Tianjin University Online Judge
Contests Virtual Contests Problems Submit Runs Status Rank List Forum

1564.   To The Max
Time Limit: 1.0 Seconds   Memory Limit: 65536K
Total Runs: 1008   Accepted Runs: 568



Problem

Given a two-dimensional array of positive and negative integers, a sub-rectangle is any contiguous sub-array of size 1 x 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
is in the lower left corner:
 9  2
-4  1
-1  8
and has a sum of 15.

Input

The input consists of an N x 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 N2 integers separated by whitespace (spaces and newlines). These are the N2 integers of the array, presented in row-major order. That is, all numbers in the first row, left to right, then all numbers in 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].

Output

Output the sum of the maximal sub-rectangle.


Sample Input

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

8 0 -2
Sample Output
15


Source: Greater New York 2001
Submit   List    Runs   Forum   Statistics

Tianjin University Online Judge v1.3.0
Maintance:G.D.Retop. Developer: SuperHacker, G.D.Retop