To the Max

Time Limit: 2 Seconds
Memory Limit: 65536 KB

**Problem**

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

The input consists of an N x 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.

**Example**

**Input**

4

0 -2 -7 0 9 2 -6 2

-4 1 -4 1 -1

8 0 -2

**Output**

15

Source:

**Greater New York 2001**
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