,8),(4,6),(4,8),(4,9),(5,10),(6,10),(7,8),(7,9),(8,11),(9,10),(9,11)],12)
=> ([(0,2),(0,4),(0,5),(0,7),(0,8),(0,9),(0,11),(1,3),(1,6),(1,7),(1,8),(1,9),(1,10),(1,11),(2,3),(2,4),(2,5),(2,8),(2,10),(2,11),(3,6),(3,7),(3,9),(3,10),(3,11),(4,5),(4,6),(4,7),(4,8),(4,9),(4,11),(5,6),(5,7),(5,8),(5,10),(5,11),(6,7),(6,9),(6,10),(6,11),(7,9),(7,10),(8,9),(8,10),(8,11),(9,10),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
01010 => ([(0,1),(0,2),(1,8),(1,9),(2,8),(2,9),(4,3),(5,3),(6,4),(6,5),(7,4),(7,5),(8,6),(8,7),(9,6),(9,7)],10)
=> ([(0,4),(0,5),(1,2),(1,3),(2,6),(2,7),(3,6),(3,7),(4,8),(4,9),(5,8),(5,9),(6,8),(6,9),(7,8),(7,9)],10)
=> ([(0,1),(0,4),(0,5),(0,8),(0,9),(1,4),(1,5),(1,8),(1,9),(2,3),(2,6),(2,7),(2,8),(2,9),(3,6),(3,7),(3,8),(3,9),(4,5),(4,6),(4,7),(4,9),(5,6),(5,7),(5,9),(6,7),(6,8),(7,8),(8,9)],10)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
01011 => ([(0,2),(0,3),(1,8),(2,10),(2,11),(3,1),(3,10),(3,11),(5,6),(6,4),(7,4),(8,7),(9,6),(9,7),(10,5),(10,9),(11,5),(11,8),(11,9)],12)
=> ([(0,5),(0,6),(1,7),(1,10),(2,4),(2,10),(3,6),(3,8),(3,11),(4,5),(4,11),(5,9),(6,9),(7,8),(7,11),(8,9),(8,10),(9,11),(10,11)],12)
=> ([(0,3),(0,7),(0,8),(0,9),(0,10),(0,11),(1,2),(1,4),(1,5),(1,6),(1,7),(1,8),(1,11),(2,4),(2,5),(2,6),(2,9),(2,10),(2,11),(3,5),(3,7),(3,8),(3,9),(3,10),(3,11),(4,5),(4,6),(4,7),(4,8),(4,9),(4,11),(5,6),(5,7),(5,10),(5,11),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(8,9),(8,10),(9,10),(9,11),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
01100 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ([(0,11),(0,12),(1,8),(1,12),(2,6),(2,7),(3,4),(3,11),(3,12),(4,5),(4,6),(5,9),(5,11),(6,9),(7,8),(7,9),(8,10),(9,10),(10,11),(10,12)],13)
=> ([(0,4),(0,5),(0,6),(0,7),(0,9),(0,10),(0,11),(0,12),(1,2),(1,3),(1,4),(1,6),(1,7),(1,8),(1,9),(1,12),(2,3),(2,6),(2,7),(2,8),(2,9),(2,11),(2,12),(3,5),(3,8),(3,9),(3,10),(3,11),(3,12),(4,5),(4,6),(4,7),(4,8),(4,10),(4,11),(4,12),(5,6),(5,7),(5,8),(5,10),(5,11),(5,12),(6,7),(6,9),(6,10),(6,11),(7,8),(7,10),(7,11),(8,9),(8,10),(8,12),(9,10),(9,11),(9,12),(10,11),(10,12),(11,12)],13)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
01101 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
=> ([(0,7),(0,11),(1,5),(1,6),(2,3),(2,10),(2,11),(3,5),(3,8),(4,6),(4,8),(4,9),(5,10),(6,10),(7,8),(7,9),(8,11),(9,10),(9,11)],12)
=> ([(0,2),(0,4),(0,5),(0,7),(0,8),(0,9),(0,11),(1,3),(1,6),(1,7),(1,8),(1,9),(1,10),(1,11),(2,3),(2,4),(2,5),(2,8),(2,10),(2,11),(3,6),(3,7),(3,9),(3,10),(3,11),(4,5),(4,6),(4,7),(4,8),(4,9),(4,11),(5,6),(5,7),(5,8),(5,10),(5,11),(6,7),(6,9),(6,10),(6,11),(7,9),(7,10),(8,9),(8,10),(8,11),(9,10),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
01110 => ([(0,3),(0,4),(1,2),(1,10),(1,11),(2,8),(2,9),(3,6),(3,7),(4,1),(4,6),(4,7),(6,11),(7,10),(8,5),(9,5),(10,8),(11,9)],12)
=> ([(0,9),(0,11),(1,7),(1,8),(2,5),(2,9),(2,11),(3,4),(3,9),(3,11),(4,7),(4,10),(5,8),(5,10),(6,7),(6,8),(6,10),(10,11)],12)
=> ([(0,2),(0,3),(0,4),(0,7),(0,8),(0,9),(0,11),(1,5),(1,6),(1,7),(1,8),(1,9),(1,10),(1,11),(2,3),(2,4),(2,5),(2,6),(2,7),(2,10),(2,11),(3,4),(3,6),(3,7),(3,9),(3,10),(3,11),(4,5),(4,7),(4,8),(4,10),(4,11),(5,6),(5,8),(5,9),(5,10),(5,11),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,11),(8,9),(8,10),(9,10),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
01111 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ([(0,3),(0,7),(1,2),(1,6),(2,8),(3,9),(4,5),(4,8),(4,9),(5,6),(5,7),(6,8),(7,9)],10)
=> ([(0,1),(0,3),(0,5),(0,6),(0,7),(0,9),(1,2),(1,5),(1,6),(1,7),(1,8),(2,3),(2,4),(2,6),(2,8),(2,9),(3,4),(3,7),(3,8),(3,9),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,7),(6,8),(7,9),(8,9)],10)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ([(0,3),(0,7),(1,2),(1,6),(2,8),(3,9),(4,5),(4,8),(4,9),(5,6),(5,7),(6,8),(7,9)],10)
=> ([(0,1),(0,3),(0,5),(0,6),(0,7),(0,9),(1,2),(1,5),(1,6),(1,7),(1,8),(2,3),(2,4),(2,6),(2,8),(2,9),(3,4),(3,7),(3,8),(3,9),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,7),(6,8),(7,9),(8,9)],10)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
10001 => ([(0,3),(0,4),(1,2),(1,10),(1,11),(2,8),(2,9),(3,6),(3,7),(4,1),(4,6),(4,7),(6,11),(7,10),(8,5),(9,5),(10,8),(11,9)],12)
=> ([(0,9),(0,11),(1,7),(1,8),(2,5),(2,9),(2,11),(3,4),(3,9),(3,11),(4,7),(4,10),(5,8),(5,10),(6,7),(6,8),(6,10),(10,11)],12)
=> ([(0,2),(0,3),(0,4),(0,7),(0,8),(0,9),(0,11),(1,5),(1,6),(1,7),(1,8),(1,9),(1,10),(1,11),(2,3),(2,4),(2,5),(2,6),(2,7),(2,10),(2,11),(3,4),(3,6),(3,7),(3,9),(3,10),(3,11),(4,5),(4,7),(4,8),(4,10),(4,11),(5,6),(5,8),(5,9),(5,10),(5,11),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,11),(8,9),(8,10),(9,10),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
10010 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
=> ([(0,7),(0,11),(1,5),(1,6),(2,3),(2,10),(2,11),(3,5),(3,8),(4,6),(4,8),(4,9),(5,10),(6,10),(7,8),(7,9),(8,11),(9,10),(9,11)],12)
=> ([(0,2),(0,4),(0,5),(0,7),(0,8),(0,9),(0,11),(1,3),(1,6),(1,7),(1,8),(1,9),(1,10),(1,11),(2,3),(2,4),(2,5),(2,8),(2,10),(2,11),(3,6),(3,7),(3,9),(3,10),(3,11),(4,5),(4,6),(4,7),(4,8),(4,9),(4,11),(5,6),(5,7),(5,8),(5,10),(5,11),(6,7),(6,9),(6,10),(6,11),(7,9),(7,10),(8,9),(8,10),(8,11),(9,10),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
10011 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ([(0,11),(0,12),(1,8),(1,12),(2,6),(2,7),(3,4),(3,11),(3,12),(4,5),(4,6),(5,9),(5,11),(6,9),(7,8),(7,9),(8,10),(9,10),(10,11),(10,12)],13)
=> ([(0,4),(0,5),(0,6),(0,7),(0,9),(0,10),(0,11),(0,12),(1,2),(1,3),(1,4),(1,6),(1,7),(1,8),(1,9),(1,12),(2,3),(2,6),(2,7),(2,8),(2,9),(2,11),(2,12),(3,5),(3,8),(3,9),(3,10),(3,11),(3,12),(4,5),(4,6),(4,7),(4,8),(4,10),(4,11),(4,12),(5,6),(5,7),(5,8),(5,10),(5,11),(5,12),(6,7),(6,9),(6,10),(6,11),(7,8),(7,10),(7,11),(8,9),(8,10),(8,12),(9,10),(9,11),(9,12),(10,11),(10,12),(11,12)],13)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
10100 => ([(0,2),(0,3),(1,8),(2,10),(2,11),(3,1),(3,10),(3,11),(5,6),(6,4),(7,4),(8,7),(9,6),(9,7),(10,5),(10,9),(11,5),(11,8),(11,9)],12)
=> ([(0,5),(0,6),(1,7),(1,10),(2,4),(2,10),(3,6),(3,8),(3,11),(4,5),(4,11),(5,9),(6,9),(7,8),(7,11),(8,9),(8,10),(9,11),(10,11)],12)
=> ([(0,3),(0,7),(0,8),(0,9),(0,10),(0,11),(1,2),(1,4),(1,5),(1,6),(1,7),(1,8),(1,11),(2,4),(2,5),(2,6),(2,9),(2,10),(2,11),(3,5),(3,7),(3,8),(3,9),(3,10),(3,11),(4,5),(4,6),(4,7),(4,8),(4,9),(4,11),(5,6),(5,7),(5,10),(5,11),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(8,9),(8,10),(9,10),(9,11),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
10101 => ([(0,1),(0,2),(1,8),(1,9),(2,8),(2,9),(4,3),(5,3),(6,4),(6,5),(7,4),(7,5),(8,6),(8,7),(9,6),(9,7)],10)
=> ([(0,4),(0,5),(1,2),(1,3),(2,6),(2,7),(3,6),(3,7),(4,8),(4,9),(5,8),(5,9),(6,8),(6,9),(7,8),(7,9)],10)
=> ([(0,1),(0,4),(0,5),(0,8),(0,9),(1,4),(1,5),(1,8),(1,9),(2,3),(2,6),(2,7),(2,8),(2,9),(3,6),(3,7),(3,8),(3,9),(4,5),(4,6),(4,7),(4,9),(5,6),(5,7),(5,9),(6,7),(6,8),(7,8),(8,9)],10)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
10110 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
=> ([(0,7),(0,11),(1,5),(1,6),(2,3),(2,10),(2,11),(3,5),(3,8),(4,6),(4,8),(4,9),(5,10),(6,10),(7,8),(7,9),(8,11),(9,10),(9,11)],12)
=> ([(0,2),(0,4),(0,5),(0,7),(0,8),(0,9),(0,11),(1,3),(1,6),(1,7),(1,8),(1,9),(1,10),(1,11),(2,3),(2,4),(2,5),(2,8),(2,10),(2,11),(3,6),(3,7),(3,9),(3,10),(3,11),(4,5),(4,6),(4,7),(4,8),(4,9),(4,11),(5,6),(5,7),(5,8),(5,10),(5,11),(6,7),(6,9),(6,10),(6,11),(7,9),(7,10),(8,9),(8,10),(8,11),(9,10),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
10111 => ([(0,3),(0,4),(1,2),(1,11),(2,8),(3,9),(3,10),(4,1),(4,9),(4,10),(6,7),(7,5),(8,5),(9,6),(10,6),(10,11),(11,7),(11,8)],12)
=> ([(0,7),(0,11),(1,5),(1,8),(2,6),(2,8),(3,4),(3,7),(3,11),(4,5),(4,9),(5,10),(6,10),(6,11),(7,9),(8,10),(9,10),(9,11)],12)
=> ([(0,3),(0,4),(0,5),(0,6),(0,9),(0,10),(0,11),(1,2),(1,4),(1,5),(1,7),(1,8),(1,10),(1,11),(2,6),(2,7),(2,8),(2,9),(2,10),(2,11),(3,4),(3,5),(3,6),(3,7),(3,8),(3,9),(3,11),(4,5),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,9),(5,10),(6,9),(6,10),(6,11),(7,8),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
11000 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ([(0,5),(0,9),(1,4),(1,9),(2,6),(2,8),(3,7),(3,8),(4,6),(4,10),(5,7),(5,10),(6,11),(7,11),(8,11),(9,10),(10,11)],12)
=> ([(0,3),(0,6),(0,7),(0,8),(0,9),(0,10),(0,11),(1,2),(1,4),(1,5),(1,8),(1,9),(1,10),(1,11),(2,3),(2,4),(2,5),(2,6),(2,7),(2,8),(2,9),(3,4),(3,5),(3,6),(3,7),(3,10),(3,11),(4,5),(4,7),(4,8),(4,9),(4,11),(5,6),(5,8),(5,9),(5,10),(6,7),(6,8),(6,10),(6,11),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
11001 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ([(0,11),(0,12),(1,8),(1,12),(2,6),(2,7),(3,4),(3,11),(3,12),(4,5),(4,6),(5,9),(5,11),(6,9),(7,8),(7,9),(8,10),(9,10),(10,11),(10,12)],13)
=> ([(0,4),(0,5),(0,6),(0,7),(0,9),(0,10),(0,11),(0,12),(1,2),(1,3),(1,4),(1,6),(1,7),(1,8),(1,9),(1,12),(2,3),(2,6),(2,7),(2,8),(2,9),(2,11),(2,12),(3,5),(3,8),(3,9),(3,10),(3,11),(3,12),(4,5),(4,6),(4,7),(4,8),(4,10),(4,11),(4,12),(5,6),(5,7),(5,8),(5,10),(5,11),(5,12),(6,7),(6,9),(6,10),(6,11),(7,8),(7,10),(7,11),(8,9),(8,10),(8,12),(9,10),(9,11),(9,12),(10,11),(10,12),(11,12)],13)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
11010 => ([(0,2),(0,3),(1,8),(2,10),(2,11),(3,1),(3,10),(3,11),(5,6),(6,4),(7,4),(8,7),(9,6),(9,7),(10,5),(10,9),(11,5),(11,8),(11,9)],12)
=> ([(0,5),(0,6),(1,7),(1,10),(2,4),(2,10),(3,6),(3,8),(3,11),(4,5),(4,11),(5,9),(6,9),(7,8),(7,11),(8,9),(8,10),(9,11),(10,11)],12)
=> ([(0,3),(0,7),(0,8),(0,9),(0,10),(0,11),(1,2),(1,4),(1,5),(1,6),(1,7),(1,8),(1,11),(2,4),(2,5),(2,6),(2,9),(2,10),(2,11),(3,5),(3,7),(3,8),(3,9),(3,10),(3,11),(4,5),(4,6),(4,7),(4,8),(4,9),(4,11),(5,6),(5,7),(5,10),(5,11),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(8,9),(8,10),(9,10),(9,11),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
11011 => ([(0,2),(0,3),(1,5),(1,6),(2,10),(2,11),(3,1),(3,10),(3,11),(5,8),(6,7),(7,4),(8,4),(9,7),(9,8),(10,6),(10,9),(11,5),(11,9)],12)
=> ([(0,7),(0,11),(1,5),(1,6),(2,3),(2,4),(2,11),(3,6),(3,9),(4,5),(4,8),(5,10),(6,10),(7,8),(7,9),(8,10),(8,11),(9,10),(9,11)],12)
=> ([(0,3),(0,4),(0,5),(0,6),(0,8),(0,9),(0,11),(1,2),(1,5),(1,6),(1,7),(1,9),(1,10),(1,11),(2,5),(2,6),(2,7),(2,8),(2,10),(2,11),(3,4),(3,7),(3,8),(3,9),(3,10),(3,11),(4,5),(4,6),(4,7),(4,8),(4,9),(4,11),(5,6),(5,7),(5,8),(5,10),(6,7),(6,9),(6,10),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
11100 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ([(0,5),(0,9),(1,4),(1,9),(2,6),(2,8),(3,7),(3,8),(4,6),(4,10),(5,7),(5,10),(6,11),(7,11),(8,11),(9,10),(10,11)],12)
=> ([(0,3),(0,6),(0,7),(0,8),(0,9),(0,10),(0,11),(1,2),(1,4),(1,5),(1,8),(1,9),(1,10),(1,11),(2,3),(2,4),(2,5),(2,6),(2,7),(2,8),(2,9),(3,4),(3,5),(3,6),(3,7),(3,10),(3,11),(4,5),(4,7),(4,8),(4,9),(4,11),(5,6),(5,8),(5,9),(5,10),(6,7),(6,8),(6,10),(6,11),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
11101 => ([(0,3),(0,4),(1,2),(1,11),(2,8),(3,9),(3,10),(4,1),(4,9),(4,10),(6,7),(7,5),(8,5),(9,6),(10,6),(10,11),(11,7),(11,8)],12)
=> ([(0,7),(0,11),(1,5),(1,8),(2,6),(2,8),(3,4),(3,7),(3,11),(4,5),(4,9),(5,10),(6,10),(6,11),(7,9),(8,10),(9,10),(9,11)],12)
=> ([(0,3),(0,4),(0,5),(0,6),(0,9),(0,10),(0,11),(1,2),(1,4),(1,5),(1,7),(1,8),(1,10),(1,11),(2,6),(2,7),(2,8),(2,9),(2,10),(2,11),(3,4),(3,5),(3,6),(3,7),(3,8),(3,9),(3,11),(4,5),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,9),(5,10),(6,9),(6,10),(6,11),(7,8),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
11110 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ([(0,3),(0,7),(1,2),(1,6),(2,8),(3,9),(4,5),(4,8),(4,9),(5,6),(5,7),(6,8),(7,9)],10)
=> ([(0,1),(0,3),(0,5),(0,6),(0,7),(0,9),(1,2),(1,5),(1,6),(1,7),(1,8),(2,3),(2,4),(2,6),(2,8),(2,9),(3,4),(3,7),(3,8),(3,9),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,7),(6,8),(7,9),(8,9)],10)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 1
11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> ([(0,1),(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 2 = 1 + 1
000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
=> ([(0,1),(0,3),(0,4),(0,6),(1,2),(1,4),(1,5),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 2 + 1
000001 => ([(0,2),(0,6),(1,8),(2,7),(3,5),(3,9),(4,3),(4,11),(5,1),(5,10),(6,4),(6,7),(7,11),(9,10),(10,8),(11,9)],12)
=> ([(0,3),(0,11),(1,2),(1,8),(2,9),(3,10),(4,5),(4,6),(4,8),(5,7),(5,9),(6,7),(6,10),(7,11),(8,9),(10,11)],12)
=> ([(0,2),(0,3),(0,5),(0,6),(0,7),(0,9),(0,10),(0,11),(1,2),(1,3),(1,4),(1,6),(1,7),(1,8),(1,10),(1,11),(2,4),(2,5),(2,6),(2,8),(2,9),(2,10),(3,4),(3,5),(3,7),(3,8),(3,9),(3,11),(4,7),(4,8),(4,9),(4,10),(4,11),(5,6),(5,8),(5,9),(5,10),(5,11),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11),(8,10),(8,11),(9,10),(9,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3} + 1
000010 => ([(0,4),(0,5),(1,3),(1,12),(2,11),(3,2),(3,14),(4,10),(4,13),(5,1),(5,10),(5,13),(7,8),(8,9),(9,6),(10,7),(11,6),(12,8),(12,14),(13,7),(13,12),(14,9),(14,11)],15)
=> ([(0,9),(0,14),(1,7),(1,10),(2,8),(2,10),(3,4),(3,9),(3,14),(4,5),(4,11),(5,7),(5,13),(6,8),(6,13),(6,14),(7,12),(8,12),(9,11),(10,12),(11,13),(11,14),(12,13)],15)
=> ([(0,3),(0,5),(0,6),(0,8),(0,9),(0,10),(0,11),(0,12),(0,13),(0,14),(1,2),(1,4),(1,7),(1,8),(1,9),(1,10),(1,11),(1,12),(1,13),(1,14),(2,3),(2,4),(2,6),(2,7),(2,8),(2,9),(2,10),(2,13),(2,14),(3,4),(3,5),(3,6),(3,7),(3,11),(3,12),(3,13),(3,14),(4,5),(4,6),(4,7),(4,8),(4,9),(4,10),(4,13),(4,14),(5,6),(5,7),(5,8),(5,10),(5,11),(5,12),(5,13),(5,14),(6,8),(6,9),(6,11),(6,12),(6,13),(6,14),(7,8),(7,9),(7,10),(7,12),(7,13),(7,14),(8,9),(8,10),(8,11),(8,12),(9,10),(9,11),(9,12),(9,13),(10,11),(10,12),(10,14),(11,12),(11,13),(11,14),(12,13),(12,14),(13,14)],15)
=> ? ∊ {1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3} + 1
000011 => ([(0,5),(0,6),(1,4),(1,14),(2,11),(3,10),(4,3),(4,12),(5,1),(5,13),(6,2),(6,13),(8,9),(9,7),(10,7),(11,8),(12,9),(12,10),(13,11),(13,14),(14,8),(14,12)],15)
=> ([(0,7),(0,11),(1,6),(1,10),(2,8),(2,10),(3,9),(3,11),(4,8),(4,9),(4,14),(5,6),(5,7),(5,14),(6,12),(7,13),(8,12),(9,13),(10,12),(11,13),(12,14),(13,14)],15)
=> ([(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,11),(0,12),(0,13),(0,14),(1,2),(1,4),(1,7),(1,8),(1,9),(1,10),(1,11),(1,12),(1,13),(1,14),(2,3),(2,5),(2,6),(2,9),(2,10),(2,11),(2,12),(2,13),(2,14),(3,4),(3,5),(3,6),(3,7),(3,8),(3,9),(3,10),(3,11),(3,12),(4,5),(4,6),(4,7),(4,8),(4,9),(4,10),(4,13),(4,14),(5,6),(5,7),(5,8),(5,10),(5,11),(5,12),(5,14),(6,7),(6,8),(6,9),(6,11),(6,12),(6,13),(7,8),(7,9),(7,11),(7,13),(7,14),(8,10),(8,12),(8,13),(8,14),(9,10),(9,11),(9,12),(9,13),(9,14),(10,11),(10,12),(10,13),(10,14),(11,12),(11,13),(11,14),(12,13),(12,14),(13,14)],15)
=> ? ∊ {1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3} + 1
000100 => ([(0,3),(0,4),(1,10),(2,1),(2,6),(2,12),(3,14),(3,15),(4,2),(4,14),(4,15),(6,7),(7,8),(8,5),(9,5),(10,9),(11,7),(11,13),(12,10),(12,13),(13,8),(13,9),(14,6),(14,11),(15,11),(15,12)],16)
=> ([(0,7),(0,15),(1,5),(1,14),(2,6),(2,8),(3,4),(3,13),(3,15),(4,6),(4,10),(5,12),(5,13),(6,11),(7,8),(7,9),(8,11),(9,11),(9,12),(9,15),(10,11),(10,12),(10,13),(12,14),(13,14),(14,15)],16)
=> ([(0,1),(0,3),(0,4),(0,5),(0,7),(0,8),(0,9),(0,11),(0,13),(0,14),(0,15),(1,4),(1,5),(1,6),(1,7),(1,10),(1,11),(1,12),(1,13),(1,14),(1,15),(2,3),(2,5),(2,6),(2,8),(2,9),(2,10),(2,11),(2,12),(2,13),(2,14),(2,15),(3,6),(3,7),(3,8),(3,9),(3,10),(3,12),(3,13),(3,14),(3,15),(4,5),(4,7),(4,8),(4,9),(4,10),(4,11),(4,13),(4,14),(4,15),(5,7),(5,8),(5,9),(5,11),(5,12),(5,13),(5,15),(6,7),(6,8),(6,9),(6,10),(6,11),(6,12),(6,13),(6,14),(7,9),(7,11),(7,12),(7,13),(7,14),(7,15),(8,9),(8,10),(8,11),(8,12),(8,14),(8,15),(9,10),(9,12),(9,14),(9,15),(10,11),(10,12),(10,13),(10,14),(10,15),(11,12),(11,13),(11,15),(12,13),(12,14),(13,14),(13,15),(14,15)],16)
=> ? ∊ {1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3} + 1
000101 => ([(0,3),(0,4),(1,2),(1,14),(2,6),(3,13),(3,15),(4,1),(4,13),(4,15),(6,9),(7,8),(8,10),(9,5),(10,5),(11,8),(11,12),(12,9),(12,10),(13,7),(13,11),(14,6),(14,12),(15,7),(15,11),(15,14)],16)
=> ([(0,5),(0,7),(1,6),(1,8),(2,9),(2,14),(3,4),(3,8),(3,13),(4,10),(4,15),(5,6),(5,11),(6,12),(7,11),(7,14),(8,12),(9,10),(9,15),(10,13),(10,14),(11,12),(11,15),(12,13),(13,15),(14,15)],16)
=> ([(0,4),(0,5),(0,8),(0,9),(0,10),(0,11),(0,12),(0,13),(0,14),(0,15),(1,2),(1,3),(1,6),(1,7),(1,8),(1,9),(1,11),(1,12),(1,13),(1,14),(1,15),(2,3),(2,5),(2,6),(2,7),(2,9),(2,10),(2,11),(2,12),(2,14),(2,15),(3,4),(3,6),(3,7),(3,10),(3,11),(3,12),(3,13),(3,14),(3,15),(4,5),(4,8),(4,9),(4,10),(4,11),(4,12),(4,13),(4,14),(4,15),(5,6),(5,7),(5,8),(5,9),(5,10),(5,13),(5,14),(5,15),(6,7),(6,8),(6,9),(6,10),(6,11),(6,12),(6,14),(6,15),(7,8),(7,9),(7,11),(7,12),(7,13),(7,14),(7,15),(8,9),(8,10),(8,11),(8,12),(8,13),(8,15),(9,10),(9,11),(9,13),(9,15),(10,12),(10,13),(10,14),(10,15),(11,12),(11,13),(11,14),(12,13),(12,14),(13,14),(13,15),(14,15)],16)
=> ? ∊ {1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3} + 1
000110 => ([(0,4),(0,5),(1,11),(2,1),(2,13),(3,7),(3,14),(4,2),(4,12),(4,16),(5,3),(5,12),(5,16),(7,8),(8,9),(9,6),(10,6),(11,10),(12,7),(13,11),(13,15),(14,8),(14,15),(15,9),(15,10),(16,13),(16,14)],17)
=> ([(0,15),(0,16),(1,7),(1,10),(2,8),(2,9),(3,4),(3,5),(3,6),(4,15),(4,16),(5,11),(5,15),(6,8),(6,11),(7,14),(7,16),(8,13),(9,10),(9,13),(10,14),(11,12),(11,13),(12,14),(12,15),(12,16),(13,14)],17)
=> ([(0,3),(0,6),(0,7),(0,8),(0,9),(0,10),(0,11),(0,12),(0,13),(0,14),(0,15),(0,16),(1,2),(1,4),(1,5),(1,6),(1,7),(1,8),(1,9),(1,12),(1,13),(1,14),(1,15),(1,16),(2,4),(2,5),(2,7),(2,8),(2,10),(2,11),(2,12),(2,13),(2,14),(2,15),(2,16),(3,4),(3,5),(3,6),(3,9),(3,10),(3,11),(3,12),(3,13),(3,14),(3,15),(3,16),(4,5),(4,6),(4,7),(4,8),(4,9),(4,11),(4,13),(4,15),(4,16),(5,7),(5,8),(5,9),(5,10),(5,11),(5,13),(5,15),(5,16),(6,7),(6,8),(6,9),(6,10),(6,11),(6,12),(6,13),(6,14),(6,16),(7,8),(7,9),(7,10),(7,12),(7,13),(7,14),(7,15),(8,10),(8,11),(8,12),(8,13),(8,14),(8,15),(9,10),(9,11),(9,12),(9,13),(9,14),(9,16),(10,11),(10,12),(10,14),(10,15),(10,16),(11,12),(11,14),(11,15),(11,16),(12,14),(12,15),(12,16),(13,14),(13,15),(13,16),(14,15),(14,16),(15,16)],17)
=> ? ∊ {1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3} + 1
111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
=> ([(0,1),(0,3),(0,4),(0,6),(1,2),(1,4),(1,5),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 2 + 1
Description
The arboricity of a graph.
This is the minimum number of forests that covers all edges of the graph.
Matching statistic: St001580
Values
0 => ([(0,1)],2)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 2 = 0 + 2
1 => ([(0,1)],2)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 2 = 0 + 2
00 => ([(0,2),(2,1)],3)
=> ([(0,2),(1,2)],3)
=> ([(0,2),(1,2)],3)
=> 2 = 0 + 2
01 => ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> 3 = 1 + 2
10 => ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> 3 = 1 + 2
11 => ([(0,2),(2,1)],3)
=> ([(0,2),(1,2)],3)
=> ([(0,2),(1,2)],3)
=> 2 = 0 + 2
000 => ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(1,2),(2,3)],4)
=> ([(0,3),(1,2),(2,3)],4)
=> 2 = 0 + 2
001 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,5),(3,4),(4,5)],6)
=> 3 = 1 + 2
010 => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6)
=> 3 = 1 + 2
011 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,5),(3,4),(4,5)],6)
=> 3 = 1 + 2
100 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,5),(3,4),(4,5)],6)
=> 3 = 1 + 2
101 => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6)
=> 3 = 1 + 2
110 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,5),(3,4),(4,5)],6)
=> 3 = 1 + 2
111 => ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(1,2),(2,3)],4)
=> ([(0,3),(1,2),(2,3)],4)
=> 2 = 0 + 2
0000 => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> 3 = 1 + 2
0001 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,3),(0,7),(1,2),(1,4),(2,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ([(0,3),(0,5),(0,6),(0,7),(1,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6),(6,7)],8)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2} + 2
0010 => ([(0,2),(0,3),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,5),(8,5),(8,6)],9)
=> ([(0,5),(0,8),(1,4),(1,6),(2,6),(2,8),(3,4),(3,5),(3,8),(4,7),(5,7),(6,7),(7,8)],9)
=> ([(0,2),(0,3),(0,4),(0,8),(1,5),(1,6),(1,7),(1,8),(2,3),(2,4),(2,5),(2,6),(3,4),(3,7),(3,8),(4,6),(4,7),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2} + 2
0011 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,6),(0,7),(1,4),(1,5),(2,5),(2,7),(3,4),(3,6),(4,8),(5,8),(6,8),(7,8)],9)
=> ([(0,5),(0,6),(0,7),(0,8),(1,2),(1,3),(1,4),(1,7),(1,8),(2,3),(2,4),(2,5),(2,6),(3,4),(3,6),(3,8),(4,5),(4,7),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2} + 2
0100 => ([(0,2),(0,3),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,5),(8,5),(8,6)],9)
=> ([(0,5),(0,8),(1,4),(1,6),(2,6),(2,8),(3,4),(3,5),(3,8),(4,7),(5,7),(6,7),(7,8)],9)
=> ([(0,2),(0,3),(0,4),(0,8),(1,5),(1,6),(1,7),(1,8),(2,3),(2,4),(2,5),(2,6),(3,4),(3,7),(3,8),(4,6),(4,7),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2} + 2
0101 => ([(0,1),(0,2),(1,6),(1,7),(2,6),(2,7),(4,3),(5,3),(6,4),(6,5),(7,4),(7,5)],8)
=> ([(0,4),(0,5),(1,2),(1,3),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
=> ([(0,1),(0,6),(0,7),(1,6),(1,7),(2,3),(2,4),(2,5),(2,7),(3,4),(3,5),(3,7),(4,5),(4,6),(5,6),(6,7)],8)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2} + 2
0110 => ([(0,2),(0,3),(1,5),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,6),(8,5)],9)
=> ([(0,5),(0,6),(1,7),(1,8),(2,5),(2,6),(2,8),(3,6),(3,7),(3,8),(4,5),(4,7),(4,8)],9)
=> ([(0,4),(0,5),(0,6),(0,8),(1,2),(1,3),(1,4),(1,7),(1,8),(2,3),(2,6),(2,7),(2,8),(3,5),(3,7),(3,8),(4,5),(4,6),(4,8),(5,6),(5,7),(6,7),(7,8)],9)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2} + 2
0111 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,3),(0,7),(1,2),(1,4),(2,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ([(0,3),(0,5),(0,6),(0,7),(1,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6),(6,7)],8)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2} + 2
1000 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,3),(0,7),(1,2),(1,4),(2,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ([(0,3),(0,5),(0,6),(0,7),(1,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6),(6,7)],8)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2} + 2
1001 => ([(0,2),(0,3),(1,5),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,6),(8,5)],9)
=> ([(0,5),(0,6),(1,7),(1,8),(2,5),(2,6),(2,8),(3,6),(3,7),(3,8),(4,5),(4,7),(4,8)],9)
=> ([(0,4),(0,5),(0,6),(0,8),(1,2),(1,3),(1,4),(1,7),(1,8),(2,3),(2,6),(2,7),(2,8),(3,5),(3,7),(3,8),(4,5),(4,6),(4,8),(5,6),(5,7),(6,7),(7,8)],9)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2} + 2
1010 => ([(0,1),(0,2),(1,6),(1,7),(2,6),(2,7),(4,3),(5,3),(6,4),(6,5),(7,4),(7,5)],8)
=> ([(0,4),(0,5),(1,2),(1,3),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
=> ([(0,1),(0,6),(0,7),(1,6),(1,7),(2,3),(2,4),(2,5),(2,7),(3,4),(3,5),(3,7),(4,5),(4,6),(5,6),(6,7)],8)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2} + 2
1011 => ([(0,2),(0,3),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,5),(8,5),(8,6)],9)
=> ([(0,5),(0,8),(1,4),(1,6),(2,6),(2,8),(3,4),(3,5),(3,8),(4,7),(5,7),(6,7),(7,8)],9)
=> ([(0,2),(0,3),(0,4),(0,8),(1,5),(1,6),(1,7),(1,8),(2,3),(2,4),(2,5),(2,6),(3,4),(3,7),(3,8),(4,6),(4,7),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2} + 2
1100 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,6),(0,7),(1,4),(1,5),(2,5),(2,7),(3,4),(3,6),(4,8),(5,8),(6,8),(7,8)],9)
=> ([(0,5),(0,6),(0,7),(0,8),(1,2),(1,3),(1,4),(1,7),(1,8),(2,3),(2,4),(2,5),(2,6),(3,4),(3,6),(3,8),(4,5),(4,7),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2} + 2
1101 => ([(0,2),(0,3),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,5),(8,5),(8,6)],9)
=> ([(0,5),(0,8),(1,4),(1,6),(2,6),(2,8),(3,4),(3,5),(3,8),(4,7),(5,7),(6,7),(7,8)],9)
=> ([(0,2),(0,3),(0,4),(0,8),(1,5),(1,6),(1,7),(1,8),(2,3),(2,4),(2,5),(2,6),(3,4),(3,7),(3,8),(4,6),(4,7),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2} + 2
1110 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,3),(0,7),(1,2),(1,4),(2,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ([(0,3),(0,5),(0,6),(0,7),(1,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6),(6,7)],8)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2} + 2
1111 => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> 3 = 1 + 2
00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> ([(0,1),(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 4 = 2 + 2
00001 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ([(0,3),(0,7),(1,2),(1,6),(2,8),(3,9),(4,5),(4,8),(4,9),(5,6),(5,7),(6,8),(7,9)],10)
=> ([(0,1),(0,3),(0,5),(0,6),(0,7),(0,9),(1,2),(1,5),(1,6),(1,7),(1,8),(2,3),(2,4),(2,6),(2,8),(2,9),(3,4),(3,7),(3,8),(3,9),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,7),(6,8),(7,9),(8,9)],10)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 2
00010 => ([(0,3),(0,4),(1,2),(1,11),(2,8),(3,9),(3,10),(4,1),(4,9),(4,10),(6,7),(7,5),(8,5),(9,6),(10,6),(10,11),(11,7),(11,8)],12)
=> ([(0,7),(0,11),(1,5),(1,8),(2,6),(2,8),(3,4),(3,7),(3,11),(4,5),(4,9),(5,10),(6,10),(6,11),(7,9),(8,10),(9,10),(9,11)],12)
=> ([(0,3),(0,4),(0,5),(0,6),(0,9),(0,10),(0,11),(1,2),(1,4),(1,5),(1,7),(1,8),(1,10),(1,11),(2,6),(2,7),(2,8),(2,9),(2,10),(2,11),(3,4),(3,5),(3,6),(3,7),(3,8),(3,9),(3,11),(4,5),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,9),(5,10),(6,9),(6,10),(6,11),(7,8),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 2
00011 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ([(0,5),(0,9),(1,4),(1,9),(2,6),(2,8),(3,7),(3,8),(4,6),(4,10),(5,7),(5,10),(6,11),(7,11),(8,11),(9,10),(10,11)],12)
=> ([(0,3),(0,6),(0,7),(0,8),(0,9),(0,10),(0,11),(1,2),(1,4),(1,5),(1,8),(1,9),(1,10),(1,11),(2,3),(2,4),(2,5),(2,6),(2,7),(2,8),(2,9),(3,4),(3,5),(3,6),(3,7),(3,10),(3,11),(4,5),(4,7),(4,8),(4,9),(4,11),(5,6),(5,8),(5,9),(5,10),(6,7),(6,8),(6,10),(6,11),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 2
00100 => ([(0,2),(0,3),(1,5),(1,6),(2,10),(2,11),(3,1),(3,10),(3,11),(5,8),(6,7),(7,4),(8,4),(9,7),(9,8),(10,6),(10,9),(11,5),(11,9)],12)
=> ([(0,7),(0,11),(1,5),(1,6),(2,3),(2,4),(2,11),(3,6),(3,9),(4,5),(4,8),(5,10),(6,10),(7,8),(7,9),(8,10),(8,11),(9,10),(9,11)],12)
=> ([(0,3),(0,4),(0,5),(0,6),(0,8),(0,9),(0,11),(1,2),(1,5),(1,6),(1,7),(1,9),(1,10),(1,11),(2,5),(2,6),(2,7),(2,8),(2,10),(2,11),(3,4),(3,7),(3,8),(3,9),(3,10),(3,11),(4,5),(4,6),(4,7),(4,8),(4,9),(4,11),(5,6),(5,7),(5,8),(5,10),(6,7),(6,9),(6,10),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 2
00101 => ([(0,2),(0,3),(1,8),(2,10),(2,11),(3,1),(3,10),(3,11),(5,6),(6,4),(7,4),(8,7),(9,6),(9,7),(10,5),(10,9),(11,5),(11,8),(11,9)],12)
=> ([(0,5),(0,6),(1,7),(1,10),(2,4),(2,10),(3,6),(3,8),(3,11),(4,5),(4,11),(5,9),(6,9),(7,8),(7,11),(8,9),(8,10),(9,11),(10,11)],12)
=> ([(0,3),(0,7),(0,8),(0,9),(0,10),(0,11),(1,2),(1,4),(1,5),(1,6),(1,7),(1,8),(1,11),(2,4),(2,5),(2,6),(2,9),(2,10),(2,11),(3,5),(3,7),(3,8),(3,9),(3,10),(3,11),(4,5),(4,6),(4,7),(4,8),(4,9),(4,11),(5,6),(5,7),(5,10),(5,11),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(8,9),(8,10),(9,10),(9,11),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 2
00110 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ([(0,11),(0,12),(1,8),(1,12),(2,6),(2,7),(3,4),(3,11),(3,12),(4,5),(4,6),(5,9),(5,11),(6,9),(7,8),(7,9),(8,10),(9,10),(10,11),(10,12)],13)
=> ([(0,4),(0,5),(0,6),(0,7),(0,9),(0,10),(0,11),(0,12),(1,2),(1,3),(1,4),(1,6),(1,7),(1,8),(1,9),(1,12),(2,3),(2,6),(2,7),(2,8),(2,9),(2,11),(2,12),(3,5),(3,8),(3,9),(3,10),(3,11),(3,12),(4,5),(4,6),(4,7),(4,8),(4,10),(4,11),(4,12),(5,6),(5,7),(5,8),(5,10),(5,11),(5,12),(6,7),(6,9),(6,10),(6,11),(7,8),(7,10),(7,11),(8,9),(8,10),(8,12),(9,10),(9,11),(9,12),(10,11),(10,12),(11,12)],13)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 2
00111 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ([(0,5),(0,9),(1,4),(1,9),(2,6),(2,8),(3,7),(3,8),(4,6),(4,10),(5,7),(5,10),(6,11),(7,11),(8,11),(9,10),(10,11)],12)
=> ([(0,3),(0,6),(0,7),(0,8),(0,9),(0,10),(0,11),(1,2),(1,4),(1,5),(1,8),(1,9),(1,10),(1,11),(2,3),(2,4),(2,5),(2,6),(2,7),(2,8),(2,9),(3,4),(3,5),(3,6),(3,7),(3,10),(3,11),(4,5),(4,7),(4,8),(4,9),(4,11),(5,6),(5,8),(5,9),(5,10),(6,7),(6,8),(6,10),(6,11),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 2
01000 => ([(0,3),(0,4),(1,2),(1,11),(2,8),(3,9),(3,10),(4,1),(4,9),(4,10),(6,7),(7,5),(8,5),(9,6),(10,6),(10,11),(11,7),(11,8)],12)
=> ([(0,7),(0,11),(1,5),(1,8),(2,6),(2,8),(3,4),(3,7),(3,11),(4,5),(4,9),(5,10),(6,10),(6,11),(7,9),(8,10),(9,10),(9,11)],12)
=> ([(0,3),(0,4),(0,5),(0,6),(0,9),(0,10),(0,11),(1,2),(1,4),(1,5),(1,7),(1,8),(1,10),(1,11),(2,6),(2,7),(2,8),(2,9),(2,10),(2,11),(3,4),(3,5),(3,6),(3,7),(3,8),(3,9),(3,11),(4,5),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,9),(5,10),(6,9),(6,10),(6,11),(7,8),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 2
01001 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
=> ([(0,7),(0,11),(1,5),(1,6),(2,3),(2,10),(2,11),(3,5),(3,8),(4,6),(4,8),(4,9),(5,10),(6,10),(7,8),(7,9),(8,11),(9,10),(9,11)],12)
=> ([(0,2),(0,4),(0,5),(0,7),(0,8),(0,9),(0,11),(1,3),(1,6),(1,7),(1,8),(1,9),(1,10),(1,11),(2,3),(2,4),(2,5),(2,8),(2,10),(2,11),(3,6),(3,7),(3,9),(3,10),(3,11),(4,5),(4,6),(4,7),(4,8),(4,9),(4,11),(5,6),(5,7),(5,8),(5,10),(5,11),(6,7),(6,9),(6,10),(6,11),(7,9),(7,10),(8,9),(8,10),(8,11),(9,10),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 2
01010 => ([(0,1),(0,2),(1,8),(1,9),(2,8),(2,9),(4,3),(5,3),(6,4),(6,5),(7,4),(7,5),(8,6),(8,7),(9,6),(9,7)],10)
=> ([(0,4),(0,5),(1,2),(1,3),(2,6),(2,7),(3,6),(3,7),(4,8),(4,9),(5,8),(5,9),(6,8),(6,9),(7,8),(7,9)],10)
=> ([(0,1),(0,4),(0,5),(0,8),(0,9),(1,4),(1,5),(1,8),(1,9),(2,3),(2,6),(2,7),(2,8),(2,9),(3,6),(3,7),(3,8),(3,9),(4,5),(4,6),(4,7),(4,9),(5,6),(5,7),(5,9),(6,7),(6,8),(7,8),(8,9)],10)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 2
01011 => ([(0,2),(0,3),(1,8),(2,10),(2,11),(3,1),(3,10),(3,11),(5,6),(6,4),(7,4),(8,7),(9,6),(9,7),(10,5),(10,9),(11,5),(11,8),(11,9)],12)
=> ([(0,5),(0,6),(1,7),(1,10),(2,4),(2,10),(3,6),(3,8),(3,11),(4,5),(4,11),(5,9),(6,9),(7,8),(7,11),(8,9),(8,10),(9,11),(10,11)],12)
=> ([(0,3),(0,7),(0,8),(0,9),(0,10),(0,11),(1,2),(1,4),(1,5),(1,6),(1,7),(1,8),(1,11),(2,4),(2,5),(2,6),(2,9),(2,10),(2,11),(3,5),(3,7),(3,8),(3,9),(3,10),(3,11),(4,5),(4,6),(4,7),(4,8),(4,9),(4,11),(5,6),(5,7),(5,10),(5,11),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(8,9),(8,10),(9,10),(9,11),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 2
01100 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ([(0,11),(0,12),(1,8),(1,12),(2,6),(2,7),(3,4),(3,11),(3,12),(4,5),(4,6),(5,9),(5,11),(6,9),(7,8),(7,9),(8,10),(9,10),(10,11),(10,12)],13)
=> ([(0,4),(0,5),(0,6),(0,7),(0,9),(0,10),(0,11),(0,12),(1,2),(1,3),(1,4),(1,6),(1,7),(1,8),(1,9),(1,12),(2,3),(2,6),(2,7),(2,8),(2,9),(2,11),(2,12),(3,5),(3,8),(3,9),(3,10),(3,11),(3,12),(4,5),(4,6),(4,7),(4,8),(4,10),(4,11),(4,12),(5,6),(5,7),(5,8),(5,10),(5,11),(5,12),(6,7),(6,9),(6,10),(6,11),(7,8),(7,10),(7,11),(8,9),(8,10),(8,12),(9,10),(9,11),(9,12),(10,11),(10,12),(11,12)],13)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 2
01101 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
=> ([(0,7),(0,11),(1,5),(1,6),(2,3),(2,10),(2,11),(3,5),(3,8),(4,6),(4,8),(4,9),(5,10),(6,10),(7,8),(7,9),(8,11),(9,10),(9,11)],12)
=> ([(0,2),(0,4),(0,5),(0,7),(0,8),(0,9),(0,11),(1,3),(1,6),(1,7),(1,8),(1,9),(1,10),(1,11),(2,3),(2,4),(2,5),(2,8),(2,10),(2,11),(3,6),(3,7),(3,9),(3,10),(3,11),(4,5),(4,6),(4,7),(4,8),(4,9),(4,11),(5,6),(5,7),(5,8),(5,10),(5,11),(6,7),(6,9),(6,10),(6,11),(7,9),(7,10),(8,9),(8,10),(8,11),(9,10),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 2
01110 => ([(0,3),(0,4),(1,2),(1,10),(1,11),(2,8),(2,9),(3,6),(3,7),(4,1),(4,6),(4,7),(6,11),(7,10),(8,5),(9,5),(10,8),(11,9)],12)
=> ([(0,9),(0,11),(1,7),(1,8),(2,5),(2,9),(2,11),(3,4),(3,9),(3,11),(4,7),(4,10),(5,8),(5,10),(6,7),(6,8),(6,10),(10,11)],12)
=> ([(0,2),(0,3),(0,4),(0,7),(0,8),(0,9),(0,11),(1,5),(1,6),(1,7),(1,8),(1,9),(1,10),(1,11),(2,3),(2,4),(2,5),(2,6),(2,7),(2,10),(2,11),(3,4),(3,6),(3,7),(3,9),(3,10),(3,11),(4,5),(4,7),(4,8),(4,10),(4,11),(5,6),(5,8),(5,9),(5,10),(5,11),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,11),(8,9),(8,10),(9,10),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 2
01111 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ([(0,3),(0,7),(1,2),(1,6),(2,8),(3,9),(4,5),(4,8),(4,9),(5,6),(5,7),(6,8),(7,9)],10)
=> ([(0,1),(0,3),(0,5),(0,6),(0,7),(0,9),(1,2),(1,5),(1,6),(1,7),(1,8),(2,3),(2,4),(2,6),(2,8),(2,9),(3,4),(3,7),(3,8),(3,9),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,7),(6,8),(7,9),(8,9)],10)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 2
10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ([(0,3),(0,7),(1,2),(1,6),(2,8),(3,9),(4,5),(4,8),(4,9),(5,6),(5,7),(6,8),(7,9)],10)
=> ([(0,1),(0,3),(0,5),(0,6),(0,7),(0,9),(1,2),(1,5),(1,6),(1,7),(1,8),(2,3),(2,4),(2,6),(2,8),(2,9),(3,4),(3,7),(3,8),(3,9),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,7),(6,8),(7,9),(8,9)],10)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 2
10001 => ([(0,3),(0,4),(1,2),(1,10),(1,11),(2,8),(2,9),(3,6),(3,7),(4,1),(4,6),(4,7),(6,11),(7,10),(8,5),(9,5),(10,8),(11,9)],12)
=> ([(0,9),(0,11),(1,7),(1,8),(2,5),(2,9),(2,11),(3,4),(3,9),(3,11),(4,7),(4,10),(5,8),(5,10),(6,7),(6,8),(6,10),(10,11)],12)
=> ([(0,2),(0,3),(0,4),(0,7),(0,8),(0,9),(0,11),(1,5),(1,6),(1,7),(1,8),(1,9),(1,10),(1,11),(2,3),(2,4),(2,5),(2,6),(2,7),(2,10),(2,11),(3,4),(3,6),(3,7),(3,9),(3,10),(3,11),(4,5),(4,7),(4,8),(4,10),(4,11),(5,6),(5,8),(5,9),(5,10),(5,11),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,11),(8,9),(8,10),(9,10),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 2
10010 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
=> ([(0,7),(0,11),(1,5),(1,6),(2,3),(2,10),(2,11),(3,5),(3,8),(4,6),(4,8),(4,9),(5,10),(6,10),(7,8),(7,9),(8,11),(9,10),(9,11)],12)
=> ([(0,2),(0,4),(0,5),(0,7),(0,8),(0,9),(0,11),(1,3),(1,6),(1,7),(1,8),(1,9),(1,10),(1,11),(2,3),(2,4),(2,5),(2,8),(2,10),(2,11),(3,6),(3,7),(3,9),(3,10),(3,11),(4,5),(4,6),(4,7),(4,8),(4,9),(4,11),(5,6),(5,7),(5,8),(5,10),(5,11),(6,7),(6,9),(6,10),(6,11),(7,9),(7,10),(8,9),(8,10),(8,11),(9,10),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 2
10011 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ([(0,11),(0,12),(1,8),(1,12),(2,6),(2,7),(3,4),(3,11),(3,12),(4,5),(4,6),(5,9),(5,11),(6,9),(7,8),(7,9),(8,10),(9,10),(10,11),(10,12)],13)
=> ([(0,4),(0,5),(0,6),(0,7),(0,9),(0,10),(0,11),(0,12),(1,2),(1,3),(1,4),(1,6),(1,7),(1,8),(1,9),(1,12),(2,3),(2,6),(2,7),(2,8),(2,9),(2,11),(2,12),(3,5),(3,8),(3,9),(3,10),(3,11),(3,12),(4,5),(4,6),(4,7),(4,8),(4,10),(4,11),(4,12),(5,6),(5,7),(5,8),(5,10),(5,11),(5,12),(6,7),(6,9),(6,10),(6,11),(7,8),(7,10),(7,11),(8,9),(8,10),(8,12),(9,10),(9,11),(9,12),(10,11),(10,12),(11,12)],13)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 2
10100 => ([(0,2),(0,3),(1,8),(2,10),(2,11),(3,1),(3,10),(3,11),(5,6),(6,4),(7,4),(8,7),(9,6),(9,7),(10,5),(10,9),(11,5),(11,8),(11,9)],12)
=> ([(0,5),(0,6),(1,7),(1,10),(2,4),(2,10),(3,6),(3,8),(3,11),(4,5),(4,11),(5,9),(6,9),(7,8),(7,11),(8,9),(8,10),(9,11),(10,11)],12)
=> ([(0,3),(0,7),(0,8),(0,9),(0,10),(0,11),(1,2),(1,4),(1,5),(1,6),(1,7),(1,8),(1,11),(2,4),(2,5),(2,6),(2,9),(2,10),(2,11),(3,5),(3,7),(3,8),(3,9),(3,10),(3,11),(4,5),(4,6),(4,7),(4,8),(4,9),(4,11),(5,6),(5,7),(5,10),(5,11),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(8,9),(8,10),(9,10),(9,11),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 2
10101 => ([(0,1),(0,2),(1,8),(1,9),(2,8),(2,9),(4,3),(5,3),(6,4),(6,5),(7,4),(7,5),(8,6),(8,7),(9,6),(9,7)],10)
=> ([(0,4),(0,5),(1,2),(1,3),(2,6),(2,7),(3,6),(3,7),(4,8),(4,9),(5,8),(5,9),(6,8),(6,9),(7,8),(7,9)],10)
=> ([(0,1),(0,4),(0,5),(0,8),(0,9),(1,4),(1,5),(1,8),(1,9),(2,3),(2,6),(2,7),(2,8),(2,9),(3,6),(3,7),(3,8),(3,9),(4,5),(4,6),(4,7),(4,9),(5,6),(5,7),(5,9),(6,7),(6,8),(7,8),(8,9)],10)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 2
10110 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
=> ([(0,7),(0,11),(1,5),(1,6),(2,3),(2,10),(2,11),(3,5),(3,8),(4,6),(4,8),(4,9),(5,10),(6,10),(7,8),(7,9),(8,11),(9,10),(9,11)],12)
=> ([(0,2),(0,4),(0,5),(0,7),(0,8),(0,9),(0,11),(1,3),(1,6),(1,7),(1,8),(1,9),(1,10),(1,11),(2,3),(2,4),(2,5),(2,8),(2,10),(2,11),(3,6),(3,7),(3,9),(3,10),(3,11),(4,5),(4,6),(4,7),(4,8),(4,9),(4,11),(5,6),(5,7),(5,8),(5,10),(5,11),(6,7),(6,9),(6,10),(6,11),(7,9),(7,10),(8,9),(8,10),(8,11),(9,10),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 2
10111 => ([(0,3),(0,4),(1,2),(1,11),(2,8),(3,9),(3,10),(4,1),(4,9),(4,10),(6,7),(7,5),(8,5),(9,6),(10,6),(10,11),(11,7),(11,8)],12)
=> ([(0,7),(0,11),(1,5),(1,8),(2,6),(2,8),(3,4),(3,7),(3,11),(4,5),(4,9),(5,10),(6,10),(6,11),(7,9),(8,10),(9,10),(9,11)],12)
=> ([(0,3),(0,4),(0,5),(0,6),(0,9),(0,10),(0,11),(1,2),(1,4),(1,5),(1,7),(1,8),(1,10),(1,11),(2,6),(2,7),(2,8),(2,9),(2,10),(2,11),(3,4),(3,5),(3,6),(3,7),(3,8),(3,9),(3,11),(4,5),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,9),(5,10),(6,9),(6,10),(6,11),(7,8),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 2
11000 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ([(0,5),(0,9),(1,4),(1,9),(2,6),(2,8),(3,7),(3,8),(4,6),(4,10),(5,7),(5,10),(6,11),(7,11),(8,11),(9,10),(10,11)],12)
=> ([(0,3),(0,6),(0,7),(0,8),(0,9),(0,10),(0,11),(1,2),(1,4),(1,5),(1,8),(1,9),(1,10),(1,11),(2,3),(2,4),(2,5),(2,6),(2,7),(2,8),(2,9),(3,4),(3,5),(3,6),(3,7),(3,10),(3,11),(4,5),(4,7),(4,8),(4,9),(4,11),(5,6),(5,8),(5,9),(5,10),(6,7),(6,8),(6,10),(6,11),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 2
11001 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ([(0,11),(0,12),(1,8),(1,12),(2,6),(2,7),(3,4),(3,11),(3,12),(4,5),(4,6),(5,9),(5,11),(6,9),(7,8),(7,9),(8,10),(9,10),(10,11),(10,12)],13)
=> ([(0,4),(0,5),(0,6),(0,7),(0,9),(0,10),(0,11),(0,12),(1,2),(1,3),(1,4),(1,6),(1,7),(1,8),(1,9),(1,12),(2,3),(2,6),(2,7),(2,8),(2,9),(2,11),(2,12),(3,5),(3,8),(3,9),(3,10),(3,11),(3,12),(4,5),(4,6),(4,7),(4,8),(4,10),(4,11),(4,12),(5,6),(5,7),(5,8),(5,10),(5,11),(5,12),(6,7),(6,9),(6,10),(6,11),(7,8),(7,10),(7,11),(8,9),(8,10),(8,12),(9,10),(9,11),(9,12),(10,11),(10,12),(11,12)],13)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 2
11010 => ([(0,2),(0,3),(1,8),(2,10),(2,11),(3,1),(3,10),(3,11),(5,6),(6,4),(7,4),(8,7),(9,6),(9,7),(10,5),(10,9),(11,5),(11,8),(11,9)],12)
=> ([(0,5),(0,6),(1,7),(1,10),(2,4),(2,10),(3,6),(3,8),(3,11),(4,5),(4,11),(5,9),(6,9),(7,8),(7,11),(8,9),(8,10),(9,11),(10,11)],12)
=> ([(0,3),(0,7),(0,8),(0,9),(0,10),(0,11),(1,2),(1,4),(1,5),(1,6),(1,7),(1,8),(1,11),(2,4),(2,5),(2,6),(2,9),(2,10),(2,11),(3,5),(3,7),(3,8),(3,9),(3,10),(3,11),(4,5),(4,6),(4,7),(4,8),(4,9),(4,11),(5,6),(5,7),(5,10),(5,11),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(8,9),(8,10),(9,10),(9,11),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 2
11011 => ([(0,2),(0,3),(1,5),(1,6),(2,10),(2,11),(3,1),(3,10),(3,11),(5,8),(6,7),(7,4),(8,4),(9,7),(9,8),(10,6),(10,9),(11,5),(11,9)],12)
=> ([(0,7),(0,11),(1,5),(1,6),(2,3),(2,4),(2,11),(3,6),(3,9),(4,5),(4,8),(5,10),(6,10),(7,8),(7,9),(8,10),(8,11),(9,10),(9,11)],12)
=> ([(0,3),(0,4),(0,5),(0,6),(0,8),(0,9),(0,11),(1,2),(1,5),(1,6),(1,7),(1,9),(1,10),(1,11),(2,5),(2,6),(2,7),(2,8),(2,10),(2,11),(3,4),(3,7),(3,8),(3,9),(3,10),(3,11),(4,5),(4,6),(4,7),(4,8),(4,9),(4,11),(5,6),(5,7),(5,8),(5,10),(6,7),(6,9),(6,10),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 2
11100 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ([(0,5),(0,9),(1,4),(1,9),(2,6),(2,8),(3,7),(3,8),(4,6),(4,10),(5,7),(5,10),(6,11),(7,11),(8,11),(9,10),(10,11)],12)
=> ([(0,3),(0,6),(0,7),(0,8),(0,9),(0,10),(0,11),(1,2),(1,4),(1,5),(1,8),(1,9),(1,10),(1,11),(2,3),(2,4),(2,5),(2,6),(2,7),(2,8),(2,9),(3,4),(3,5),(3,6),(3,7),(3,10),(3,11),(4,5),(4,7),(4,8),(4,9),(4,11),(5,6),(5,8),(5,9),(5,10),(6,7),(6,8),(6,10),(6,11),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 2
11101 => ([(0,3),(0,4),(1,2),(1,11),(2,8),(3,9),(3,10),(4,1),(4,9),(4,10),(6,7),(7,5),(8,5),(9,6),(10,6),(10,11),(11,7),(11,8)],12)
=> ([(0,7),(0,11),(1,5),(1,8),(2,6),(2,8),(3,4),(3,7),(3,11),(4,5),(4,9),(5,10),(6,10),(6,11),(7,9),(8,10),(9,10),(9,11)],12)
=> ([(0,3),(0,4),(0,5),(0,6),(0,9),(0,10),(0,11),(1,2),(1,4),(1,5),(1,7),(1,8),(1,10),(1,11),(2,6),(2,7),(2,8),(2,9),(2,10),(2,11),(3,4),(3,5),(3,6),(3,7),(3,8),(3,9),(3,11),(4,5),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,9),(5,10),(6,9),(6,10),(6,11),(7,8),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 2
11110 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ([(0,3),(0,7),(1,2),(1,6),(2,8),(3,9),(4,5),(4,8),(4,9),(5,6),(5,7),(6,8),(7,9)],10)
=> ([(0,1),(0,3),(0,5),(0,6),(0,7),(0,9),(1,2),(1,5),(1,6),(1,7),(1,8),(2,3),(2,4),(2,6),(2,8),(2,9),(3,4),(3,7),(3,8),(3,9),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,7),(6,8),(7,9),(8,9)],10)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} + 2
11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> ([(0,1),(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 4 = 2 + 2
000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
=> ([(0,1),(0,3),(0,4),(0,6),(1,2),(1,4),(1,5),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 5 = 3 + 2
000001 => ([(0,2),(0,6),(1,8),(2,7),(3,5),(3,9),(4,3),(4,11),(5,1),(5,10),(6,4),(6,7),(7,11),(9,10),(10,8),(11,9)],12)
=> ([(0,3),(0,11),(1,2),(1,8),(2,9),(3,10),(4,5),(4,6),(4,8),(5,7),(5,9),(6,7),(6,10),(7,11),(8,9),(10,11)],12)
=> ([(0,2),(0,3),(0,5),(0,6),(0,7),(0,9),(0,10),(0,11),(1,2),(1,3),(1,4),(1,6),(1,7),(1,8),(1,10),(1,11),(2,4),(2,5),(2,6),(2,8),(2,9),(2,10),(3,4),(3,5),(3,7),(3,8),(3,9),(3,11),(4,7),(4,8),(4,9),(4,10),(4,11),(5,6),(5,8),(5,9),(5,10),(5,11),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11),(8,10),(8,11),(9,10),(9,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3} + 2
000010 => ([(0,4),(0,5),(1,3),(1,12),(2,11),(3,2),(3,14),(4,10),(4,13),(5,1),(5,10),(5,13),(7,8),(8,9),(9,6),(10,7),(11,6),(12,8),(12,14),(13,7),(13,12),(14,9),(14,11)],15)
=> ([(0,9),(0,14),(1,7),(1,10),(2,8),(2,10),(3,4),(3,9),(3,14),(4,5),(4,11),(5,7),(5,13),(6,8),(6,13),(6,14),(7,12),(8,12),(9,11),(10,12),(11,13),(11,14),(12,13)],15)
=> ([(0,3),(0,5),(0,6),(0,8),(0,9),(0,10),(0,11),(0,12),(0,13),(0,14),(1,2),(1,4),(1,7),(1,8),(1,9),(1,10),(1,11),(1,12),(1,13),(1,14),(2,3),(2,4),(2,6),(2,7),(2,8),(2,9),(2,10),(2,13),(2,14),(3,4),(3,5),(3,6),(3,7),(3,11),(3,12),(3,13),(3,14),(4,5),(4,6),(4,7),(4,8),(4,9),(4,10),(4,13),(4,14),(5,6),(5,7),(5,8),(5,10),(5,11),(5,12),(5,13),(5,14),(6,8),(6,9),(6,11),(6,12),(6,13),(6,14),(7,8),(7,9),(7,10),(7,12),(7,13),(7,14),(8,9),(8,10),(8,11),(8,12),(9,10),(9,11),(9,12),(9,13),(10,11),(10,12),(10,14),(11,12),(11,13),(11,14),(12,13),(12,14),(13,14)],15)
=> ? ∊ {1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3} + 2
000011 => ([(0,5),(0,6),(1,4),(1,14),(2,11),(3,10),(4,3),(4,12),(5,1),(5,13),(6,2),(6,13),(8,9),(9,7),(10,7),(11,8),(12,9),(12,10),(13,11),(13,14),(14,8),(14,12)],15)
=> ([(0,7),(0,11),(1,6),(1,10),(2,8),(2,10),(3,9),(3,11),(4,8),(4,9),(4,14),(5,6),(5,7),(5,14),(6,12),(7,13),(8,12),(9,13),(10,12),(11,13),(12,14),(13,14)],15)
=> ([(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,11),(0,12),(0,13),(0,14),(1,2),(1,4),(1,7),(1,8),(1,9),(1,10),(1,11),(1,12),(1,13),(1,14),(2,3),(2,5),(2,6),(2,9),(2,10),(2,11),(2,12),(2,13),(2,14),(3,4),(3,5),(3,6),(3,7),(3,8),(3,9),(3,10),(3,11),(3,12),(4,5),(4,6),(4,7),(4,8),(4,9),(4,10),(4,13),(4,14),(5,6),(5,7),(5,8),(5,10),(5,11),(5,12),(5,14),(6,7),(6,8),(6,9),(6,11),(6,12),(6,13),(7,8),(7,9),(7,11),(7,13),(7,14),(8,10),(8,12),(8,13),(8,14),(9,10),(9,11),(9,12),(9,13),(9,14),(10,11),(10,12),(10,13),(10,14),(11,12),(11,13),(11,14),(12,13),(12,14),(13,14)],15)
=> ? ∊ {1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3} + 2
000100 => ([(0,3),(0,4),(1,10),(2,1),(2,6),(2,12),(3,14),(3,15),(4,2),(4,14),(4,15),(6,7),(7,8),(8,5),(9,5),(10,9),(11,7),(11,13),(12,10),(12,13),(13,8),(13,9),(14,6),(14,11),(15,11),(15,12)],16)
=> ([(0,7),(0,15),(1,5),(1,14),(2,6),(2,8),(3,4),(3,13),(3,15),(4,6),(4,10),(5,12),(5,13),(6,11),(7,8),(7,9),(8,11),(9,11),(9,12),(9,15),(10,11),(10,12),(10,13),(12,14),(13,14),(14,15)],16)
=> ([(0,1),(0,3),(0,4),(0,5),(0,7),(0,8),(0,9),(0,11),(0,13),(0,14),(0,15),(1,4),(1,5),(1,6),(1,7),(1,10),(1,11),(1,12),(1,13),(1,14),(1,15),(2,3),(2,5),(2,6),(2,8),(2,9),(2,10),(2,11),(2,12),(2,13),(2,14),(2,15),(3,6),(3,7),(3,8),(3,9),(3,10),(3,12),(3,13),(3,14),(3,15),(4,5),(4,7),(4,8),(4,9),(4,10),(4,11),(4,13),(4,14),(4,15),(5,7),(5,8),(5,9),(5,11),(5,12),(5,13),(5,15),(6,7),(6,8),(6,9),(6,10),(6,11),(6,12),(6,13),(6,14),(7,9),(7,11),(7,12),(7,13),(7,14),(7,15),(8,9),(8,10),(8,11),(8,12),(8,14),(8,15),(9,10),(9,12),(9,14),(9,15),(10,11),(10,12),(10,13),(10,14),(10,15),(11,12),(11,13),(11,15),(12,13),(12,14),(13,14),(13,15),(14,15)],16)
=> ? ∊ {1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3} + 2
000101 => ([(0,3),(0,4),(1,2),(1,14),(2,6),(3,13),(3,15),(4,1),(4,13),(4,15),(6,9),(7,8),(8,10),(9,5),(10,5),(11,8),(11,12),(12,9),(12,10),(13,7),(13,11),(14,6),(14,12),(15,7),(15,11),(15,14)],16)
=> ([(0,5),(0,7),(1,6),(1,8),(2,9),(2,14),(3,4),(3,8),(3,13),(4,10),(4,15),(5,6),(5,11),(6,12),(7,11),(7,14),(8,12),(9,10),(9,15),(10,13),(10,14),(11,12),(11,15),(12,13),(13,15),(14,15)],16)
=> ([(0,4),(0,5),(0,8),(0,9),(0,10),(0,11),(0,12),(0,13),(0,14),(0,15),(1,2),(1,3),(1,6),(1,7),(1,8),(1,9),(1,11),(1,12),(1,13),(1,14),(1,15),(2,3),(2,5),(2,6),(2,7),(2,9),(2,10),(2,11),(2,12),(2,14),(2,15),(3,4),(3,6),(3,7),(3,10),(3,11),(3,12),(3,13),(3,14),(3,15),(4,5),(4,8),(4,9),(4,10),(4,11),(4,12),(4,13),(4,14),(4,15),(5,6),(5,7),(5,8),(5,9),(5,10),(5,13),(5,14),(5,15),(6,7),(6,8),(6,9),(6,10),(6,11),(6,12),(6,14),(6,15),(7,8),(7,9),(7,11),(7,12),(7,13),(7,14),(7,15),(8,9),(8,10),(8,11),(8,12),(8,13),(8,15),(9,10),(9,11),(9,13),(9,15),(10,12),(10,13),(10,14),(10,15),(11,12),(11,13),(11,14),(12,13),(12,14),(13,14),(13,15),(14,15)],16)
=> ? ∊ {1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3} + 2
000110 => ([(0,4),(0,5),(1,11),(2,1),(2,13),(3,7),(3,14),(4,2),(4,12),(4,16),(5,3),(5,12),(5,16),(7,8),(8,9),(9,6),(10,6),(11,10),(12,7),(13,11),(13,15),(14,8),(14,15),(15,9),(15,10),(16,13),(16,14)],17)
=> ([(0,15),(0,16),(1,7),(1,10),(2,8),(2,9),(3,4),(3,5),(3,6),(4,15),(4,16),(5,11),(5,15),(6,8),(6,11),(7,14),(7,16),(8,13),(9,10),(9,13),(10,14),(11,12),(11,13),(12,14),(12,15),(12,16),(13,14)],17)
=> ([(0,3),(0,6),(0,7),(0,8),(0,9),(0,10),(0,11),(0,12),(0,13),(0,14),(0,15),(0,16),(1,2),(1,4),(1,5),(1,6),(1,7),(1,8),(1,9),(1,12),(1,13),(1,14),(1,15),(1,16),(2,4),(2,5),(2,7),(2,8),(2,10),(2,11),(2,12),(2,13),(2,14),(2,15),(2,16),(3,4),(3,5),(3,6),(3,9),(3,10),(3,11),(3,12),(3,13),(3,14),(3,15),(3,16),(4,5),(4,6),(4,7),(4,8),(4,9),(4,11),(4,13),(4,15),(4,16),(5,7),(5,8),(5,9),(5,10),(5,11),(5,13),(5,15),(5,16),(6,7),(6,8),(6,9),(6,10),(6,11),(6,12),(6,13),(6,14),(6,16),(7,8),(7,9),(7,10),(7,12),(7,13),(7,14),(7,15),(8,10),(8,11),(8,12),(8,13),(8,14),(8,15),(9,10),(9,11),(9,12),(9,13),(9,14),(9,16),(10,11),(10,12),(10,14),(10,15),(10,16),(11,12),(11,14),(11,15),(11,16),(12,14),(12,15),(12,16),(13,14),(13,15),(13,16),(14,15),(14,16),(15,16)],17)
=> ? ∊ {1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3} + 2
111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
=> ([(0,1),(0,3),(0,4),(0,6),(1,2),(1,4),(1,5),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 5 = 3 + 2
Description
The acyclic chromatic number of a graph.
This is the smallest size of a vertex partition $\{V_1,\dots,V_k\}$ such that each $V_i$ is an independent set and for all $i,j$ the subgraph inducted by $V_i\cup V_j$ does not contain a cycle.
Sorry, this statistic was not found in the database
or
add this statistic to the database – it's very simple and we need your support!