p02326 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.

Constraints

* 1 ≤ H, W ≤ 1,400

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.

Example

Input

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


Output

4
```python
h,w=map(int,input().split())
grid=[list(map(int,input().split())) for i in range(h)]

def Largest_Square(grid):
    h=len(grid);w=len(grid[0])
    dp=[[0]*w for i in range(h)]
    maxlenth=0
    for i in range(h):
        for j in range(w):
            dp[i][j]=(grid[i][j]+1)%2
            maxlenth=max(maxlenth,dp[i][j])
    for i in range(1,h):
        for j in range(1,w):
            if grid[i][j]:
                continue
            else:
                dp[i][j]=min(dp[i-1][j],dp[i-1][j-1],dp[i][j-1])+1
                maxlenth=max(maxlenth,dp[i][j])
    return maxlenth**2
print(Largest_Square(grid))




```