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 1x1or 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.
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 N2 integers separated by white-space (newlines and spaces). These N2 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 500. The numbers in the array will be in the range [-127, 127].
The output is the sum of the maximal sub-rectangle.