Question 117
An $m \times n$ table is given, in each cell of which a number $+1$ or $-1$ is written. It is known that initially exactly one $-1$ is in the table, all the other numbers being $+1$. During a move, it is allowed to choose any cell containing $-1$, replace this $-1$ by $0$, and simultaneously multiply all the numbers in the neighboring cells by $-1$ (we say that two cells are neighboring if they have a common side). Find all $(m, n)$ for which using such moves one can obtain the table containing zeroes only, regardless of the cell in which the initial $-1$ stands.