Given a 2dimensional array of positive and negative integers, find the subrectangle with the largest sum. The sum of a rectangle is the sum of all the elements in that rectangle. In this problem the subrectangle with the largest sum is referred to as the maximal subrectangle. A subrectangle is any contiguous subarray of size 1 × 1 or greater located within the whole array.
As an example, the maximal subrectangle of the array:
0 
−2 
−7 
0 
9 
2 
−6 
2 
−4 
1 
−4 
1 
−1 
8 
0 
−2 
is in the lowerlefthand corner and has the sum of 15.
Input
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 whitespace (newlines and spaces).
These N^{ 2} integers make up the array in rowmajor order (i.e., all numbers on the first row, lefttoright, then all numbers on the second row, lefttoright, etc.). N may be as large as 100. The numbers in the array will be in the range [−127, 127].
Output
The output is the sum of the maximal subrectangle.
Sample
input  output 

4
0 2 7 0
9 2 6 2
4 1 4 1
1 8 0 2
 15
