Finding "pair groups" in array

Hello everybody,

i'm solving currently one task, and I transformed it into another , I think more simple task which I cant solve in good ( e.g. not exponencial or something) time.

I have for example n inputs , every of them is in format like 10001001010 or 00000101111 (same lenght ) , so example for N=4

10001111010
10001111010
00100011010
01000100001

And, the problem is now, how to choose subset of inputs (every input is one line) that sum of values (1 or 0) in each column must be even-numbered (2 or 4 or ...) (for example column 1 has sum=2 column 2=1 column 3=0)

If you have any idea how to do it in some good time, please post it
Thank you