To the Max

Time Limit: 1000MS		Memory Limit: 10000K
Total Submissions: 39058		Accepted: 20629

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

题目大意：

给定一个包含正负数的二维矩阵，子矩阵是任何连续大小大于或等于1*1的子阵的整个数组，这个矩阵的和就等于矩阵中所有元素之和，和最大的子矩阵被称为最大矩阵。

也就是让你输出最大矩阵的和

推荐：http://acm.nyist.net/JudgeOnline/problem.php?pid=104

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