CWMO 2012 Problem 7

Let $n$ be a positive integer $\geq 2$ . Consider a $n$ by $n$ grid with all entries $1$ . Define an operation on a square to be changing the signs of all squares adjacent to it but not the sign of its own. Find all $n$ such that it is possible after a finite sequence of operations to reach a $n$ by $n$ grid with all entries $-1$