Problem:
Largest Square

Given a matrix (H × W) which contains only 1 and 0, find the area of the largest square matrix which only contains 0s.

Input

H W
c1,1 c1,2 ... c1,W
c2,1 c2,2 ... c2,W
:
cH,1 cH,2 ... cH,W

In the first line, two integers H and W separated by a space character are given. In the following H lines, ci,j, elements of the H × W matrix, are given.

Output

Print the area (the number of 0s) of the largest square.

Constraints

1 ≤ H, W ≤ 1,400

Sample Input

4 5
0 0 1 0 0
1 0 0 0 0
0 0 0 1 0
0 0 0 1 0

Sample Output

4

Solution in Python (judge verdict: Accepted)

H,W = map(int, raw_input().split())
C = [map(int, raw_input().split()) for _ in range(H)]

DP = [[0]*(W+1) for _ in range(H+1)]

for i in range(1, H+1):
    for j in range(1, W+1):
        if C[i-1][j-1] != 1:
            DP[i][j] = min(
                DP[i-1][j-1],
                DP[i-1][j],
                DP[i][j-1]) + 1

ans = max([max(dp) for dp in DP]) ** 2
print ans