Description

Given a two-dimensional array of positive and negative integers, a sub-rectangle is any contiguous sub-array of size 1 x 1 or greater located within the whole array. The sum of a rectangle is the sum of all the elements in that rectangle. In this problem the sub-rectangle with the largest sum is referred to as the maximal sub-rectangle.

As an example, the maximal sub-rectangle of the array:

0 -2 -7 0
9 2 -6 2
-4 1 -4 1
-1 8 0 -2

is in the lower left corner:

9 2
-4 1
-1 8

and has a sum of 15.

The input consists of an N x N array of integers. The input begins with a single positive integer N on a line by itself, indicating the size of the square two-dimensional array. This is followed by N 2 integers separated by whitespace (spaces and newlines). These are the N 2 integers of the array, presented in row-major order. That is, all numbers in the first row, left to right, then all numbers in the second row, left to right, etc. N may be as large as 100. The numbers in the array will be in the range [-127,127].

Output

Output the sum of the maximal sub-rectangle.

Example
Input

4
0 -2 -7 0 9 2 -6 2
-4 1 -4 1 -1
8 0 -2

Output

15

#include <bits/stdc++.h>

using namespace std;

int a[110][110];
int b[110];

int main()
{
    int n;
    int max = -0xffff;
    while (~scanf("%d", &n))
    {
        for (int i = 0; i < n; i++)
            for (int j = 0; j < n; j++)
                scanf("%d", &a[i][j]);
        max = -0xffff;
        for (int i = 0; i < n; i++)
        {
            memset(b, 0, sizeof(b));
            for (int j = i; j < n; j++)
            {
                int sum = 0;
                for (int k = 0; k < n; k++)
                {
                    b[k] += a[j][k];
                    sum += b[k];
                    if (b[k] > sum)
                        sum = b[k];
                    if (sum > max)
                        max = sum;
                }
            }
        }
        printf("%d\n", max);
    }
    return 0;
}