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

 9 2 
-4 1 
-1 8