To the MaxTime Limit: 1000MS Memory Limit: 10000K

Total Submissions: 37431 Accepted: 19715

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

4

0 -2 -7 0 9 2 -6 2

-4 1 -4 1 -1

8 0 -2

Sample Output

15

Source

Greater New York 2001

//208K    16MS    C++    862B//二维dp，枚举全部矩形 #include
     
      #include
      
       int g[105][105];int dp[105];int main(void){    int n;    while(scanf("%d",&n)!=EOF)    {        for(int i=0;i
       
        tmax) tmax=t;                }                if(tmax>ans) ans=tmax;            }        }        printf("%d\n",ans);    }    return 0;}