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 Python3 (judge verdict: Wrong Answer)

H,W = map(int,input().split())
tile = [[0 for i in range(W)] for i in range(H)]
buf = [[1 for i in range(W)] for i in range(H)]
maxsquare = 0

for i in range(H):
    tile[i] = list(map(int,input().split()))

for i in range(1,H):
    for j in range(1,W):
        if tile[i][j]!=1:
            if tile[i-1][j]==1 or tile[i][j-1]==1 or tile[i-1][j-1]==1:
                buf[i][j] = 1
            elif tile[i-1][j]==tile[i][j-1]:
                buf[i][j] = buf[i-1][j-1]+1
            else:
                buf[i][j] = min(buf[i-1][j] , buf[i][j-1])+1

            if buf[i][j] > maxsquare:
                maxsquare = buf[i][j]


print(maxsquare**2)