## 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 09 2 -6 2-4 1 -4  1-1 8  0 -2`

## Sample Output

`15`

0 -2 -7  0

9  2 -6  2

-4  1 -4  1

-1  8  0 -2

0 -2 -7   0

9  2 -6   2

-4  1 -4   1

a: 5  1 -17 3

`import java.util.*;public class test {  public static void main(String[] args) {    int[][] a = new int[100][100];    int[] b = new int[100];    int n;    Scanner in = new Scanner(System.in);    n = in.nextInt();    for (int i = 0; i < n; i++) {      for (int j = 0; j < n; j++) {        a[i][j] = in.nextInt();      }    }    int ans = 0;    for (int i = 0; i < n; i++) {      for (int j = i; j < n; j++) {        for (int k = 0; k < n; k++) {          b[k] = 0;          for (int l = i; l <= j; l++) {            b[k] += a[l][k];//合并i到j行          }        }        // 动态规划        int sum = 0;//当前和        int max = 0;//最大和        //dp[i] = max(dp[i], dp[i - 1] + a[i]);        for (int k = 0; k < n; k++) {          sum += b[k];// 含有第k个元素的最大连续子段和          if (sum > max) {            max = sum;          }          if (sum < 0) {            sum = 0;          }        }        if (max > ans) {//更新ans          ans = max;        }      }    }    System.out.println(ans);  }}`