To the Max



Description

Given a two-dimensional array of positive and negative integers, a sub-rectangle is any contiguous sub-array of size 1*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.

Input

The input consists of an N * 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.

Sample Input

40 -2 -7 0 9 2 -6 2-4 1 -4  1 -18  0 -2

Sample Output

15

#include<iostream>#include<cstdio>#include<cstring>#include<algorithm>#define INF 0x3f3f3f3fusing namespace std;int a[105][105],sum[105],mm,n;int main(){    while(~scanf("%d",&n))    {        mm=-INF;        for(int i=0;i<n;i++)            for(int j=0;j<n;j++)                scanf("%d",&a[i][j]);        for(int i=0;i<n;i++)        {            memset(sum,0,sizeof(sum));            for(int k=i;k<=n;k++)            {                int t=0;                for(int j=0;j<n;j++)                {                    sum[j]+=a[k][j];                    if(t<=0) t=sum[j];                    else t+=sum[j];                    if(t>mm) mm=t;                }            }        }        printf("%d\n",mm);    }    return 0;}