JMO 1991 Problem 4

A rectangular of a $10*14$ is divided into small 140 unit squares and painted in red and white like chess board as below. We put $0$ or $1$ in the square such that each row and column has an odd numbers of $1$. Prove that the number of $1$ contained in red-painted square is even.

The pattern arranged by a red and a white square alternatively.

RWRWRWRW..... WRWRWRWR..... RWRWRWRW..... WRWRWRWR.....