Building a ranch

Mr. Land wants to spend his retirement money on a plot of land and build a ranch on it. The plot he was shown is a rectangle, mostly open field, with trees that are hard to cut down and rocks that cannot be cleared scattered across it.

The ranch is a single square, and no tree or rock may stand inside it. Mr. Land wants that square to be as large as possible.

The plot is $M$ meters tall and $N$ meters wide. Cut it into a grid of 1 meter cells and write it as an $M \times N$ matrix. In the matrix, 0 means open field, 1 means a tree, and 2 means a rock.

Find the side length $L$ of the largest square ranch that can be built. If the plot has no open field cell at all, $L$ is 0.

The first line contains $M$ and $N$, separated by a space.

Each of the next $M$ lines contains $N$ integers separated by spaces. Each value is 0, 1, or 2.

• $1 \le M \le 1000$
• $1 \le N \le 1000$

Print the side length $L$ of the largest square ranch on one line.