# UVA 108: Maximum Sum (solution)

__Maximum Sum__

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**Background**

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**The Problem**

*maximal sub-rectangle*. A sub-rectangle is any contiguous sub-array of size 1 x 1 or greater located within the whole array. 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-hand corner:

9 2 -4 1 -1 8

and has the sum of 15.

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**Input / ****Output**

The input consists of an NxN 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 white-space (newlines and spaces). These N^2 integers make up the array in row-major order (i.e., all numbers on the first row, left-to-right, then all numbers on 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].

The output is the sum of the maximal sub-rectangle.

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**Sample Input**

4 0 -2 -7 0 9 2 -6 2 -4 1 -4 1 -1 8 0 -2

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**Sample Output**

15

SOLUTION: C++

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