js-rhino, 96 bytes

Result

WA

Code [DL]

for(;;)print(+!(Math.sqrt(8*parseInt(new java.io.DataInputStream(System.in).readLine(),2)+1)%1))

stdin

10110110
00110111
01001110
10011001
00001010
11010010
00101000
00001111
10101011
10111101
10001010
10111110
01100111
00010010
00000110
00100100
00100000
10001000
10001101
01011011
11010101
00000001
00100101
11100111
10110010
01101001
00111011
10011100
00001011
00000000
10001100
11111101
10100100
00100001
00010011
01111000
00101101
01000010
00000011
01000000
01000111
01101101
11011110
00000100
10101011
00011100
11010010
01010101
11110010
00010101

stdout

stderr

js: uncaught JavaScript runtime exception: ReferenceError: "System" is not defined.

strace