js-rhino, 77 bytes

Result

WA

Code [DL]

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

stdin

01110000
00001100
00011100
01111000
00000011
01001111
11110100
10101011
11101100
01000000
10111110
10110011
00001010
00100010
11111101
00000110
11101001
10011001
10110100
00110100
11100111
01101100
00110101
10011001
01101001
01000010
00000001
00000000
11000000
00110111
11001101
00101100
00010101
01000100
01100110
10000111
00100111
00000011
00100100
10110110
11010010
00000111
00001111
01011011
10001000
10010101
01001110
10001101
00101101
00101000

stdout

stderr

js: uncaught JavaScript runtime exception: TypeError: Cannot find function readLine in object java.io.BufferedInputStream@449b2d27.

strace