Identifier
Mp00097:
Binary words
—delta morphism⟶
Integer compositions
Mp00038: Integer compositions —reverse⟶ Integer compositions
Mp00038: Integer compositions —reverse⟶ Integer compositions
Images
=>
0=>[1]=>[1]
1=>[1]=>[1]
00=>[2]=>[2]
01=>[1,1]=>[1,1]
10=>[1,1]=>[1,1]
11=>[2]=>[2]
000=>[3]=>[3]
001=>[2,1]=>[1,2]
010=>[1,1,1]=>[1,1,1]
011=>[1,2]=>[2,1]
100=>[1,2]=>[2,1]
101=>[1,1,1]=>[1,1,1]
110=>[2,1]=>[1,2]
111=>[3]=>[3]
0000=>[4]=>[4]
0001=>[3,1]=>[1,3]
0010=>[2,1,1]=>[1,1,2]
0011=>[2,2]=>[2,2]
0100=>[1,1,2]=>[2,1,1]
0101=>[1,1,1,1]=>[1,1,1,1]
0110=>[1,2,1]=>[1,2,1]
0111=>[1,3]=>[3,1]
1000=>[1,3]=>[3,1]
1001=>[1,2,1]=>[1,2,1]
1010=>[1,1,1,1]=>[1,1,1,1]
1011=>[1,1,2]=>[2,1,1]
1100=>[2,2]=>[2,2]
1101=>[2,1,1]=>[1,1,2]
1110=>[3,1]=>[1,3]
1111=>[4]=>[4]
00000=>[5]=>[5]
00001=>[4,1]=>[1,4]
00010=>[3,1,1]=>[1,1,3]
00011=>[3,2]=>[2,3]
00100=>[2,1,2]=>[2,1,2]
00101=>[2,1,1,1]=>[1,1,1,2]
00110=>[2,2,1]=>[1,2,2]
00111=>[2,3]=>[3,2]
01000=>[1,1,3]=>[3,1,1]
01001=>[1,1,2,1]=>[1,2,1,1]
01010=>[1,1,1,1,1]=>[1,1,1,1,1]
01011=>[1,1,1,2]=>[2,1,1,1]
01100=>[1,2,2]=>[2,2,1]
01101=>[1,2,1,1]=>[1,1,2,1]
01110=>[1,3,1]=>[1,3,1]
01111=>[1,4]=>[4,1]
10000=>[1,4]=>[4,1]
10001=>[1,3,1]=>[1,3,1]
10010=>[1,2,1,1]=>[1,1,2,1]
10011=>[1,2,2]=>[2,2,1]
10100=>[1,1,1,2]=>[2,1,1,1]
10101=>[1,1,1,1,1]=>[1,1,1,1,1]
10110=>[1,1,2,1]=>[1,2,1,1]
10111=>[1,1,3]=>[3,1,1]
11000=>[2,3]=>[3,2]
11001=>[2,2,1]=>[1,2,2]
11010=>[2,1,1,1]=>[1,1,1,2]
11011=>[2,1,2]=>[2,1,2]
11100=>[3,2]=>[2,3]
11101=>[3,1,1]=>[1,1,3]
11110=>[4,1]=>[1,4]
11111=>[5]=>[5]
000000=>[6]=>[6]
000001=>[5,1]=>[1,5]
000010=>[4,1,1]=>[1,1,4]
000011=>[4,2]=>[2,4]
000100=>[3,1,2]=>[2,1,3]
000101=>[3,1,1,1]=>[1,1,1,3]
000110=>[3,2,1]=>[1,2,3]
000111=>[3,3]=>[3,3]
001000=>[2,1,3]=>[3,1,2]
001001=>[2,1,2,1]=>[1,2,1,2]
001010=>[2,1,1,1,1]=>[1,1,1,1,2]
001011=>[2,1,1,2]=>[2,1,1,2]
001100=>[2,2,2]=>[2,2,2]
001101=>[2,2,1,1]=>[1,1,2,2]
001110=>[2,3,1]=>[1,3,2]
001111=>[2,4]=>[4,2]
010000=>[1,1,4]=>[4,1,1]
010001=>[1,1,3,1]=>[1,3,1,1]
010010=>[1,1,2,1,1]=>[1,1,2,1,1]
010011=>[1,1,2,2]=>[2,2,1,1]
010100=>[1,1,1,1,2]=>[2,1,1,1,1]
010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
010110=>[1,1,1,2,1]=>[1,2,1,1,1]
010111=>[1,1,1,3]=>[3,1,1,1]
011000=>[1,2,3]=>[3,2,1]
011001=>[1,2,2,1]=>[1,2,2,1]
011010=>[1,2,1,1,1]=>[1,1,1,2,1]
011011=>[1,2,1,2]=>[2,1,2,1]
011100=>[1,3,2]=>[2,3,1]
011101=>[1,3,1,1]=>[1,1,3,1]
011110=>[1,4,1]=>[1,4,1]
011111=>[1,5]=>[5,1]
100000=>[1,5]=>[5,1]
100001=>[1,4,1]=>[1,4,1]
100010=>[1,3,1,1]=>[1,1,3,1]
100011=>[1,3,2]=>[2,3,1]
100100=>[1,2,1,2]=>[2,1,2,1]
100101=>[1,2,1,1,1]=>[1,1,1,2,1]
100110=>[1,2,2,1]=>[1,2,2,1]
100111=>[1,2,3]=>[3,2,1]
101000=>[1,1,1,3]=>[3,1,1,1]
101001=>[1,1,1,2,1]=>[1,2,1,1,1]
101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
101011=>[1,1,1,1,2]=>[2,1,1,1,1]
101100=>[1,1,2,2]=>[2,2,1,1]
101101=>[1,1,2,1,1]=>[1,1,2,1,1]
101110=>[1,1,3,1]=>[1,3,1,1]
101111=>[1,1,4]=>[4,1,1]
110000=>[2,4]=>[4,2]
110001=>[2,3,1]=>[1,3,2]
110010=>[2,2,1,1]=>[1,1,2,2]
110011=>[2,2,2]=>[2,2,2]
110100=>[2,1,1,2]=>[2,1,1,2]
110101=>[2,1,1,1,1]=>[1,1,1,1,2]
110110=>[2,1,2,1]=>[1,2,1,2]
110111=>[2,1,3]=>[3,1,2]
111000=>[3,3]=>[3,3]
111001=>[3,2,1]=>[1,2,3]
111010=>[3,1,1,1]=>[1,1,1,3]
111011=>[3,1,2]=>[2,1,3]
111100=>[4,2]=>[2,4]
111101=>[4,1,1]=>[1,1,4]
111110=>[5,1]=>[1,5]
111111=>[6]=>[6]
0000000=>[7]=>[7]
0000001=>[6,1]=>[1,6]
0000010=>[5,1,1]=>[1,1,5]
0000011=>[5,2]=>[2,5]
0000100=>[4,1,2]=>[2,1,4]
0000101=>[4,1,1,1]=>[1,1,1,4]
0000110=>[4,2,1]=>[1,2,4]
0000111=>[4,3]=>[3,4]
0001000=>[3,1,3]=>[3,1,3]
0001001=>[3,1,2,1]=>[1,2,1,3]
0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
0001011=>[3,1,1,2]=>[2,1,1,3]
0001100=>[3,2,2]=>[2,2,3]
0001101=>[3,2,1,1]=>[1,1,2,3]
0001110=>[3,3,1]=>[1,3,3]
0001111=>[3,4]=>[4,3]
0010000=>[2,1,4]=>[4,1,2]
0010001=>[2,1,3,1]=>[1,3,1,2]
0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
0010011=>[2,1,2,2]=>[2,2,1,2]
0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
0010111=>[2,1,1,3]=>[3,1,1,2]
0011000=>[2,2,3]=>[3,2,2]
0011001=>[2,2,2,1]=>[1,2,2,2]
0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
0011011=>[2,2,1,2]=>[2,1,2,2]
0011100=>[2,3,2]=>[2,3,2]
0011101=>[2,3,1,1]=>[1,1,3,2]
0011110=>[2,4,1]=>[1,4,2]
0011111=>[2,5]=>[5,2]
0100000=>[1,1,5]=>[5,1,1]
0100001=>[1,1,4,1]=>[1,4,1,1]
0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
0100011=>[1,1,3,2]=>[2,3,1,1]
0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
0100111=>[1,1,2,3]=>[3,2,1,1]
0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
0101110=>[1,1,1,3,1]=>[1,3,1,1,1]
0101111=>[1,1,1,4]=>[4,1,1,1]
0110000=>[1,2,4]=>[4,2,1]
0110001=>[1,2,3,1]=>[1,3,2,1]
0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
0110011=>[1,2,2,2]=>[2,2,2,1]
0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
0110111=>[1,2,1,3]=>[3,1,2,1]
0111000=>[1,3,3]=>[3,3,1]
0111001=>[1,3,2,1]=>[1,2,3,1]
0111010=>[1,3,1,1,1]=>[1,1,1,3,1]
0111011=>[1,3,1,2]=>[2,1,3,1]
0111100=>[1,4,2]=>[2,4,1]
0111101=>[1,4,1,1]=>[1,1,4,1]
0111110=>[1,5,1]=>[1,5,1]
0111111=>[1,6]=>[6,1]
1000000=>[1,6]=>[6,1]
1000001=>[1,5,1]=>[1,5,1]
1000010=>[1,4,1,1]=>[1,1,4,1]
1000011=>[1,4,2]=>[2,4,1]
1000100=>[1,3,1,2]=>[2,1,3,1]
1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
1000110=>[1,3,2,1]=>[1,2,3,1]
1000111=>[1,3,3]=>[3,3,1]
1001000=>[1,2,1,3]=>[3,1,2,1]
1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
1001100=>[1,2,2,2]=>[2,2,2,1]
1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
1001110=>[1,2,3,1]=>[1,3,2,1]
1001111=>[1,2,4]=>[4,2,1]
1010000=>[1,1,1,4]=>[4,1,1,1]
1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
1010111=>[1,1,1,1,3]=>[3,1,1,1,1]
1011000=>[1,1,2,3]=>[3,2,1,1]
1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
1011100=>[1,1,3,2]=>[2,3,1,1]
1011101=>[1,1,3,1,1]=>[1,1,3,1,1]
1011110=>[1,1,4,1]=>[1,4,1,1]
1011111=>[1,1,5]=>[5,1,1]
1100000=>[2,5]=>[5,2]
1100001=>[2,4,1]=>[1,4,2]
1100010=>[2,3,1,1]=>[1,1,3,2]
1100011=>[2,3,2]=>[2,3,2]
1100100=>[2,2,1,2]=>[2,1,2,2]
1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
1100110=>[2,2,2,1]=>[1,2,2,2]
1100111=>[2,2,3]=>[3,2,2]
1101000=>[2,1,1,3]=>[3,1,1,2]
1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
1101100=>[2,1,2,2]=>[2,2,1,2]
1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
1101110=>[2,1,3,1]=>[1,3,1,2]
1101111=>[2,1,4]=>[4,1,2]
1110000=>[3,4]=>[4,3]
1110001=>[3,3,1]=>[1,3,3]
1110010=>[3,2,1,1]=>[1,1,2,3]
1110011=>[3,2,2]=>[2,2,3]
1110100=>[3,1,1,2]=>[2,1,1,3]
1110101=>[3,1,1,1,1]=>[1,1,1,1,3]
1110110=>[3,1,2,1]=>[1,2,1,3]
1110111=>[3,1,3]=>[3,1,3]
1111000=>[4,3]=>[3,4]
1111001=>[4,2,1]=>[1,2,4]
1111010=>[4,1,1,1]=>[1,1,1,4]
1111011=>[4,1,2]=>[2,1,4]
1111100=>[5,2]=>[2,5]
1111101=>[5,1,1]=>[1,1,5]
1111110=>[6,1]=>[1,6]
1111111=>[7]=>[7]
00000000=>[8]=>[8]
00000001=>[7,1]=>[1,7]
00000010=>[6,1,1]=>[1,1,6]
00000011=>[6,2]=>[2,6]
00000100=>[5,1,2]=>[2,1,5]
00000101=>[5,1,1,1]=>[1,1,1,5]
00000110=>[5,2,1]=>[1,2,5]
00000111=>[5,3]=>[3,5]
00001000=>[4,1,3]=>[3,1,4]
00001001=>[4,1,2,1]=>[1,2,1,4]
00001010=>[4,1,1,1,1]=>[1,1,1,1,4]
00001011=>[4,1,1,2]=>[2,1,1,4]
00001100=>[4,2,2]=>[2,2,4]
00001101=>[4,2,1,1]=>[1,1,2,4]
00001110=>[4,3,1]=>[1,3,4]
00001111=>[4,4]=>[4,4]
00010000=>[3,1,4]=>[4,1,3]
00010001=>[3,1,3,1]=>[1,3,1,3]
00010010=>[3,1,2,1,1]=>[1,1,2,1,3]
00010011=>[3,1,2,2]=>[2,2,1,3]
00010100=>[3,1,1,1,2]=>[2,1,1,1,3]
00010101=>[3,1,1,1,1,1]=>[1,1,1,1,1,3]
00010110=>[3,1,1,2,1]=>[1,2,1,1,3]
00010111=>[3,1,1,3]=>[3,1,1,3]
00011000=>[3,2,3]=>[3,2,3]
00011001=>[3,2,2,1]=>[1,2,2,3]
00011010=>[3,2,1,1,1]=>[1,1,1,2,3]
00011011=>[3,2,1,2]=>[2,1,2,3]
00011100=>[3,3,2]=>[2,3,3]
00011101=>[3,3,1,1]=>[1,1,3,3]
00011110=>[3,4,1]=>[1,4,3]
00011111=>[3,5]=>[5,3]
00100000=>[2,1,5]=>[5,1,2]
00100001=>[2,1,4,1]=>[1,4,1,2]
00100010=>[2,1,3,1,1]=>[1,1,3,1,2]
00100011=>[2,1,3,2]=>[2,3,1,2]
00100100=>[2,1,2,1,2]=>[2,1,2,1,2]
00100101=>[2,1,2,1,1,1]=>[1,1,1,2,1,2]
00100110=>[2,1,2,2,1]=>[1,2,2,1,2]
00100111=>[2,1,2,3]=>[3,2,1,2]
00101000=>[2,1,1,1,3]=>[3,1,1,1,2]
00101001=>[2,1,1,1,2,1]=>[1,2,1,1,1,2]
00101010=>[2,1,1,1,1,1,1]=>[1,1,1,1,1,1,2]
00101011=>[2,1,1,1,1,2]=>[2,1,1,1,1,2]
00101100=>[2,1,1,2,2]=>[2,2,1,1,2]
00101101=>[2,1,1,2,1,1]=>[1,1,2,1,1,2]
00101110=>[2,1,1,3,1]=>[1,3,1,1,2]
00101111=>[2,1,1,4]=>[4,1,1,2]
00110000=>[2,2,4]=>[4,2,2]
00110001=>[2,2,3,1]=>[1,3,2,2]
00110010=>[2,2,2,1,1]=>[1,1,2,2,2]
00110011=>[2,2,2,2]=>[2,2,2,2]
00110100=>[2,2,1,1,2]=>[2,1,1,2,2]
00110101=>[2,2,1,1,1,1]=>[1,1,1,1,2,2]
00110110=>[2,2,1,2,1]=>[1,2,1,2,2]
00110111=>[2,2,1,3]=>[3,1,2,2]
00111000=>[2,3,3]=>[3,3,2]
00111001=>[2,3,2,1]=>[1,2,3,2]
00111010=>[2,3,1,1,1]=>[1,1,1,3,2]
00111011=>[2,3,1,2]=>[2,1,3,2]
00111100=>[2,4,2]=>[2,4,2]
00111101=>[2,4,1,1]=>[1,1,4,2]
00111110=>[2,5,1]=>[1,5,2]
00111111=>[2,6]=>[6,2]
01000000=>[1,1,6]=>[6,1,1]
01000001=>[1,1,5,1]=>[1,5,1,1]
01000010=>[1,1,4,1,1]=>[1,1,4,1,1]
01000011=>[1,1,4,2]=>[2,4,1,1]
01000100=>[1,1,3,1,2]=>[2,1,3,1,1]
01000101=>[1,1,3,1,1,1]=>[1,1,1,3,1,1]
01000110=>[1,1,3,2,1]=>[1,2,3,1,1]
01000111=>[1,1,3,3]=>[3,3,1,1]
01001000=>[1,1,2,1,3]=>[3,1,2,1,1]
01001001=>[1,1,2,1,2,1]=>[1,2,1,2,1,1]
01001010=>[1,1,2,1,1,1,1]=>[1,1,1,1,2,1,1]
01001011=>[1,1,2,1,1,2]=>[2,1,1,2,1,1]
01001100=>[1,1,2,2,2]=>[2,2,2,1,1]
01001101=>[1,1,2,2,1,1]=>[1,1,2,2,1,1]
01001110=>[1,1,2,3,1]=>[1,3,2,1,1]
01001111=>[1,1,2,4]=>[4,2,1,1]
01010000=>[1,1,1,1,4]=>[4,1,1,1,1]
01010001=>[1,1,1,1,3,1]=>[1,3,1,1,1,1]
01010010=>[1,1,1,1,2,1,1]=>[1,1,2,1,1,1,1]
01010011=>[1,1,1,1,2,2]=>[2,2,1,1,1,1]
01010100=>[1,1,1,1,1,1,2]=>[2,1,1,1,1,1,1]
01010101=>[1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1]
01010110=>[1,1,1,1,1,2,1]=>[1,2,1,1,1,1,1]
01010111=>[1,1,1,1,1,3]=>[3,1,1,1,1,1]
01011000=>[1,1,1,2,3]=>[3,2,1,1,1]
01011001=>[1,1,1,2,2,1]=>[1,2,2,1,1,1]
01011010=>[1,1,1,2,1,1,1]=>[1,1,1,2,1,1,1]
01011011=>[1,1,1,2,1,2]=>[2,1,2,1,1,1]
01011100=>[1,1,1,3,2]=>[2,3,1,1,1]
01011101=>[1,1,1,3,1,1]=>[1,1,3,1,1,1]
01011110=>[1,1,1,4,1]=>[1,4,1,1,1]
01011111=>[1,1,1,5]=>[5,1,1,1]
01100000=>[1,2,5]=>[5,2,1]
01100001=>[1,2,4,1]=>[1,4,2,1]
01100010=>[1,2,3,1,1]=>[1,1,3,2,1]
01100011=>[1,2,3,2]=>[2,3,2,1]
01100100=>[1,2,2,1,2]=>[2,1,2,2,1]
01100101=>[1,2,2,1,1,1]=>[1,1,1,2,2,1]
01100110=>[1,2,2,2,1]=>[1,2,2,2,1]
01100111=>[1,2,2,3]=>[3,2,2,1]
01101000=>[1,2,1,1,3]=>[3,1,1,2,1]
01101001=>[1,2,1,1,2,1]=>[1,2,1,1,2,1]
01101010=>[1,2,1,1,1,1,1]=>[1,1,1,1,1,2,1]
01101011=>[1,2,1,1,1,2]=>[2,1,1,1,2,1]
01101100=>[1,2,1,2,2]=>[2,2,1,2,1]
01101101=>[1,2,1,2,1,1]=>[1,1,2,1,2,1]
01101110=>[1,2,1,3,1]=>[1,3,1,2,1]
01101111=>[1,2,1,4]=>[4,1,2,1]
01110000=>[1,3,4]=>[4,3,1]
01110001=>[1,3,3,1]=>[1,3,3,1]
01110010=>[1,3,2,1,1]=>[1,1,2,3,1]
01110011=>[1,3,2,2]=>[2,2,3,1]
01110100=>[1,3,1,1,2]=>[2,1,1,3,1]
01110101=>[1,3,1,1,1,1]=>[1,1,1,1,3,1]
01110110=>[1,3,1,2,1]=>[1,2,1,3,1]
01110111=>[1,3,1,3]=>[3,1,3,1]
01111000=>[1,4,3]=>[3,4,1]
01111001=>[1,4,2,1]=>[1,2,4,1]
01111010=>[1,4,1,1,1]=>[1,1,1,4,1]
01111011=>[1,4,1,2]=>[2,1,4,1]
01111100=>[1,5,2]=>[2,5,1]
01111101=>[1,5,1,1]=>[1,1,5,1]
01111110=>[1,6,1]=>[1,6,1]
01111111=>[1,7]=>[7,1]
10000000=>[1,7]=>[7,1]
10000001=>[1,6,1]=>[1,6,1]
10000010=>[1,5,1,1]=>[1,1,5,1]
10000011=>[1,5,2]=>[2,5,1]
10000100=>[1,4,1,2]=>[2,1,4,1]
10000101=>[1,4,1,1,1]=>[1,1,1,4,1]
10000110=>[1,4,2,1]=>[1,2,4,1]
10000111=>[1,4,3]=>[3,4,1]
10001000=>[1,3,1,3]=>[3,1,3,1]
10001001=>[1,3,1,2,1]=>[1,2,1,3,1]
10001010=>[1,3,1,1,1,1]=>[1,1,1,1,3,1]
10001011=>[1,3,1,1,2]=>[2,1,1,3,1]
10001100=>[1,3,2,2]=>[2,2,3,1]
10001101=>[1,3,2,1,1]=>[1,1,2,3,1]
10001110=>[1,3,3,1]=>[1,3,3,1]
10001111=>[1,3,4]=>[4,3,1]
10010000=>[1,2,1,4]=>[4,1,2,1]
10010001=>[1,2,1,3,1]=>[1,3,1,2,1]
10010010=>[1,2,1,2,1,1]=>[1,1,2,1,2,1]
10010011=>[1,2,1,2,2]=>[2,2,1,2,1]
10010100=>[1,2,1,1,1,2]=>[2,1,1,1,2,1]
10010101=>[1,2,1,1,1,1,1]=>[1,1,1,1,1,2,1]
10010110=>[1,2,1,1,2,1]=>[1,2,1,1,2,1]
10010111=>[1,2,1,1,3]=>[3,1,1,2,1]
10011000=>[1,2,2,3]=>[3,2,2,1]
10011001=>[1,2,2,2,1]=>[1,2,2,2,1]
10011010=>[1,2,2,1,1,1]=>[1,1,1,2,2,1]
10011011=>[1,2,2,1,2]=>[2,1,2,2,1]
10011100=>[1,2,3,2]=>[2,3,2,1]
10011101=>[1,2,3,1,1]=>[1,1,3,2,1]
10011110=>[1,2,4,1]=>[1,4,2,1]
10011111=>[1,2,5]=>[5,2,1]
10100000=>[1,1,1,5]=>[5,1,1,1]
10100001=>[1,1,1,4,1]=>[1,4,1,1,1]
10100010=>[1,1,1,3,1,1]=>[1,1,3,1,1,1]
10100011=>[1,1,1,3,2]=>[2,3,1,1,1]
10100100=>[1,1,1,2,1,2]=>[2,1,2,1,1,1]
10100101=>[1,1,1,2,1,1,1]=>[1,1,1,2,1,1,1]
10100110=>[1,1,1,2,2,1]=>[1,2,2,1,1,1]
10100111=>[1,1,1,2,3]=>[3,2,1,1,1]
10101000=>[1,1,1,1,1,3]=>[3,1,1,1,1,1]
10101001=>[1,1,1,1,1,2,1]=>[1,2,1,1,1,1,1]
10101010=>[1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1]
10101011=>[1,1,1,1,1,1,2]=>[2,1,1,1,1,1,1]
10101100=>[1,1,1,1,2,2]=>[2,2,1,1,1,1]
10101101=>[1,1,1,1,2,1,1]=>[1,1,2,1,1,1,1]
10101110=>[1,1,1,1,3,1]=>[1,3,1,1,1,1]
10101111=>[1,1,1,1,4]=>[4,1,1,1,1]
10110000=>[1,1,2,4]=>[4,2,1,1]
10110001=>[1,1,2,3,1]=>[1,3,2,1,1]
10110010=>[1,1,2,2,1,1]=>[1,1,2,2,1,1]
10110011=>[1,1,2,2,2]=>[2,2,2,1,1]
10110100=>[1,1,2,1,1,2]=>[2,1,1,2,1,1]
10110101=>[1,1,2,1,1,1,1]=>[1,1,1,1,2,1,1]
10110110=>[1,1,2,1,2,1]=>[1,2,1,2,1,1]
10110111=>[1,1,2,1,3]=>[3,1,2,1,1]
10111000=>[1,1,3,3]=>[3,3,1,1]
10111001=>[1,1,3,2,1]=>[1,2,3,1,1]
10111010=>[1,1,3,1,1,1]=>[1,1,1,3,1,1]
10111011=>[1,1,3,1,2]=>[2,1,3,1,1]
10111100=>[1,1,4,2]=>[2,4,1,1]
10111101=>[1,1,4,1,1]=>[1,1,4,1,1]
10111110=>[1,1,5,1]=>[1,5,1,1]
10111111=>[1,1,6]=>[6,1,1]
11000000=>[2,6]=>[6,2]
11000001=>[2,5,1]=>[1,5,2]
11000010=>[2,4,1,1]=>[1,1,4,2]
11000011=>[2,4,2]=>[2,4,2]
11000100=>[2,3,1,2]=>[2,1,3,2]
11000101=>[2,3,1,1,1]=>[1,1,1,3,2]
11000110=>[2,3,2,1]=>[1,2,3,2]
11000111=>[2,3,3]=>[3,3,2]
11001000=>[2,2,1,3]=>[3,1,2,2]
11001001=>[2,2,1,2,1]=>[1,2,1,2,2]
11001010=>[2,2,1,1,1,1]=>[1,1,1,1,2,2]
11001011=>[2,2,1,1,2]=>[2,1,1,2,2]
11001100=>[2,2,2,2]=>[2,2,2,2]
11001101=>[2,2,2,1,1]=>[1,1,2,2,2]
11001110=>[2,2,3,1]=>[1,3,2,2]
11001111=>[2,2,4]=>[4,2,2]
11010000=>[2,1,1,4]=>[4,1,1,2]
11010001=>[2,1,1,3,1]=>[1,3,1,1,2]
11010010=>[2,1,1,2,1,1]=>[1,1,2,1,1,2]
11010011=>[2,1,1,2,2]=>[2,2,1,1,2]
11010100=>[2,1,1,1,1,2]=>[2,1,1,1,1,2]
11010101=>[2,1,1,1,1,1,1]=>[1,1,1,1,1,1,2]
11010110=>[2,1,1,1,2,1]=>[1,2,1,1,1,2]
11010111=>[2,1,1,1,3]=>[3,1,1,1,2]
11011000=>[2,1,2,3]=>[3,2,1,2]
11011001=>[2,1,2,2,1]=>[1,2,2,1,2]
11011010=>[2,1,2,1,1,1]=>[1,1,1,2,1,2]
11011011=>[2,1,2,1,2]=>[2,1,2,1,2]
11011100=>[2,1,3,2]=>[2,3,1,2]
11011101=>[2,1,3,1,1]=>[1,1,3,1,2]
11011110=>[2,1,4,1]=>[1,4,1,2]
11011111=>[2,1,5]=>[5,1,2]
11100000=>[3,5]=>[5,3]
11100001=>[3,4,1]=>[1,4,3]
11100010=>[3,3,1,1]=>[1,1,3,3]
11100011=>[3,3,2]=>[2,3,3]
11100100=>[3,2,1,2]=>[2,1,2,3]
11100101=>[3,2,1,1,1]=>[1,1,1,2,3]
11100110=>[3,2,2,1]=>[1,2,2,3]
11100111=>[3,2,3]=>[3,2,3]
11101000=>[3,1,1,3]=>[3,1,1,3]
11101001=>[3,1,1,2,1]=>[1,2,1,1,3]
11101010=>[3,1,1,1,1,1]=>[1,1,1,1,1,3]
11101011=>[3,1,1,1,2]=>[2,1,1,1,3]
11101100=>[3,1,2,2]=>[2,2,1,3]
11101101=>[3,1,2,1,1]=>[1,1,2,1,3]
11101110=>[3,1,3,1]=>[1,3,1,3]
11101111=>[3,1,4]=>[4,1,3]
11110000=>[4,4]=>[4,4]
11110001=>[4,3,1]=>[1,3,4]
11110010=>[4,2,1,1]=>[1,1,2,4]
11110011=>[4,2,2]=>[2,2,4]
11110100=>[4,1,1,2]=>[2,1,1,4]
11110101=>[4,1,1,1,1]=>[1,1,1,1,4]
11110110=>[4,1,2,1]=>[1,2,1,4]
11110111=>[4,1,3]=>[3,1,4]
11111000=>[5,3]=>[3,5]
11111001=>[5,2,1]=>[1,2,5]
11111010=>[5,1,1,1]=>[1,1,1,5]
11111011=>[5,1,2]=>[2,1,5]
11111100=>[6,2]=>[2,6]
11111101=>[6,1,1]=>[1,1,6]
11111110=>[7,1]=>[1,7]
11111111=>[8]=>[8]
000000000=>[9]=>[9]
000000001=>[8,1]=>[1,8]
000000010=>[7,1,1]=>[1,1,7]
000000011=>[7,2]=>[2,7]
000000100=>[6,1,2]=>[2,1,6]
000000101=>[6,1,1,1]=>[1,1,1,6]
000000110=>[6,2,1]=>[1,2,6]
000000111=>[6,3]=>[3,6]
000001000=>[5,1,3]=>[3,1,5]
000001001=>[5,1,2,1]=>[1,2,1,5]
000001010=>[5,1,1,1,1]=>[1,1,1,1,5]
000001011=>[5,1,1,2]=>[2,1,1,5]
000001100=>[5,2,2]=>[2,2,5]
000001101=>[5,2,1,1]=>[1,1,2,5]
000001110=>[5,3,1]=>[1,3,5]
000001111=>[5,4]=>[4,5]
000010000=>[4,1,4]=>[4,1,4]
000010001=>[4,1,3,1]=>[1,3,1,4]
000010010=>[4,1,2,1,1]=>[1,1,2,1,4]
000010011=>[4,1,2,2]=>[2,2,1,4]
000010100=>[4,1,1,1,2]=>[2,1,1,1,4]
000010101=>[4,1,1,1,1,1]=>[1,1,1,1,1,4]
000010110=>[4,1,1,2,1]=>[1,2,1,1,4]
000010111=>[4,1,1,3]=>[3,1,1,4]
000011000=>[4,2,3]=>[3,2,4]
000011001=>[4,2,2,1]=>[1,2,2,4]
000011010=>[4,2,1,1,1]=>[1,1,1,2,4]
000011011=>[4,2,1,2]=>[2,1,2,4]
000011100=>[4,3,2]=>[2,3,4]
000011101=>[4,3,1,1]=>[1,1,3,4]
000011110=>[4,4,1]=>[1,4,4]
000011111=>[4,5]=>[5,4]
000100000=>[3,1,5]=>[5,1,3]
000100001=>[3,1,4,1]=>[1,4,1,3]
000100010=>[3,1,3,1,1]=>[1,1,3,1,3]
000100011=>[3,1,3,2]=>[2,3,1,3]
000100100=>[3,1,2,1,2]=>[2,1,2,1,3]
000100101=>[3,1,2,1,1,1]=>[1,1,1,2,1,3]
000100110=>[3,1,2,2,1]=>[1,2,2,1,3]
000100111=>[3,1,2,3]=>[3,2,1,3]
000101000=>[3,1,1,1,3]=>[3,1,1,1,3]
000101001=>[3,1,1,1,2,1]=>[1,2,1,1,1,3]
000101010=>[3,1,1,1,1,1,1]=>[1,1,1,1,1,1,3]
000101011=>[3,1,1,1,1,2]=>[2,1,1,1,1,3]
000101100=>[3,1,1,2,2]=>[2,2,1,1,3]
000101101=>[3,1,1,2,1,1]=>[1,1,2,1,1,3]
000101110=>[3,1,1,3,1]=>[1,3,1,1,3]
000101111=>[3,1,1,4]=>[4,1,1,3]
000110000=>[3,2,4]=>[4,2,3]
000110001=>[3,2,3,1]=>[1,3,2,3]
000110010=>[3,2,2,1,1]=>[1,1,2,2,3]
000110011=>[3,2,2,2]=>[2,2,2,3]
000110100=>[3,2,1,1,2]=>[2,1,1,2,3]
000110101=>[3,2,1,1,1,1]=>[1,1,1,1,2,3]
000110110=>[3,2,1,2,1]=>[1,2,1,2,3]
000110111=>[3,2,1,3]=>[3,1,2,3]
000111000=>[3,3,3]=>[3,3,3]
000111001=>[3,3,2,1]=>[1,2,3,3]
000111010=>[3,3,1,1,1]=>[1,1,1,3,3]
000111011=>[3,3,1,2]=>[2,1,3,3]
000111100=>[3,4,2]=>[2,4,3]
000111101=>[3,4,1,1]=>[1,1,4,3]
000111110=>[3,5,1]=>[1,5,3]
000111111=>[3,6]=>[6,3]
001000000=>[2,1,6]=>[6,1,2]
001000001=>[2,1,5,1]=>[1,5,1,2]
001000010=>[2,1,4,1,1]=>[1,1,4,1,2]
001000011=>[2,1,4,2]=>[2,4,1,2]
001000100=>[2,1,3,1,2]=>[2,1,3,1,2]
001000101=>[2,1,3,1,1,1]=>[1,1,1,3,1,2]
001000110=>[2,1,3,2,1]=>[1,2,3,1,2]
001000111=>[2,1,3,3]=>[3,3,1,2]
001001000=>[2,1,2,1,3]=>[3,1,2,1,2]
001001001=>[2,1,2,1,2,1]=>[1,2,1,2,1,2]
001001010=>[2,1,2,1,1,1,1]=>[1,1,1,1,2,1,2]
001001011=>[2,1,2,1,1,2]=>[2,1,1,2,1,2]
001001100=>[2,1,2,2,2]=>[2,2,2,1,2]
001001101=>[2,1,2,2,1,1]=>[1,1,2,2,1,2]
001001110=>[2,1,2,3,1]=>[1,3,2,1,2]
001001111=>[2,1,2,4]=>[4,2,1,2]
001010000=>[2,1,1,1,4]=>[4,1,1,1,2]
001010001=>[2,1,1,1,3,1]=>[1,3,1,1,1,2]
001010010=>[2,1,1,1,2,1,1]=>[1,1,2,1,1,1,2]
001010011=>[2,1,1,1,2,2]=>[2,2,1,1,1,2]
001010100=>[2,1,1,1,1,1,2]=>[2,1,1,1,1,1,2]
001010101=>[2,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,2]
001010110=>[2,1,1,1,1,2,1]=>[1,2,1,1,1,1,2]
001010111=>[2,1,1,1,1,3]=>[3,1,1,1,1,2]
001011000=>[2,1,1,2,3]=>[3,2,1,1,2]
001011001=>[2,1,1,2,2,1]=>[1,2,2,1,1,2]
001011010=>[2,1,1,2,1,1,1]=>[1,1,1,2,1,1,2]
001011011=>[2,1,1,2,1,2]=>[2,1,2,1,1,2]
001011100=>[2,1,1,3,2]=>[2,3,1,1,2]
001011101=>[2,1,1,3,1,1]=>[1,1,3,1,1,2]
001011110=>[2,1,1,4,1]=>[1,4,1,1,2]
001011111=>[2,1,1,5]=>[5,1,1,2]
001100000=>[2,2,5]=>[5,2,2]
001100001=>[2,2,4,1]=>[1,4,2,2]
001100010=>[2,2,3,1,1]=>[1,1,3,2,2]
001100011=>[2,2,3,2]=>[2,3,2,2]
001100100=>[2,2,2,1,2]=>[2,1,2,2,2]
001100101=>[2,2,2,1,1,1]=>[1,1,1,2,2,2]
001100110=>[2,2,2,2,1]=>[1,2,2,2,2]
001100111=>[2,2,2,3]=>[3,2,2,2]
001101000=>[2,2,1,1,3]=>[3,1,1,2,2]
001101001=>[2,2,1,1,2,1]=>[1,2,1,1,2,2]
001101010=>[2,2,1,1,1,1,1]=>[1,1,1,1,1,2,2]
001101011=>[2,2,1,1,1,2]=>[2,1,1,1,2,2]
001101100=>[2,2,1,2,2]=>[2,2,1,2,2]
001101101=>[2,2,1,2,1,1]=>[1,1,2,1,2,2]
001101110=>[2,2,1,3,1]=>[1,3,1,2,2]
001101111=>[2,2,1,4]=>[4,1,2,2]
001110000=>[2,3,4]=>[4,3,2]
001110001=>[2,3,3,1]=>[1,3,3,2]
001110010=>[2,3,2,1,1]=>[1,1,2,3,2]
001110011=>[2,3,2,2]=>[2,2,3,2]
001110100=>[2,3,1,1,2]=>[2,1,1,3,2]
001110101=>[2,3,1,1,1,1]=>[1,1,1,1,3,2]
001110110=>[2,3,1,2,1]=>[1,2,1,3,2]
001110111=>[2,3,1,3]=>[3,1,3,2]
001111000=>[2,4,3]=>[3,4,2]
001111001=>[2,4,2,1]=>[1,2,4,2]
001111010=>[2,4,1,1,1]=>[1,1,1,4,2]
001111011=>[2,4,1,2]=>[2,1,4,2]
001111100=>[2,5,2]=>[2,5,2]
001111101=>[2,5,1,1]=>[1,1,5,2]
001111110=>[2,6,1]=>[1,6,2]
001111111=>[2,7]=>[7,2]
010000000=>[1,1,7]=>[7,1,1]
010000001=>[1,1,6,1]=>[1,6,1,1]
010000010=>[1,1,5,1,1]=>[1,1,5,1,1]
010000011=>[1,1,5,2]=>[2,5,1,1]
010000100=>[1,1,4,1,2]=>[2,1,4,1,1]
010000101=>[1,1,4,1,1,1]=>[1,1,1,4,1,1]
010000110=>[1,1,4,2,1]=>[1,2,4,1,1]
010000111=>[1,1,4,3]=>[3,4,1,1]
010001000=>[1,1,3,1,3]=>[3,1,3,1,1]
010001001=>[1,1,3,1,2,1]=>[1,2,1,3,1,1]
010001010=>[1,1,3,1,1,1,1]=>[1,1,1,1,3,1,1]
010001011=>[1,1,3,1,1,2]=>[2,1,1,3,1,1]
010001100=>[1,1,3,2,2]=>[2,2,3,1,1]
010001101=>[1,1,3,2,1,1]=>[1,1,2,3,1,1]
010001110=>[1,1,3,3,1]=>[1,3,3,1,1]
010001111=>[1,1,3,4]=>[4,3,1,1]
010010000=>[1,1,2,1,4]=>[4,1,2,1,1]
010010001=>[1,1,2,1,3,1]=>[1,3,1,2,1,1]
010010010=>[1,1,2,1,2,1,1]=>[1,1,2,1,2,1,1]
010010011=>[1,1,2,1,2,2]=>[2,2,1,2,1,1]
010010100=>[1,1,2,1,1,1,2]=>[2,1,1,1,2,1,1]
010010101=>[1,1,2,1,1,1,1,1]=>[1,1,1,1,1,2,1,1]
010010110=>[1,1,2,1,1,2,1]=>[1,2,1,1,2,1,1]
010010111=>[1,1,2,1,1,3]=>[3,1,1,2,1,1]
010011000=>[1,1,2,2,3]=>[3,2,2,1,1]
010011001=>[1,1,2,2,2,1]=>[1,2,2,2,1,1]
010011010=>[1,1,2,2,1,1,1]=>[1,1,1,2,2,1,1]
010011011=>[1,1,2,2,1,2]=>[2,1,2,2,1,1]
010011100=>[1,1,2,3,2]=>[2,3,2,1,1]
010011101=>[1,1,2,3,1,1]=>[1,1,3,2,1,1]
010011110=>[1,1,2,4,1]=>[1,4,2,1,1]
010011111=>[1,1,2,5]=>[5,2,1,1]
010100000=>[1,1,1,1,5]=>[5,1,1,1,1]
010100001=>[1,1,1,1,4,1]=>[1,4,1,1,1,1]
010100010=>[1,1,1,1,3,1,1]=>[1,1,3,1,1,1,1]
010100011=>[1,1,1,1,3,2]=>[2,3,1,1,1,1]
010100100=>[1,1,1,1,2,1,2]=>[2,1,2,1,1,1,1]
010100101=>[1,1,1,1,2,1,1,1]=>[1,1,1,2,1,1,1,1]
010100110=>[1,1,1,1,2,2,1]=>[1,2,2,1,1,1,1]
010100111=>[1,1,1,1,2,3]=>[3,2,1,1,1,1]
010101000=>[1,1,1,1,1,1,3]=>[3,1,1,1,1,1,1]
010101001=>[1,1,1,1,1,1,2,1]=>[1,2,1,1,1,1,1,1]
010101010=>[1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1]
010101011=>[1,1,1,1,1,1,1,2]=>[2,1,1,1,1,1,1,1]
010101100=>[1,1,1,1,1,2,2]=>[2,2,1,1,1,1,1]
010101101=>[1,1,1,1,1,2,1,1]=>[1,1,2,1,1,1,1,1]
010101110=>[1,1,1,1,1,3,1]=>[1,3,1,1,1,1,1]
010101111=>[1,1,1,1,1,4]=>[4,1,1,1,1,1]
010110000=>[1,1,1,2,4]=>[4,2,1,1,1]
010110001=>[1,1,1,2,3,1]=>[1,3,2,1,1,1]
010110010=>[1,1,1,2,2,1,1]=>[1,1,2,2,1,1,1]
010110011=>[1,1,1,2,2,2]=>[2,2,2,1,1,1]
010110100=>[1,1,1,2,1,1,2]=>[2,1,1,2,1,1,1]
010110101=>[1,1,1,2,1,1,1,1]=>[1,1,1,1,2,1,1,1]
010110110=>[1,1,1,2,1,2,1]=>[1,2,1,2,1,1,1]
010110111=>[1,1,1,2,1,3]=>[3,1,2,1,1,1]
010111000=>[1,1,1,3,3]=>[3,3,1,1,1]
010111001=>[1,1,1,3,2,1]=>[1,2,3,1,1,1]
010111010=>[1,1,1,3,1,1,1]=>[1,1,1,3,1,1,1]
010111011=>[1,1,1,3,1,2]=>[2,1,3,1,1,1]
010111100=>[1,1,1,4,2]=>[2,4,1,1,1]
010111101=>[1,1,1,4,1,1]=>[1,1,4,1,1,1]
010111110=>[1,1,1,5,1]=>[1,5,1,1,1]
010111111=>[1,1,1,6]=>[6,1,1,1]
011000000=>[1,2,6]=>[6,2,1]
011000001=>[1,2,5,1]=>[1,5,2,1]
011000010=>[1,2,4,1,1]=>[1,1,4,2,1]
011000011=>[1,2,4,2]=>[2,4,2,1]
011000100=>[1,2,3,1,2]=>[2,1,3,2,1]
011000101=>[1,2,3,1,1,1]=>[1,1,1,3,2,1]
011000110=>[1,2,3,2,1]=>[1,2,3,2,1]
011000111=>[1,2,3,3]=>[3,3,2,1]
011001000=>[1,2,2,1,3]=>[3,1,2,2,1]
011001001=>[1,2,2,1,2,1]=>[1,2,1,2,2,1]
011001010=>[1,2,2,1,1,1,1]=>[1,1,1,1,2,2,1]
011001011=>[1,2,2,1,1,2]=>[2,1,1,2,2,1]
011001100=>[1,2,2,2,2]=>[2,2,2,2,1]
011001101=>[1,2,2,2,1,1]=>[1,1,2,2,2,1]
011001110=>[1,2,2,3,1]=>[1,3,2,2,1]
011001111=>[1,2,2,4]=>[4,2,2,1]
011010000=>[1,2,1,1,4]=>[4,1,1,2,1]
011010001=>[1,2,1,1,3,1]=>[1,3,1,1,2,1]
011010010=>[1,2,1,1,2,1,1]=>[1,1,2,1,1,2,1]
011010011=>[1,2,1,1,2,2]=>[2,2,1,1,2,1]
011010100=>[1,2,1,1,1,1,2]=>[2,1,1,1,1,2,1]
011010101=>[1,2,1,1,1,1,1,1]=>[1,1,1,1,1,1,2,1]
011010110=>[1,2,1,1,1,2,1]=>[1,2,1,1,1,2,1]
011010111=>[1,2,1,1,1,3]=>[3,1,1,1,2,1]
011011000=>[1,2,1,2,3]=>[3,2,1,2,1]
011011001=>[1,2,1,2,2,1]=>[1,2,2,1,2,1]
011011010=>[1,2,1,2,1,1,1]=>[1,1,1,2,1,2,1]
011011011=>[1,2,1,2,1,2]=>[2,1,2,1,2,1]
011011100=>[1,2,1,3,2]=>[2,3,1,2,1]
011011101=>[1,2,1,3,1,1]=>[1,1,3,1,2,1]
011011110=>[1,2,1,4,1]=>[1,4,1,2,1]
011011111=>[1,2,1,5]=>[5,1,2,1]
011100000=>[1,3,5]=>[5,3,1]
011100001=>[1,3,4,1]=>[1,4,3,1]
011100010=>[1,3,3,1,1]=>[1,1,3,3,1]
011100011=>[1,3,3,2]=>[2,3,3,1]
011100100=>[1,3,2,1,2]=>[2,1,2,3,1]
011100101=>[1,3,2,1,1,1]=>[1,1,1,2,3,1]
011100110=>[1,3,2,2,1]=>[1,2,2,3,1]
011100111=>[1,3,2,3]=>[3,2,3,1]
011101000=>[1,3,1,1,3]=>[3,1,1,3,1]
011101001=>[1,3,1,1,2,1]=>[1,2,1,1,3,1]
011101010=>[1,3,1,1,1,1,1]=>[1,1,1,1,1,3,1]
011101011=>[1,3,1,1,1,2]=>[2,1,1,1,3,1]
011101100=>[1,3,1,2,2]=>[2,2,1,3,1]
011101101=>[1,3,1,2,1,1]=>[1,1,2,1,3,1]
011101110=>[1,3,1,3,1]=>[1,3,1,3,1]
011101111=>[1,3,1,4]=>[4,1,3,1]
011110000=>[1,4,4]=>[4,4,1]
011110001=>[1,4,3,1]=>[1,3,4,1]
011110010=>[1,4,2,1,1]=>[1,1,2,4,1]
011110011=>[1,4,2,2]=>[2,2,4,1]
011110100=>[1,4,1,1,2]=>[2,1,1,4,1]
011110101=>[1,4,1,1,1,1]=>[1,1,1,1,4,1]
011110110=>[1,4,1,2,1]=>[1,2,1,4,1]
011110111=>[1,4,1,3]=>[3,1,4,1]
011111000=>[1,5,3]=>[3,5,1]
011111001=>[1,5,2,1]=>[1,2,5,1]
011111010=>[1,5,1,1,1]=>[1,1,1,5,1]
011111011=>[1,5,1,2]=>[2,1,5,1]
011111100=>[1,6,2]=>[2,6,1]
011111101=>[1,6,1,1]=>[1,1,6,1]
011111110=>[1,7,1]=>[1,7,1]
011111111=>[1,8]=>[8,1]
100000000=>[1,8]=>[8,1]
100000001=>[1,7,1]=>[1,7,1]
100000010=>[1,6,1,1]=>[1,1,6,1]
100000011=>[1,6,2]=>[2,6,1]
100000100=>[1,5,1,2]=>[2,1,5,1]
100000101=>[1,5,1,1,1]=>[1,1,1,5,1]
100000110=>[1,5,2,1]=>[1,2,5,1]
100000111=>[1,5,3]=>[3,5,1]
100001000=>[1,4,1,3]=>[3,1,4,1]
100001001=>[1,4,1,2,1]=>[1,2,1,4,1]
100001010=>[1,4,1,1,1,1]=>[1,1,1,1,4,1]
100001011=>[1,4,1,1,2]=>[2,1,1,4,1]
100001100=>[1,4,2,2]=>[2,2,4,1]
100001101=>[1,4,2,1,1]=>[1,1,2,4,1]
100001110=>[1,4,3,1]=>[1,3,4,1]
100001111=>[1,4,4]=>[4,4,1]
100010000=>[1,3,1,4]=>[4,1,3,1]
100010001=>[1,3,1,3,1]=>[1,3,1,3,1]
100010010=>[1,3,1,2,1,1]=>[1,1,2,1,3,1]
100010011=>[1,3,1,2,2]=>[2,2,1,3,1]
100010100=>[1,3,1,1,1,2]=>[2,1,1,1,3,1]
100010101=>[1,3,1,1,1,1,1]=>[1,1,1,1,1,3,1]
100010110=>[1,3,1,1,2,1]=>[1,2,1,1,3,1]
100010111=>[1,3,1,1,3]=>[3,1,1,3,1]
100011000=>[1,3,2,3]=>[3,2,3,1]
100011001=>[1,3,2,2,1]=>[1,2,2,3,1]
100011010=>[1,3,2,1,1,1]=>[1,1,1,2,3,1]
100011011=>[1,3,2,1,2]=>[2,1,2,3,1]
100011100=>[1,3,3,2]=>[2,3,3,1]
100011101=>[1,3,3,1,1]=>[1,1,3,3,1]
100011110=>[1,3,4,1]=>[1,4,3,1]
100011111=>[1,3,5]=>[5,3,1]
100100000=>[1,2,1,5]=>[5,1,2,1]
100100001=>[1,2,1,4,1]=>[1,4,1,2,1]
100100010=>[1,2,1,3,1,1]=>[1,1,3,1,2,1]
100100011=>[1,2,1,3,2]=>[2,3,1,2,1]
100100100=>[1,2,1,2,1,2]=>[2,1,2,1,2,1]
100100101=>[1,2,1,2,1,1,1]=>[1,1,1,2,1,2,1]
100100110=>[1,2,1,2,2,1]=>[1,2,2,1,2,1]
100100111=>[1,2,1,2,3]=>[3,2,1,2,1]
100101000=>[1,2,1,1,1,3]=>[3,1,1,1,2,1]
100101001=>[1,2,1,1,1,2,1]=>[1,2,1,1,1,2,1]
100101010=>[1,2,1,1,1,1,1,1]=>[1,1,1,1,1,1,2,1]
100101011=>[1,2,1,1,1,1,2]=>[2,1,1,1,1,2,1]
100101100=>[1,2,1,1,2,2]=>[2,2,1,1,2,1]
100101101=>[1,2,1,1,2,1,1]=>[1,1,2,1,1,2,1]
100101110=>[1,2,1,1,3,1]=>[1,3,1,1,2,1]
100101111=>[1,2,1,1,4]=>[4,1,1,2,1]
100110000=>[1,2,2,4]=>[4,2,2,1]
100110001=>[1,2,2,3,1]=>[1,3,2,2,1]
100110010=>[1,2,2,2,1,1]=>[1,1,2,2,2,1]
100110011=>[1,2,2,2,2]=>[2,2,2,2,1]
100110100=>[1,2,2,1,1,2]=>[2,1,1,2,2,1]
100110101=>[1,2,2,1,1,1,1]=>[1,1,1,1,2,2,1]
100110110=>[1,2,2,1,2,1]=>[1,2,1,2,2,1]
100110111=>[1,2,2,1,3]=>[3,1,2,2,1]
100111000=>[1,2,3,3]=>[3,3,2,1]
100111001=>[1,2,3,2,1]=>[1,2,3,2,1]
100111010=>[1,2,3,1,1,1]=>[1,1,1,3,2,1]
100111011=>[1,2,3,1,2]=>[2,1,3,2,1]
100111100=>[1,2,4,2]=>[2,4,2,1]
100111101=>[1,2,4,1,1]=>[1,1,4,2,1]
100111110=>[1,2,5,1]=>[1,5,2,1]
100111111=>[1,2,6]=>[6,2,1]
101000000=>[1,1,1,6]=>[6,1,1,1]
101000001=>[1,1,1,5,1]=>[1,5,1,1,1]
101000010=>[1,1,1,4,1,1]=>[1,1,4,1,1,1]
101000011=>[1,1,1,4,2]=>[2,4,1,1,1]
101000100=>[1,1,1,3,1,2]=>[2,1,3,1,1,1]
101000101=>[1,1,1,3,1,1,1]=>[1,1,1,3,1,1,1]
101000110=>[1,1,1,3,2,1]=>[1,2,3,1,1,1]
101000111=>[1,1,1,3,3]=>[3,3,1,1,1]
101001000=>[1,1,1,2,1,3]=>[3,1,2,1,1,1]
101001001=>[1,1,1,2,1,2,1]=>[1,2,1,2,1,1,1]
101001010=>[1,1,1,2,1,1,1,1]=>[1,1,1,1,2,1,1,1]
101001011=>[1,1,1,2,1,1,2]=>[2,1,1,2,1,1,1]
101001100=>[1,1,1,2,2,2]=>[2,2,2,1,1,1]
101001101=>[1,1,1,2,2,1,1]=>[1,1,2,2,1,1,1]
101001110=>[1,1,1,2,3,1]=>[1,3,2,1,1,1]
101001111=>[1,1,1,2,4]=>[4,2,1,1,1]
101010000=>[1,1,1,1,1,4]=>[4,1,1,1,1,1]
101010001=>[1,1,1,1,1,3,1]=>[1,3,1,1,1,1,1]
101010010=>[1,1,1,1,1,2,1,1]=>[1,1,2,1,1,1,1,1]
101010011=>[1,1,1,1,1,2,2]=>[2,2,1,1,1,1,1]
101010100=>[1,1,1,1,1,1,1,2]=>[2,1,1,1,1,1,1,1]
101010101=>[1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1]
101010110=>[1,1,1,1,1,1,2,1]=>[1,2,1,1,1,1,1,1]
101010111=>[1,1,1,1,1,1,3]=>[3,1,1,1,1,1,1]
101011000=>[1,1,1,1,2,3]=>[3,2,1,1,1,1]
101011001=>[1,1,1,1,2,2,1]=>[1,2,2,1,1,1,1]
101011010=>[1,1,1,1,2,1,1,1]=>[1,1,1,2,1,1,1,1]
101011011=>[1,1,1,1,2,1,2]=>[2,1,2,1,1,1,1]
101011100=>[1,1,1,1,3,2]=>[2,3,1,1,1,1]
101011101=>[1,1,1,1,3,1,1]=>[1,1,3,1,1,1,1]
101011110=>[1,1,1,1,4,1]=>[1,4,1,1,1,1]
101011111=>[1,1,1,1,5]=>[5,1,1,1,1]
101100000=>[1,1,2,5]=>[5,2,1,1]
101100001=>[1,1,2,4,1]=>[1,4,2,1,1]
101100010=>[1,1,2,3,1,1]=>[1,1,3,2,1,1]
101100011=>[1,1,2,3,2]=>[2,3,2,1,1]
101100100=>[1,1,2,2,1,2]=>[2,1,2,2,1,1]
101100101=>[1,1,2,2,1,1,1]=>[1,1,1,2,2,1,1]
101100110=>[1,1,2,2,2,1]=>[1,2,2,2,1,1]
101100111=>[1,1,2,2,3]=>[3,2,2,1,1]
101101000=>[1,1,2,1,1,3]=>[3,1,1,2,1,1]
101101001=>[1,1,2,1,1,2,1]=>[1,2,1,1,2,1,1]
101101010=>[1,1,2,1,1,1,1,1]=>[1,1,1,1,1,2,1,1]
101101011=>[1,1,2,1,1,1,2]=>[2,1,1,1,2,1,1]
101101100=>[1,1,2,1,2,2]=>[2,2,1,2,1,1]
101101101=>[1,1,2,1,2,1,1]=>[1,1,2,1,2,1,1]
101101110=>[1,1,2,1,3,1]=>[1,3,1,2,1,1]
101101111=>[1,1,2,1,4]=>[4,1,2,1,1]
101110000=>[1,1,3,4]=>[4,3,1,1]
101110001=>[1,1,3,3,1]=>[1,3,3,1,1]
101110010=>[1,1,3,2,1,1]=>[1,1,2,3,1,1]
101110011=>[1,1,3,2,2]=>[2,2,3,1,1]
101110100=>[1,1,3,1,1,2]=>[2,1,1,3,1,1]
101110101=>[1,1,3,1,1,1,1]=>[1,1,1,1,3,1,1]
101110110=>[1,1,3,1,2,1]=>[1,2,1,3,1,1]
101110111=>[1,1,3,1,3]=>[3,1,3,1,1]
101111000=>[1,1,4,3]=>[3,4,1,1]
101111001=>[1,1,4,2,1]=>[1,2,4,1,1]
101111010=>[1,1,4,1,1,1]=>[1,1,1,4,1,1]
101111011=>[1,1,4,1,2]=>[2,1,4,1,1]
101111100=>[1,1,5,2]=>[2,5,1,1]
101111101=>[1,1,5,1,1]=>[1,1,5,1,1]
101111110=>[1,1,6,1]=>[1,6,1,1]
101111111=>[1,1,7]=>[7,1,1]
110000000=>[2,7]=>[7,2]
110000001=>[2,6,1]=>[1,6,2]
110000010=>[2,5,1,1]=>[1,1,5,2]
110000011=>[2,5,2]=>[2,5,2]
110000100=>[2,4,1,2]=>[2,1,4,2]
110000101=>[2,4,1,1,1]=>[1,1,1,4,2]
110000110=>[2,4,2,1]=>[1,2,4,2]
110000111=>[2,4,3]=>[3,4,2]
110001000=>[2,3,1,3]=>[3,1,3,2]
110001001=>[2,3,1,2,1]=>[1,2,1,3,2]
110001010=>[2,3,1,1,1,1]=>[1,1,1,1,3,2]
110001011=>[2,3,1,1,2]=>[2,1,1,3,2]
110001100=>[2,3,2,2]=>[2,2,3,2]
110001101=>[2,3,2,1,1]=>[1,1,2,3,2]
110001110=>[2,3,3,1]=>[1,3,3,2]
110001111=>[2,3,4]=>[4,3,2]
110010000=>[2,2,1,4]=>[4,1,2,2]
110010001=>[2,2,1,3,1]=>[1,3,1,2,2]
110010010=>[2,2,1,2,1,1]=>[1,1,2,1,2,2]
110010011=>[2,2,1,2,2]=>[2,2,1,2,2]
110010100=>[2,2,1,1,1,2]=>[2,1,1,1,2,2]
110010101=>[2,2,1,1,1,1,1]=>[1,1,1,1,1,2,2]
110010110=>[2,2,1,1,2,1]=>[1,2,1,1,2,2]
110010111=>[2,2,1,1,3]=>[3,1,1,2,2]
110011000=>[2,2,2,3]=>[3,2,2,2]
110011001=>[2,2,2,2,1]=>[1,2,2,2,2]
110011010=>[2,2,2,1,1,1]=>[1,1,1,2,2,2]
110011011=>[2,2,2,1,2]=>[2,1,2,2,2]
110011100=>[2,2,3,2]=>[2,3,2,2]
110011101=>[2,2,3,1,1]=>[1,1,3,2,2]
110011110=>[2,2,4,1]=>[1,4,2,2]
110011111=>[2,2,5]=>[5,2,2]
110100000=>[2,1,1,5]=>[5,1,1,2]
110100001=>[2,1,1,4,1]=>[1,4,1,1,2]
110100010=>[2,1,1,3,1,1]=>[1,1,3,1,1,2]
110100011=>[2,1,1,3,2]=>[2,3,1,1,2]
110100100=>[2,1,1,2,1,2]=>[2,1,2,1,1,2]
110100101=>[2,1,1,2,1,1,1]=>[1,1,1,2,1,1,2]
110100110=>[2,1,1,2,2,1]=>[1,2,2,1,1,2]
110100111=>[2,1,1,2,3]=>[3,2,1,1,2]
110101000=>[2,1,1,1,1,3]=>[3,1,1,1,1,2]
110101001=>[2,1,1,1,1,2,1]=>[1,2,1,1,1,1,2]
110101010=>[2,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,2]
110101011=>[2,1,1,1,1,1,2]=>[2,1,1,1,1,1,2]
110101100=>[2,1,1,1,2,2]=>[2,2,1,1,1,2]
110101101=>[2,1,1,1,2,1,1]=>[1,1,2,1,1,1,2]
110101110=>[2,1,1,1,3,1]=>[1,3,1,1,1,2]
110101111=>[2,1,1,1,4]=>[4,1,1,1,2]
110110000=>[2,1,2,4]=>[4,2,1,2]
110110001=>[2,1,2,3,1]=>[1,3,2,1,2]
110110010=>[2,1,2,2,1,1]=>[1,1,2,2,1,2]
110110011=>[2,1,2,2,2]=>[2,2,2,1,2]
110110100=>[2,1,2,1,1,2]=>[2,1,1,2,1,2]
110110101=>[2,1,2,1,1,1,1]=>[1,1,1,1,2,1,2]
110110110=>[2,1,2,1,2,1]=>[1,2,1,2,1,2]
110110111=>[2,1,2,1,3]=>[3,1,2,1,2]
110111000=>[2,1,3,3]=>[3,3,1,2]
110111001=>[2,1,3,2,1]=>[1,2,3,1,2]
110111010=>[2,1,3,1,1,1]=>[1,1,1,3,1,2]
110111011=>[2,1,3,1,2]=>[2,1,3,1,2]
110111100=>[2,1,4,2]=>[2,4,1,2]
110111101=>[2,1,4,1,1]=>[1,1,4,1,2]
110111110=>[2,1,5,1]=>[1,5,1,2]
110111111=>[2,1,6]=>[6,1,2]
111000000=>[3,6]=>[6,3]
111000001=>[3,5,1]=>[1,5,3]
111000010=>[3,4,1,1]=>[1,1,4,3]
111000011=>[3,4,2]=>[2,4,3]
111000100=>[3,3,1,2]=>[2,1,3,3]
111000101=>[3,3,1,1,1]=>[1,1,1,3,3]
111000110=>[3,3,2,1]=>[1,2,3,3]
111000111=>[3,3,3]=>[3,3,3]
111001000=>[3,2,1,3]=>[3,1,2,3]
111001001=>[3,2,1,2,1]=>[1,2,1,2,3]
111001010=>[3,2,1,1,1,1]=>[1,1,1,1,2,3]
111001011=>[3,2,1,1,2]=>[2,1,1,2,3]
111001100=>[3,2,2,2]=>[2,2,2,3]
111001101=>[3,2,2,1,1]=>[1,1,2,2,3]
111001110=>[3,2,3,1]=>[1,3,2,3]
111001111=>[3,2,4]=>[4,2,3]
111010000=>[3,1,1,4]=>[4,1,1,3]
111010001=>[3,1,1,3,1]=>[1,3,1,1,3]
111010010=>[3,1,1,2,1,1]=>[1,1,2,1,1,3]
111010011=>[3,1,1,2,2]=>[2,2,1,1,3]
111010100=>[3,1,1,1,1,2]=>[2,1,1,1,1,3]
111010101=>[3,1,1,1,1,1,1]=>[1,1,1,1,1,1,3]
111010110=>[3,1,1,1,2,1]=>[1,2,1,1,1,3]
111010111=>[3,1,1,1,3]=>[3,1,1,1,3]
111011000=>[3,1,2,3]=>[3,2,1,3]
111011001=>[3,1,2,2,1]=>[1,2,2,1,3]
111011010=>[3,1,2,1,1,1]=>[1,1,1,2,1,3]
111011011=>[3,1,2,1,2]=>[2,1,2,1,3]
111011100=>[3,1,3,2]=>[2,3,1,3]
111011101=>[3,1,3,1,1]=>[1,1,3,1,3]
111011110=>[3,1,4,1]=>[1,4,1,3]
111011111=>[3,1,5]=>[5,1,3]
111100000=>[4,5]=>[5,4]
111100001=>[4,4,1]=>[1,4,4]
111100010=>[4,3,1,1]=>[1,1,3,4]
111100011=>[4,3,2]=>[2,3,4]
111100100=>[4,2,1,2]=>[2,1,2,4]
111100101=>[4,2,1,1,1]=>[1,1,1,2,4]
111100110=>[4,2,2,1]=>[1,2,2,4]
111100111=>[4,2,3]=>[3,2,4]
111101000=>[4,1,1,3]=>[3,1,1,4]
111101001=>[4,1,1,2,1]=>[1,2,1,1,4]
111101010=>[4,1,1,1,1,1]=>[1,1,1,1,1,4]
111101011=>[4,1,1,1,2]=>[2,1,1,1,4]
111101100=>[4,1,2,2]=>[2,2,1,4]
111101101=>[4,1,2,1,1]=>[1,1,2,1,4]
111101110=>[4,1,3,1]=>[1,3,1,4]
111101111=>[4,1,4]=>[4,1,4]
111110000=>[5,4]=>[4,5]
111110001=>[5,3,1]=>[1,3,5]
111110010=>[5,2,1,1]=>[1,1,2,5]
111110011=>[5,2,2]=>[2,2,5]
111110100=>[5,1,1,2]=>[2,1,1,5]
111110101=>[5,1,1,1,1]=>[1,1,1,1,5]
111110110=>[5,1,2,1]=>[1,2,1,5]
111110111=>[5,1,3]=>[3,1,5]
111111000=>[6,3]=>[3,6]
111111001=>[6,2,1]=>[1,2,6]
111111010=>[6,1,1,1]=>[1,1,1,6]
111111011=>[6,1,2]=>[2,1,6]
111111100=>[7,2]=>[2,7]
111111101=>[7,1,1]=>[1,1,7]
111111110=>[8,1]=>[1,8]
111111111=>[9]=>[9]
1010101010=>[1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1]
1010101100=>[1,1,1,1,1,1,2,2]=>[2,2,1,1,1,1,1,1]
1010110010=>[1,1,1,1,2,2,1,1]=>[1,1,2,2,1,1,1,1]
1010110100=>[1,1,1,1,2,1,1,2]=>[2,1,1,2,1,1,1,1]
1010111000=>[1,1,1,1,3,3]=>[3,3,1,1,1,1]
1011001010=>[1,1,2,2,1,1,1,1]=>[1,1,1,1,2,2,1,1]
1011001100=>[1,1,2,2,2,2]=>[2,2,2,2,1,1]
1011010010=>[1,1,2,1,1,2,1,1]=>[1,1,2,1,1,2,1,1]
1011010100=>[1,1,2,1,1,1,1,2]=>[2,1,1,1,1,2,1,1]
1011011000=>[1,1,2,1,2,3]=>[3,2,1,2,1,1]
1011100010=>[1,1,3,3,1,1]=>[1,1,3,3,1,1]
1011100100=>[1,1,3,2,1,2]=>[2,1,2,3,1,1]
1011101000=>[1,1,3,1,1,3]=>[3,1,1,3,1,1]
1011110000=>[1,1,4,4]=>[4,4,1,1]
1100101010=>[2,2,1,1,1,1,1,1]=>[1,1,1,1,1,1,2,2]
1100101100=>[2,2,1,1,2,2]=>[2,2,1,1,2,2]
1100110010=>[2,2,2,2,1,1]=>[1,1,2,2,2,2]
1100110100=>[2,2,2,1,1,2]=>[2,1,1,2,2,2]
1100111000=>[2,2,3,3]=>[3,3,2,2]
1101001010=>[2,1,1,2,1,1,1,1]=>[1,1,1,1,2,1,1,2]
1101001100=>[2,1,1,2,2,2]=>[2,2,2,1,1,2]
1101010010=>[2,1,1,1,1,2,1,1]=>[1,1,2,1,1,1,1,2]
1101010100=>[2,1,1,1,1,1,1,2]=>[2,1,1,1,1,1,1,2]
1101011000=>[2,1,1,1,2,3]=>[3,2,1,1,1,2]
1101100010=>[2,1,2,3,1,1]=>[1,1,3,2,1,2]
1101100100=>[2,1,2,2,1,2]=>[2,1,2,2,1,2]
1101101000=>[2,1,2,1,1,3]=>[3,1,1,2,1,2]
1101110000=>[2,1,3,4]=>[4,3,1,2]
1110001010=>[3,3,1,1,1,1]=>[1,1,1,1,3,3]
1110001100=>[3,3,2,2]=>[2,2,3,3]
1110010010=>[3,2,1,2,1,1]=>[1,1,2,1,2,3]
1110010100=>[3,2,1,1,1,2]=>[2,1,1,1,2,3]
1110011000=>[3,2,2,3]=>[3,2,2,3]
1110100010=>[3,1,1,3,1,1]=>[1,1,3,1,1,3]
1110100100=>[3,1,1,2,1,2]=>[2,1,2,1,1,3]
1110101000=>[3,1,1,1,1,3]=>[3,1,1,1,1,3]
1110110000=>[3,1,2,4]=>[4,2,1,3]
1111000010=>[4,4,1,1]=>[1,1,4,4]
1111000100=>[4,3,1,2]=>[2,1,3,4]
1111001000=>[4,2,1,3]=>[3,1,2,4]
1111010000=>[4,1,1,4]=>[4,1,1,4]
1111100000=>[5,5]=>[5,5]
101010101010=>[1,1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1,1,1]
101010101100=>[1,1,1,1,1,1,1,1,2,2]=>[2,2,1,1,1,1,1,1,1,1]
101010110010=>[1,1,1,1,1,1,2,2,1,1]=>[1,1,2,2,1,1,1,1,1,1]
101010110100=>[1,1,1,1,1,1,2,1,1,2]=>[2,1,1,2,1,1,1,1,1,1]
101010111000=>[1,1,1,1,1,1,3,3]=>[3,3,1,1,1,1,1,1]
101011001010=>[1,1,1,1,2,2,1,1,1,1]=>[1,1,1,1,2,2,1,1,1,1]
101011001100=>[1,1,1,1,2,2,2,2]=>[2,2,2,2,1,1,1,1]
101011010010=>[1,1,1,1,2,1,1,2,1,1]=>[1,1,2,1,1,2,1,1,1,1]
101011010100=>[1,1,1,1,2,1,1,1,1,2]=>[2,1,1,1,1,2,1,1,1,1]
101011011000=>[1,1,1,1,2,1,2,3]=>[3,2,1,2,1,1,1,1]
101011100010=>[1,1,1,1,3,3,1,1]=>[1,1,3,3,1,1,1,1]
101011100100=>[1,1,1,1,3,2,1,2]=>[2,1,2,3,1,1,1,1]
101011101000=>[1,1,1,1,3,1,1,3]=>[3,1,1,3,1,1,1,1]
101011110000=>[1,1,1,1,4,4]=>[4,4,1,1,1,1]
101100101010=>[1,1,2,2,1,1,1,1,1,1]=>[1,1,1,1,1,1,2,2,1,1]
101100101100=>[1,1,2,2,1,1,2,2]=>[2,2,1,1,2,2,1,1]
101100110010=>[1,1,2,2,2,2,1,1]=>[1,1,2,2,2,2,1,1]
101100110100=>[1,1,2,2,2,1,1,2]=>[2,1,1,2,2,2,1,1]
101100111000=>[1,1,2,2,3,3]=>[3,3,2,2,1,1]
101101001010=>[1,1,2,1,1,2,1,1,1,1]=>[1,1,1,1,2,1,1,2,1,1]
101101001100=>[1,1,2,1,1,2,2,2]=>[2,2,2,1,1,2,1,1]
101101010010=>[1,1,2,1,1,1,1,2,1,1]=>[1,1,2,1,1,1,1,2,1,1]
101101010100=>[1,1,2,1,1,1,1,1,1,2]=>[2,1,1,1,1,1,1,2,1,1]
101101011000=>[1,1,2,1,1,1,2,3]=>[3,2,1,1,1,2,1,1]
101101100010=>[1,1,2,1,2,3,1,1]=>[1,1,3,2,1,2,1,1]
101101100100=>[1,1,2,1,2,2,1,2]=>[2,1,2,2,1,2,1,1]
101101101000=>[1,1,2,1,2,1,1,3]=>[3,1,1,2,1,2,1,1]
101101110000=>[1,1,2,1,3,4]=>[4,3,1,2,1,1]
101110001010=>[1,1,3,3,1,1,1,1]=>[1,1,1,1,3,3,1,1]
101110001100=>[1,1,3,3,2,2]=>[2,2,3,3,1,1]
101110010010=>[1,1,3,2,1,2,1,1]=>[1,1,2,1,2,3,1,1]
101110010100=>[1,1,3,2,1,1,1,2]=>[2,1,1,1,2,3,1,1]
101110011000=>[1,1,3,2,2,3]=>[3,2,2,3,1,1]
101110100010=>[1,1,3,1,1,3,1,1]=>[1,1,3,1,1,3,1,1]
101110100100=>[1,1,3,1,1,2,1,2]=>[2,1,2,1,1,3,1,1]
101110101000=>[1,1,3,1,1,1,1,3]=>[3,1,1,1,1,3,1,1]
101110110000=>[1,1,3,1,2,4]=>[4,2,1,3,1,1]
101111000010=>[1,1,4,4,1,1]=>[1,1,4,4,1,1]
101111000100=>[1,1,4,3,1,2]=>[2,1,3,4,1,1]
101111001000=>[1,1,4,2,1,3]=>[3,1,2,4,1,1]
101111010000=>[1,1,4,1,1,4]=>[4,1,1,4,1,1]
101111100000=>[1,1,5,5]=>[5,5,1,1]
110010101010=>[2,2,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,2,2]
110010101100=>[2,2,1,1,1,1,2,2]=>[2,2,1,1,1,1,2,2]
110010110010=>[2,2,1,1,2,2,1,1]=>[1,1,2,2,1,1,2,2]
110010110100=>[2,2,1,1,2,1,1,2]=>[2,1,1,2,1,1,2,2]
110010111000=>[2,2,1,1,3,3]=>[3,3,1,1,2,2]
110011001010=>[2,2,2,2,1,1,1,1]=>[1,1,1,1,2,2,2,2]
110011001100=>[2,2,2,2,2,2]=>[2,2,2,2,2,2]
110011010010=>[2,2,2,1,1,2,1,1]=>[1,1,2,1,1,2,2,2]
110011010100=>[2,2,2,1,1,1,1,2]=>[2,1,1,1,1,2,2,2]
110011011000=>[2,2,2,1,2,3]=>[3,2,1,2,2,2]
110011100010=>[2,2,3,3,1,1]=>[1,1,3,3,2,2]
110011100100=>[2,2,3,2,1,2]=>[2,1,2,3,2,2]
110011101000=>[2,2,3,1,1,3]=>[3,1,1,3,2,2]
110011110000=>[2,2,4,4]=>[4,4,2,2]
110100101010=>[2,1,1,2,1,1,1,1,1,1]=>[1,1,1,1,1,1,2,1,1,2]
110100101100=>[2,1,1,2,1,1,2,2]=>[2,2,1,1,2,1,1,2]
110100110010=>[2,1,1,2,2,2,1,1]=>[1,1,2,2,2,1,1,2]
110100110100=>[2,1,1,2,2,1,1,2]=>[2,1,1,2,2,1,1,2]
110100111000=>[2,1,1,2,3,3]=>[3,3,2,1,1,2]
110101001010=>[2,1,1,1,1,2,1,1,1,1]=>[1,1,1,1,2,1,1,1,1,2]
110101001100=>[2,1,1,1,1,2,2,2]=>[2,2,2,1,1,1,1,2]
110101010010=>[2,1,1,1,1,1,1,2,1,1]=>[1,1,2,1,1,1,1,1,1,2]
110101010100=>[2,1,1,1,1,1,1,1,1,2]=>[2,1,1,1,1,1,1,1,1,2]
110101011000=>[2,1,1,1,1,1,2,3]=>[3,2,1,1,1,1,1,2]
110101100010=>[2,1,1,1,2,3,1,1]=>[1,1,3,2,1,1,1,2]
110101100100=>[2,1,1,1,2,2,1,2]=>[2,1,2,2,1,1,1,2]
110101101000=>[2,1,1,1,2,1,1,3]=>[3,1,1,2,1,1,1,2]
110101110000=>[2,1,1,1,3,4]=>[4,3,1,1,1,2]
110110001010=>[2,1,2,3,1,1,1,1]=>[1,1,1,1,3,2,1,2]
110110001100=>[2,1,2,3,2,2]=>[2,2,3,2,1,2]
110110010010=>[2,1,2,2,1,2,1,1]=>[1,1,2,1,2,2,1,2]
110110010100=>[2,1,2,2,1,1,1,2]=>[2,1,1,1,2,2,1,2]
110110011000=>[2,1,2,2,2,3]=>[3,2,2,2,1,2]
110110100010=>[2,1,2,1,1,3,1,1]=>[1,1,3,1,1,2,1,2]
110110100100=>[2,1,2,1,1,2,1,2]=>[2,1,2,1,1,2,1,2]
110110101000=>[2,1,2,1,1,1,1,3]=>[3,1,1,1,1,2,1,2]
110110110000=>[2,1,2,1,2,4]=>[4,2,1,2,1,2]
110111000010=>[2,1,3,4,1,1]=>[1,1,4,3,1,2]
110111000100=>[2,1,3,3,1,2]=>[2,1,3,3,1,2]
110111001000=>[2,1,3,2,1,3]=>[3,1,2,3,1,2]
110111010000=>[2,1,3,1,1,4]=>[4,1,1,3,1,2]
110111100000=>[2,1,4,5]=>[5,4,1,2]
111000101010=>[3,3,1,1,1,1,1,1]=>[1,1,1,1,1,1,3,3]
111000101100=>[3,3,1,1,2,2]=>[2,2,1,1,3,3]
111000110010=>[3,3,2,2,1,1]=>[1,1,2,2,3,3]
111000110100=>[3,3,2,1,1,2]=>[2,1,1,2,3,3]
111000111000=>[3,3,3,3]=>[3,3,3,3]
111001001010=>[3,2,1,2,1,1,1,1]=>[1,1,1,1,2,1,2,3]
111001001100=>[3,2,1,2,2,2]=>[2,2,2,1,2,3]
111001010010=>[3,2,1,1,1,2,1,1]=>[1,1,2,1,1,1,2,3]
111001010100=>[3,2,1,1,1,1,1,2]=>[2,1,1,1,1,1,2,3]
111001011000=>[3,2,1,1,2,3]=>[3,2,1,1,2,3]
111001100010=>[3,2,2,3,1,1]=>[1,1,3,2,2,3]
111001100100=>[3,2,2,2,1,2]=>[2,1,2,2,2,3]
111001101000=>[3,2,2,1,1,3]=>[3,1,1,2,2,3]
111001110000=>[3,2,3,4]=>[4,3,2,3]
111010001010=>[3,1,1,3,1,1,1,1]=>[1,1,1,1,3,1,1,3]
111010001100=>[3,1,1,3,2,2]=>[2,2,3,1,1,3]
111010010010=>[3,1,1,2,1,2,1,1]=>[1,1,2,1,2,1,1,3]
111010010100=>[3,1,1,2,1,1,1,2]=>[2,1,1,1,2,1,1,3]
111010011000=>[3,1,1,2,2,3]=>[3,2,2,1,1,3]
111010100010=>[3,1,1,1,1,3,1,1]=>[1,1,3,1,1,1,1,3]
111010100100=>[3,1,1,1,1,2,1,2]=>[2,1,2,1,1,1,1,3]
111010101000=>[3,1,1,1,1,1,1,3]=>[3,1,1,1,1,1,1,3]
111010110000=>[3,1,1,1,2,4]=>[4,2,1,1,1,3]
111011000010=>[3,1,2,4,1,1]=>[1,1,4,2,1,3]
111011000100=>[3,1,2,3,1,2]=>[2,1,3,2,1,3]
111011001000=>[3,1,2,2,1,3]=>[3,1,2,2,1,3]
111011010000=>[3,1,2,1,1,4]=>[4,1,1,2,1,3]
111011100000=>[3,1,3,5]=>[5,3,1,3]
111100001010=>[4,4,1,1,1,1]=>[1,1,1,1,4,4]
111100001100=>[4,4,2,2]=>[2,2,4,4]
111100010010=>[4,3,1,2,1,1]=>[1,1,2,1,3,4]
111100010100=>[4,3,1,1,1,2]=>[2,1,1,1,3,4]
111100011000=>[4,3,2,3]=>[3,2,3,4]
111100100010=>[4,2,1,3,1,1]=>[1,1,3,1,2,4]
111100100100=>[4,2,1,2,1,2]=>[2,1,2,1,2,4]
111100101000=>[4,2,1,1,1,3]=>[3,1,1,1,2,4]
111100110000=>[4,2,2,4]=>[4,2,2,4]
111101000010=>[4,1,1,4,1,1]=>[1,1,4,1,1,4]
111101000100=>[4,1,1,3,1,2]=>[2,1,3,1,1,4]
111101001000=>[4,1,1,2,1,3]=>[3,1,2,1,1,4]
111101010000=>[4,1,1,1,1,4]=>[4,1,1,1,1,4]
111101100000=>[4,1,2,5]=>[5,2,1,4]
111110000010=>[5,5,1,1]=>[1,1,5,5]
111110000100=>[5,4,1,2]=>[2,1,4,5]
111110001000=>[5,3,1,3]=>[3,1,3,5]
111110010000=>[5,2,1,4]=>[4,1,2,5]
111110100000=>[5,1,1,5]=>[5,1,1,5]
111111000000=>[6,6]=>[6,6]
1111111111=>[10]=>[10]
1111111110=>[9,1]=>[1,9]
1111110000=>[6,4]=>[4,6]
1111101000=>[5,1,1,3]=>[3,1,1,5]
1111100100=>[5,2,1,2]=>[2,1,2,5]
1111100010=>[5,3,1,1]=>[1,1,3,5]
1111100001=>[5,4,1]=>[1,4,5]
1111011000=>[4,1,2,3]=>[3,2,1,4]
1111010100=>[4,1,1,1,1,2]=>[2,1,1,1,1,4]
1111010010=>[4,1,1,2,1,1]=>[1,1,2,1,1,4]
1111010001=>[4,1,1,3,1]=>[1,3,1,1,4]
1111001100=>[4,2,2,2]=>[2,2,2,4]
1111001010=>[4,2,1,1,1,1]=>[1,1,1,1,2,4]
1111001001=>[4,2,1,2,1]=>[1,2,1,2,4]
1111000101=>[4,3,1,1,1]=>[1,1,1,3,4]
1111000011=>[4,4,2]=>[2,4,4]
1111000001=>[4,5,1]=>[1,5,4]
1110111111=>[3,1,6]=>[6,1,3]
1110111110=>[3,1,5,1]=>[1,5,1,3]
1110111000=>[3,1,3,3]=>[3,3,1,3]
1110110100=>[3,1,2,1,1,2]=>[2,1,1,2,1,3]
1110110010=>[3,1,2,2,1,1]=>[1,1,2,2,1,3]
1110110001=>[3,1,2,3,1]=>[1,3,2,1,3]
1110101100=>[3,1,1,1,2,2]=>[2,2,1,1,1,3]
1110101010=>[3,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,3]
1110101001=>[3,1,1,1,1,2,1]=>[1,2,1,1,1,1,3]
1110100101=>[3,1,1,2,1,1,1]=>[1,1,1,2,1,1,3]
1110100011=>[3,1,1,3,2]=>[2,3,1,1,3]
1110100001=>[3,1,1,4,1]=>[1,4,1,1,3]
1110011111=>[3,2,5]=>[5,2,3]
1110011001=>[3,2,2,2,1]=>[1,2,2,2,3]
1110010101=>[3,2,1,1,1,1,1]=>[1,1,1,1,1,2,3]
1110010011=>[3,2,1,2,2]=>[2,2,1,2,3]
1110010001=>[3,2,1,3,1]=>[1,3,1,2,3]
1110001101=>[3,3,2,1,1]=>[1,1,2,3,3]
1110000111=>[3,4,3]=>[3,4,3]
1110000011=>[3,5,2]=>[2,5,3]
1101111111=>[2,1,7]=>[7,1,2]
1101111110=>[2,1,6,1]=>[1,6,1,2]
1101110001=>[2,1,3,3,1]=>[1,3,3,1,2]
1101101001=>[2,1,2,1,1,2,1]=>[1,2,1,1,2,1,2]
1101100101=>[2,1,2,2,1,1,1]=>[1,1,1,2,2,1,2]
1101100011=>[2,1,2,3,2]=>[2,3,2,1,2]
1101100001=>[2,1,2,4,1]=>[1,4,2,1,2]
1101011111=>[2,1,1,1,5]=>[5,1,1,1,2]
1101011001=>[2,1,1,1,2,2,1]=>[1,2,2,1,1,1,2]
1101010101=>[2,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,2]
1101010011=>[2,1,1,1,1,2,2]=>[2,2,1,1,1,1,2]
1101010001=>[2,1,1,1,1,3,1]=>[1,3,1,1,1,1,2]
1101001111=>[2,1,1,2,4]=>[4,2,1,1,2]
1101001101=>[2,1,1,2,2,1,1]=>[1,1,2,2,1,1,2]
1101000111=>[2,1,1,3,3]=>[3,3,1,1,2]
1101000011=>[2,1,1,4,2]=>[2,4,1,1,2]
1100111111=>[2,2,6]=>[6,2,2]
1100111001=>[2,2,3,2,1]=>[1,2,3,2,2]
1100110101=>[2,2,2,1,1,1,1]=>[1,1,1,1,2,2,2]
1100110011=>[2,2,2,2,2]=>[2,2,2,2,2]
1100110001=>[2,2,2,3,1]=>[1,3,2,2,2]
1100101110=>[2,2,1,1,3,1]=>[1,3,1,1,2,2]
1100011110=>[2,3,4,1]=>[1,4,3,2]
1100011101=>[2,3,3,1,1]=>[1,1,3,3,2]
1100011100=>[2,3,3,2]=>[2,3,3,2]
1100001111=>[2,4,4]=>[4,4,2]
1100001010=>[2,4,1,1,1,1]=>[1,1,1,1,4,2]
1100000111=>[2,5,3]=>[3,5,2]
1100000110=>[2,5,2,1]=>[1,2,5,2]
1100000000=>[2,8]=>[8,2]
1011111110=>[1,1,7,1]=>[1,7,1,1]
1011100000=>[1,1,3,5]=>[5,3,1,1]
1011010101=>[1,1,2,1,1,1,1,1,1]=>[1,1,1,1,1,1,2,1,1]
1011010000=>[1,1,2,1,1,4]=>[4,1,1,2,1,1]
1011001000=>[1,1,2,2,1,3]=>[3,1,2,2,1,1]
1011000100=>[1,1,2,3,1,2]=>[2,1,3,2,1,1]
1011000010=>[1,1,2,4,1,1]=>[1,1,4,2,1,1]
1010111110=>[1,1,1,1,5,1]=>[1,5,1,1,1,1]
1010110000=>[1,1,1,1,2,4]=>[4,2,1,1,1,1]
1010101000=>[1,1,1,1,1,1,1,3]=>[3,1,1,1,1,1,1,1]
1010100100=>[1,1,1,1,1,2,1,2]=>[2,1,2,1,1,1,1,1]
1010100010=>[1,1,1,1,1,3,1,1]=>[1,1,3,1,1,1,1,1]
1010011000=>[1,1,1,2,2,3]=>[3,2,2,1,1,1]
1010010100=>[1,1,1,2,1,1,1,2]=>[2,1,1,1,2,1,1,1]
1010010010=>[1,1,1,2,1,2,1,1]=>[1,1,2,1,2,1,1,1]
1010001100=>[1,1,1,3,2,2]=>[2,2,3,1,1,1]
1010001010=>[1,1,1,3,1,1,1,1]=>[1,1,1,1,3,1,1,1]
1001111110=>[1,2,6,1]=>[1,6,2,1]
1001110000=>[1,2,3,4]=>[4,3,2,1]
1001101000=>[1,2,2,1,1,3]=>[3,1,1,2,2,1]
1001100100=>[1,2,2,2,1,2]=>[2,1,2,2,2,1]
1001100010=>[1,2,2,3,1,1]=>[1,1,3,2,2,1]
1001011110=>[1,2,1,1,4,1]=>[1,4,1,1,2,1]
1001011000=>[1,2,1,1,2,3]=>[3,2,1,1,2,1]
1001010101=>[1,2,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,2,1]
1001010100=>[1,2,1,1,1,1,1,2]=>[2,1,1,1,1,1,2,1]
1001010010=>[1,2,1,1,1,2,1,1]=>[1,1,2,1,1,1,2,1]
1001001100=>[1,2,1,2,2,2]=>[2,2,2,1,2,1]
1001001010=>[1,2,1,2,1,1,1,1]=>[1,1,1,1,2,1,2,1]
1000111110=>[1,3,5,1]=>[1,5,3,1]
1000111000=>[1,3,3,3]=>[3,3,3,1]
1000110101=>[1,3,2,1,1,1,1]=>[1,1,1,1,2,3,1]
1000110100=>[1,3,2,1,1,2]=>[2,1,1,2,3,1]
1000110010=>[1,3,2,2,1,1]=>[1,1,2,2,3,1]
1000101110=>[1,3,1,1,3,1]=>[1,3,1,1,3,1]
1000101100=>[1,3,1,1,2,2]=>[2,2,1,1,3,1]
1000101010=>[1,3,1,1,1,1,1,1]=>[1,1,1,1,1,1,3,1]
1000011110=>[1,4,4,1]=>[1,4,4,1]
1000010110=>[1,4,1,1,2,1]=>[1,2,1,1,4,1]
1000010101=>[1,4,1,1,1,1,1]=>[1,1,1,1,1,4,1]
1000001110=>[1,5,3,1]=>[1,3,5,1]
1000001101=>[1,5,2,1,1]=>[1,1,2,5,1]
1000001010=>[1,5,1,1,1,1]=>[1,1,1,1,5,1]
1000000110=>[1,6,2,1]=>[1,2,6,1]
1000000101=>[1,6,1,1,1]=>[1,1,1,6,1]
1000000100=>[1,6,1,2]=>[2,1,6,1]
1000000011=>[1,7,2]=>[2,7,1]
1000000010=>[1,7,1,1]=>[1,1,7,1]
1000000001=>[1,8,1]=>[1,8,1]
1000000000=>[1,9]=>[9,1]
10000000000=>[1,10]=>[10,1]
10000000010=>[1,8,1,1]=>[1,1,8,1]
10000000110=>[1,7,2,1]=>[1,2,7,1]
10000001110=>[1,6,3,1]=>[1,3,6,1]
10000011110=>[1,5,4,1]=>[1,4,5,1]
10000111110=>[1,4,5,1]=>[1,5,4,1]
10001111110=>[1,3,6,1]=>[1,6,3,1]
10011111110=>[1,2,7,1]=>[1,7,2,1]
10111111110=>[1,1,8,1]=>[1,8,1,1]
11111111110=>[10,1]=>[1,10]
0111111111=>[1,9]=>[9,1]
0111111101=>[1,7,1,1]=>[1,1,7,1]
0111111001=>[1,6,2,1]=>[1,2,6,1]
0111110001=>[1,5,3,1]=>[1,3,5,1]
0111100001=>[1,4,4,1]=>[1,4,4,1]
0100000001=>[1,1,7,1]=>[1,7,1,1]
0000000001=>[9,1]=>[1,9]
01111111111=>[1,10]=>[10,1]
01111111101=>[1,8,1,1]=>[1,1,8,1]
0111110101=>[1,5,1,1,1,1]=>[1,1,1,1,5,1]
0111101001=>[1,4,1,1,2,1]=>[1,2,1,1,4,1]
0111010001=>[1,3,1,1,3,1]=>[1,3,1,1,3,1]
0110100001=>[1,2,1,1,4,1]=>[1,4,1,1,2,1]
0101000001=>[1,1,1,1,5,1]=>[1,5,1,1,1,1]
00000000001=>[10,1]=>[1,10]
0101010101=>[1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1]
0101000111=>[1,1,1,1,3,3]=>[3,3,1,1,1,1]
0100110011=>[1,1,2,2,2,2]=>[2,2,2,2,1,1]
0100100111=>[1,1,2,1,2,3]=>[3,2,1,2,1,1]
0100011011=>[1,1,3,2,1,2]=>[2,1,2,3,1,1]
0100010111=>[1,1,3,1,1,3]=>[3,1,1,3,1,1]
0011010011=>[2,2,1,1,2,2]=>[2,2,1,1,2,2]
0001101011=>[3,2,1,1,1,2]=>[2,1,1,1,2,3]
0001100111=>[3,2,2,3]=>[3,2,2,3]
0000110111=>[4,2,1,3]=>[3,1,2,4]
0000011111=>[5,5]=>[5,5]
010101010101=>[1,1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1,1,1]
010101001011=>[1,1,1,1,1,1,2,1,1,2]=>[2,1,1,2,1,1,1,1,1,1]
010100011011=>[1,1,1,1,3,2,1,2]=>[2,1,2,3,1,1,1,1]
010011010011=>[1,1,2,2,1,1,2,2]=>[2,2,1,1,2,2,1,1]
010011000111=>[1,1,2,2,3,3]=>[3,3,2,2,1,1]
010010110101=>[1,1,2,1,1,2,1,1,1,1]=>[1,1,1,1,2,1,1,2,1,1]
010010101011=>[1,1,2,1,1,1,1,1,1,2]=>[2,1,1,1,1,1,1,2,1,1]
010010010111=>[1,1,2,1,2,1,1,3]=>[3,1,1,2,1,2,1,1]
010001011011=>[1,1,3,1,1,2,1,2]=>[2,1,2,1,1,3,1,1]
010000110111=>[1,1,4,2,1,3]=>[3,1,2,4,1,1]
000111010011=>[3,3,1,1,2,2]=>[2,2,1,1,3,3]
000111000111=>[3,3,3,3]=>[3,3,3,3]
000110110101=>[3,2,1,2,1,1,1,1]=>[1,1,1,1,2,1,2,3]
000110101011=>[3,2,1,1,1,1,1,2]=>[2,1,1,1,1,1,2,3]
000110010111=>[3,2,2,1,1,3]=>[3,1,1,2,2,3]
000101011011=>[3,1,1,1,1,2,1,2]=>[2,1,2,1,1,1,1,3]
000100110111=>[3,1,2,2,1,3]=>[3,1,2,2,1,3]
000001110111=>[5,3,1,3]=>[3,1,3,5]
000000111111=>[6,6]=>[6,6]
111110000001=>[5,6,1]=>[1,6,5]
111001100001=>[3,2,2,4,1]=>[1,4,2,2,3]
111000000111=>[3,6,3]=>[3,6,3]
111000110001=>[3,3,2,3,1]=>[1,3,2,3,3]
100110011001=>[1,2,2,2,2,2,1]=>[1,2,2,2,2,2,1]
0000000000=>[10]=>[10]
0000011000=>[5,2,3]=>[3,2,5]
0000011110=>[5,4,1]=>[1,4,5]
0001111110=>[3,6,1]=>[1,6,3]
0111111110=>[1,8,1]=>[1,8,1]
0100111110=>[1,1,2,5,1]=>[1,5,2,1,1]
000111111000=>[3,6,3]=>[3,6,3]
011110011000=>[1,4,2,2,3]=>[3,2,2,4,1]
011111100000=>[1,6,5]=>[5,6,1]
011100111000=>[1,3,2,3,3]=>[3,3,2,3,1]
0101010100=>[1,1,1,1,1,1,1,1,2]=>[2,1,1,1,1,1,1,1,1]
0011110100=>[2,4,1,1,2]=>[2,1,1,4,2]
0000010100=>[5,1,1,1,2]=>[2,1,1,1,5]
0111010100=>[1,3,1,1,1,1,2]=>[2,1,1,1,1,3,1]
0000000010=>[8,1,1]=>[1,1,8]
0000001110=>[6,3,1]=>[1,3,6]
0000111110=>[4,5,1]=>[1,5,4]
0011111110=>[2,7,1]=>[1,7,2]
0000000100=>[7,1,2]=>[2,1,7]
0000010110=>[5,1,1,2,1]=>[1,2,1,1,5]
0001011110=>[3,1,1,4,1]=>[1,4,1,1,3]
0010111110=>[2,1,1,5,1]=>[1,5,1,1,2]
0101111110=>[1,1,1,6,1]=>[1,6,1,1,1]
0011100010=>[2,3,3,1,1]=>[1,1,3,3,2]
0011110000=>[2,4,4]=>[4,4,2]
0100101100=>[1,1,2,1,1,2,2]=>[2,2,1,1,2,1,1]
0110001100=>[1,2,3,2,2]=>[2,2,3,2,1]
0110100100=>[1,2,1,1,2,1,2]=>[2,1,2,1,1,2,1]
0110110000=>[1,2,1,2,4]=>[4,2,1,2,1]
001100110010=>[2,2,2,2,2,1,1]=>[1,1,2,2,2,2,2]
001100111000=>[2,2,2,3,3]=>[3,3,2,2,2]
001101100010=>[2,2,1,2,3,1,1]=>[1,1,3,2,1,2,2]
001110001010=>[2,3,3,1,1,1,1]=>[1,1,1,1,3,3,2]
001110001100=>[2,3,3,2,2]=>[2,2,3,3,2]
001110010010=>[2,3,2,1,2,1,1]=>[1,1,2,1,2,3,2]
001110011000=>[2,3,2,2,3]=>[3,2,2,3,2]
001110100010=>[2,3,1,1,3,1,1]=>[1,1,3,1,1,3,2]
001111100000=>[2,5,5]=>[5,5,2]
011000110010=>[1,2,3,2,2,1,1]=>[1,1,2,2,3,2,1]
011000111000=>[1,2,3,3,3]=>[3,3,3,2,1]
011001100010=>[1,2,2,2,3,1,1]=>[1,1,3,2,2,2,1]
011100001010=>[1,3,4,1,1,1,1]=>[1,1,1,1,4,3,1]
011100001100=>[1,3,4,2,2]=>[2,2,4,3,1]
011100010010=>[1,3,3,1,2,1,1]=>[1,1,2,1,3,3,1]
011100011000=>[1,3,3,2,3]=>[3,2,3,3,1]
011100100010=>[1,3,2,1,3,1,1]=>[1,1,3,1,2,3,1]
0100001011=>[1,1,4,1,1,2]=>[2,1,1,4,1,1]
0100101111=>[1,1,2,1,1,4]=>[4,1,1,2,1,1]
0101011111=>[1,1,1,1,1,5]=>[5,1,1,1,1,1]
0110111111=>[1,2,1,6]=>[6,1,2,1]
0101110001=>[1,1,1,3,3,1]=>[1,3,3,1,1,1]
0110010101=>[1,2,2,1,1,1,1,1]=>[1,1,1,1,1,2,2,1]
0110011001=>[1,2,2,2,2,1]=>[1,2,2,2,2,1]
0110110001=>[1,2,1,2,3,1]=>[1,3,2,1,2,1]
0111001100=>[1,3,2,2,2]=>[2,2,2,3,1]
0111011000=>[1,3,1,2,3]=>[3,2,1,3,1]
0111100100=>[1,4,2,1,2]=>[2,1,2,4,1]
0111101000=>[1,4,1,1,3]=>[3,1,1,4,1]
0111110000=>[1,5,4]=>[4,5,1]
011100011001=>[1,3,3,2,2,1]=>[1,2,2,3,3,1]
011100011100=>[1,3,3,3,2]=>[2,3,3,3,1]
011100110001=>[1,3,2,2,3,1]=>[1,3,2,2,3,1]
011110001100=>[1,4,3,2,2]=>[2,2,3,4,1]
011111000001=>[1,5,5,1]=>[1,5,5,1]
0100000100=>[1,1,5,1,2]=>[2,1,5,1,1]
0011111000=>[2,5,3]=>[3,5,2]
0001111100=>[3,5,2]=>[2,5,3]
001111001100=>[2,4,2,2,2]=>[2,2,2,4,2]
001111110000=>[2,6,4]=>[4,6,2]
110001111000=>[2,3,4,3]=>[3,4,3,2]
000011111100=>[4,6,2]=>[2,6,4]
0000000101=>[7,1,1,1]=>[1,1,1,7]
0000001101=>[6,2,1,1]=>[1,1,2,6]
0001111101=>[3,5,1,1]=>[1,1,5,3]
110001110001=>[2,3,3,3,1]=>[1,3,3,3,2]
110011100001=>[2,2,3,4,1]=>[1,4,3,2,2]
0001000001=>[3,1,5,1]=>[1,5,1,3]
0001101100=>[3,2,1,2,2]=>[2,2,1,2,3]
0011000110=>[2,2,3,2,1]=>[1,2,3,2,2]
0010001110=>[2,1,3,3,1]=>[1,3,3,1,2]
0110111001=>[1,2,1,3,2,1]=>[1,2,3,1,2,1]
0001101001=>[3,2,1,1,2,1]=>[1,2,1,1,2,3]
0000010001=>[5,1,3,1]=>[1,3,1,5]
11111111111=>[11]=>[11]
110111000101=>[2,1,3,3,1,1,1]=>[1,1,1,3,3,1,2]
110111001001=>[2,1,3,2,1,2,1]=>[1,2,1,2,3,1,2]
111001011001=>[3,2,1,1,2,2,1]=>[1,2,2,1,1,2,3]
111011000101=>[3,1,2,3,1,1,1]=>[1,1,1,3,2,1,3]
111011001001=>[3,1,2,2,1,2,1]=>[1,2,1,2,2,1,3]
111100010101=>[4,3,1,1,1,1,1]=>[1,1,1,1,1,3,4]
111100100101=>[4,2,1,2,1,1,1]=>[1,1,1,2,1,2,4]
111100101001=>[4,2,1,1,1,2,1]=>[1,2,1,1,1,2,4]
111101000101=>[4,1,1,3,1,1,1]=>[1,1,1,3,1,1,4]
111101001001=>[4,1,1,2,1,2,1]=>[1,2,1,2,1,1,4]
0100100011=>[1,1,2,1,3,2]=>[2,3,1,2,1,1]
0110010011=>[1,2,2,1,2,2]=>[2,2,1,2,2,1]
0111000011=>[1,3,4,2]=>[2,4,3,1]
011110000011=>[1,4,5,2]=>[2,5,4,1]
111100000011=>[4,6,2]=>[2,6,4]
011100000111=>[1,3,5,3]=>[3,5,3,1]
110000001111=>[2,6,4]=>[4,6,2]
0101000000=>[1,1,1,1,6]=>[6,1,1,1,1]
110001110101=>[2,3,3,1,1,1,1]=>[1,1,1,1,3,3,2]
110011001101=>[2,2,2,2,2,1,1]=>[1,1,2,2,2,2,2]
110001110011=>[2,3,3,2,2]=>[2,2,3,3,2]
110011000111=>[2,2,2,3,3]=>[3,3,2,2,2]
110000011111=>[2,5,5]=>[5,5,2]
0000000011=>[8,2]=>[2,8]
0000111111=>[4,6]=>[6,4]
0011111111=>[2,8]=>[8,2]
00111111111=>[2,9]=>[9,2]
0011110001=>[2,4,3,1]=>[1,3,4,2]
000111110001=>[3,5,3,1]=>[1,3,5,3]
001111100001=>[2,5,4,1]=>[1,4,5,2]
0011111100=>[2,6,2]=>[2,6,2]
0011111001=>[2,5,2,1]=>[1,2,5,2]
0011110011=>[2,4,2,2]=>[2,2,4,2]
0011001111=>[2,2,2,4]=>[4,2,2,2]
0000001100=>[6,2,2]=>[2,2,6]
0000110011=>[4,2,2,2]=>[2,2,2,4]
001111000011=>[2,4,4,2]=>[2,4,4,2]
0110100111=>[1,2,1,1,2,3]=>[3,2,1,1,2,1]
0111100011=>[1,4,3,2]=>[2,3,4,1]
0111101111=>[1,4,1,4]=>[4,1,4,1]
0001101111=>[3,2,1,4]=>[4,1,2,3]
0110110011=>[1,2,1,2,2,2]=>[2,2,2,1,2,1]
0100101001=>[1,1,2,1,1,1,2,1]=>[1,2,1,1,1,2,1,1]
0100111011=>[1,1,2,3,1,2]=>[2,1,3,2,1,1]
011110001111=>[1,4,3,4]=>[4,3,4,1]
110011000011=>[2,2,2,4,2]=>[2,4,2,2,2]
111000011100=>[3,4,3,2]=>[2,3,4,3]
110000111100=>[2,4,4,2]=>[2,4,4,2]
0100010101=>[1,1,3,1,1,1,1,1]=>[1,1,1,1,1,3,1,1]
0001010101=>[3,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,3]
0000110101=>[4,2,1,1,1,1]=>[1,1,1,1,2,4]
0011010111=>[2,2,1,1,1,3]=>[3,1,1,1,2,2]
0111010101=>[1,3,1,1,1,1,1,1]=>[1,1,1,1,1,1,3,1]
0001110111=>[3,3,1,3]=>[3,1,3,3]
0011110101=>[2,4,1,1,1,1]=>[1,1,1,1,4,2]
0000011011=>[5,2,1,2]=>[2,1,2,5]
0001100011=>[3,2,3,2]=>[2,3,2,3]
0001001011=>[3,1,2,1,1,2]=>[2,1,1,2,1,3]
0110000011=>[1,2,5,2]=>[2,5,2,1]
0110011011=>[1,2,2,2,1,2]=>[2,1,2,2,2,1]
000110000011=>[3,2,5,2]=>[2,5,2,3]
110110011001=>[2,1,2,2,2,2,1]=>[1,2,2,2,2,1,2]
110110001101=>[2,1,2,3,2,1,1]=>[1,1,2,3,2,1,2]
110011011001=>[2,2,2,1,2,2,1]=>[1,2,2,1,2,2,2]
110011100011=>[2,2,3,3,2]=>[2,3,3,2,2]
110011100101=>[2,2,3,2,1,1,1]=>[1,1,1,2,3,2,2]
110011101001=>[2,2,3,1,1,2,1]=>[1,2,1,1,3,2,2]
110011110001=>[2,2,4,3,1]=>[1,3,4,2,2]
111001001101=>[3,2,1,2,2,1,1]=>[1,1,2,2,1,2,3]
111001100101=>[3,2,2,2,1,1,1]=>[1,1,1,2,2,2,3]
111001100011=>[3,2,2,3,2]=>[2,3,2,2,3]
111001101001=>[3,2,2,1,1,2,1]=>[1,2,1,1,2,2,3]
111001110001=>[3,2,3,3,1]=>[1,3,3,2,3]
111000110011=>[3,3,2,2,2]=>[2,2,2,3,3]
111000110101=>[3,3,2,1,1,1,1]=>[1,1,1,1,2,3,3]
111000111001=>[3,3,3,2,1]=>[1,2,3,3,3]
111010011001=>[3,1,1,2,2,2,1]=>[1,2,2,2,1,1,3]
111010001101=>[3,1,1,3,2,1,1]=>[1,1,2,3,1,1,3]
111110000011=>[5,5,2]=>[2,5,5]
0000011001=>[5,2,2,1]=>[1,2,2,5]
0011011111=>[2,2,1,5]=>[5,1,2,2]
0110011111=>[1,2,2,5]=>[5,2,2,1]
0110110111=>[1,2,1,2,1,3]=>[3,1,2,1,2,1]
001111000111=>[2,4,3,3]=>[3,3,4,2]
011110000111=>[1,4,4,3]=>[3,4,4,1]
0100100001=>[1,1,2,1,4,1]=>[1,4,1,2,1,1]
0110010001=>[1,2,2,1,3,1]=>[1,3,1,2,2,1]
0111100101=>[1,4,2,1,1,1]=>[1,1,1,2,4,1]
0110101011=>[1,2,1,1,1,1,1,2]=>[2,1,1,1,1,1,2,1]
0100111001=>[1,1,2,3,2,1]=>[1,2,3,2,1,1]
0101100011=>[1,1,1,2,3,2]=>[2,3,2,1,1,1]
0111011001=>[1,3,1,2,2,1]=>[1,2,2,1,3,1]
0101100001=>[1,1,1,2,4,1]=>[1,4,2,1,1,1]
0100011001=>[1,1,3,2,2,1]=>[1,2,2,3,1,1]
0101111001=>[1,1,1,4,2,1]=>[1,2,4,1,1,1]
0100010001=>[1,1,3,1,3,1]=>[1,3,1,3,1,1]
0100110001=>[1,1,2,2,3,1]=>[1,3,2,2,1,1]
0110111011=>[1,2,1,3,1,2]=>[2,1,3,1,2,1]
0101111011=>[1,1,1,4,1,2]=>[2,1,4,1,1,1]
0100010011=>[1,1,3,1,2,2]=>[2,2,1,3,1,1]
0101110011=>[1,1,1,3,2,2]=>[2,2,3,1,1,1]
0110100011=>[1,2,1,1,3,2]=>[2,3,1,1,2,1]
0101000011=>[1,1,1,1,4,2]=>[2,4,1,1,1,1]
0110010111=>[1,2,2,1,1,3]=>[3,1,1,2,2,1]
0100110111=>[1,1,2,2,1,3]=>[3,1,2,2,1,1]
0101110111=>[1,1,1,3,1,3]=>[3,1,3,1,1,1]
0101100111=>[1,1,1,2,2,3]=>[3,2,2,1,1,1]
0110101111=>[1,2,1,1,1,4]=>[4,1,1,1,2,1]
0101101111=>[1,1,1,2,1,4]=>[4,1,2,1,1,1]
0101001111=>[1,1,1,1,2,4]=>[4,2,1,1,1,1]
0001010000=>[3,1,1,1,4]=>[4,1,1,1,3]
0100010000=>[1,1,3,1,4]=>[4,1,3,1,1]
0001000100=>[3,1,3,1,2]=>[2,1,3,1,3]
0111011100=>[1,3,1,3,2]=>[2,3,1,3,1]
0101000101=>[1,1,1,1,3,1,1,1]=>[1,1,1,3,1,1,1,1]
0110110101=>[1,2,1,2,1,1,1,1]=>[1,1,1,1,2,1,2,1]
0101010001=>[1,1,1,1,1,1,3,1]=>[1,3,1,1,1,1,1,1]
0110001001=>[1,2,3,1,2,1]=>[1,2,1,3,2,1]
0101011011=>[1,1,1,1,1,2,1,2]=>[2,1,2,1,1,1,1,1]
0111010011=>[1,3,1,1,2,2]=>[2,2,1,1,3,1]
0111000111=>[1,3,3,3]=>[3,3,3,1]
000110001100=>[3,2,3,2,2]=>[2,2,3,2,3]
0011011110=>[2,2,1,4,1]=>[1,4,1,2,2]
0011101110=>[2,3,1,3,1]=>[1,3,1,3,2]
0011110110=>[2,4,1,2,1]=>[1,2,1,4,2]
0011111010=>[2,5,1,1,1]=>[1,1,1,5,2]
0000110100=>[4,2,1,1,2]=>[2,1,1,2,4]
11000000000=>[2,9]=>[9,2]
111100000111=>[4,5,3]=>[3,5,4]
011100110011=>[1,3,2,2,2,2]=>[2,2,2,2,3,1]
111000001111=>[3,5,4]=>[4,5,3]
000111110011=>[3,5,2,2]=>[2,2,5,3]
0111001101=>[1,3,2,2,1,1]=>[1,1,2,2,3,1]
110001111001=>[2,3,4,2,1]=>[1,2,4,3,2]
011100001111=>[1,3,4,4]=>[4,4,3,1]
011100111001=>[1,3,2,3,2,1]=>[1,2,3,2,3,1]
011111000011=>[1,5,4,2]=>[2,4,5,1]
001111100011=>[2,5,3,2]=>[2,3,5,2]
Map
delta morphism
Description
Applies the delta morphism to a binary word.
The delta morphism of a finite word $w$ is the integer compositions composed of the lengths of consecutive runs of the same letter in $w$.
The delta morphism of a finite word $w$ is the integer compositions composed of the lengths of consecutive runs of the same letter in $w$.
Map
reverse
Description
Return the reversal of a composition.
That is, the composition $(i_1, i_2, \ldots, i_k)$ is sent to $(i_k, i_{k-1}, \ldots, i_1)$.
That is, the composition $(i_1, i_2, \ldots, i_k)$ is sent to $(i_k, i_{k-1}, \ldots, i_1)$.
searching the database
Sorry, this map was not found in the database.