goruby, 64 bytes

Result

WA

Code [DL]

50.times{a=(((8*gets.to_i+1)**(0.5)-1)/2);puts (a.to_i==a).to_i}

stdin

10101011
01001111
11100111
00000110
01000010
00010011
10100100
00010101
00000011
11000001
11100110
11100000
11101110
10101001
10100010
10100101
00100100
01111001
01001110
01101001
00011100
00110001
11111101
00100001
00001010
01111000
10001000
01000011
00001111
00000000
00110111
10011001
10110000
00000001
11001111
00010111
11010010
01111011
00010101
10001000
11101010
01011011
00111000
00000101
11010110
00011000
01010011
10111110
00101101
10111111

stdout

stderr

<internal:golf_prelude>:7:in `method_missing': wrong number of arguments (given 0, expected 1+) (ArgumentError)
	from <internal:golf_prelude>:14:in `method_missing'
	from /volume/CODE:1:in `block in <main>'
	from /volume/CODE:1:in `times'
	from /volume/CODE:1:in `<main>'

strace