To the Max(动态规划DP)

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

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