The Best Matrix

A matrix $A$ of size $N \times M$ is said to be **best** if and only if all of the following conditions are satisfied: - $|A[x_1][y_1] - A[x_2][y_2]| = 1$ for all adjacent pair of cells $(x_1, y_1)$ and $(x_2, y_2)$ - $(x_1, y_1)$ and $(x_2, y_2)$ are said to be adjacent if and only if $|x_1 - x_2| + |y_1 - y_2| = 1$. - $A[x][y] = \dfrac{A[x - 1][y] + A[x + 1][y]}{2}$ for all $1 < x < N$ and