php, 60 bytes

Result

WA

Code [DL]

<?=for(;$c=fgets(STDIN);)echo+!fmod(sqrt(8*bindec($c)+1),1);

stdin

10001111
10011001
00111001
11100010
10111101
10100101
01101001
00000001
10010010
00010111
11111101
00000011
00000000
01001110
11100111
11000000
00100000
11101011
11100001
11010010
00001111
11110011
01001011
11001110
00010101
01011011
10101011
00000110
01010111
01001101
00011100
10111110
11100111
10001000
11011111
10000100
10001011
00100100
00110100
00001010
01000010
10101101
11001011
10100100
01111000
00100100
00110111
00101101
01100110
11000111

stdout

stderr

PHP Parse error:  syntax error, unexpected 'for' (T_FOR) in /volume/CODE on line 1

strace