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 C (judge verdict: Time Limit Exceeded)

#include<stdio.h>
#define min(a,b) ((a)<(b)?(a):(b))
#define max(a,b) ((a)>(b)?(a):(b))
int H,W,i,j,k,t,B[2000][2000],dp[2000][2000]={0},R=0;

int main()
{
	scanf("%d%d",&H,&W);
	for(i=1;i<=H;i++)
		for(j=1;j<=W;j++)
			scanf("%d",&B[i][j]);
	for(i=1;i<=H;i++)
	{
		for(j=1;j<=W;j++)
			dp[i][j]=dp[i-1][j];
		t=0;
		for(j=1;j<=W;j++)
		{
			t+=B[i][j];
			dp[i][j]+=t;
		}
	}
	for(i=1;i<=H;i++)
		for(j=1;j<=W;j++)
			for(k=0;i+k<=H&&j+k<=W;k++)
			{
				if(dp[i+k][j+k]-(dp[i-1][j+k]+dp[i+k][j-1]-dp[i-1][j-1])==0)
					R=max(R,(k+1)*(k+1));
				else
					break;
			}
	printf("%d\n",R);
	return 0;
}