RMO 2014 B6

Suppose $n$ is odd and each square of an $n \times n$ grid is arbitrarily filled with either by $1$ or by $-1$ . Let $r_j$ and $c_k$ denote the product of all numbers in $j$ -th row and $k$ -th column respectively, $1 \le j, k \le n$ . Prove that $$\sum_{j=1}^{n} r_j+ \sum_{k=1}^{n} c_k\ne 0$$