Given a 2-dimensional array of positive and negative integers, find the sub-rectangle with the largest sum. 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. A sub-rectangle is any contiguous sub-array of size 1 × 1 or greater located within the whole array.
As an example, the maximal sub-rectangle of the array:
is in the lower-left-hand corner and has the sum of 15.
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 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.
0 -2 -7 0
9 2 -6 2
-4 1 -4 1
-1 8 0 -2