#2014 The Matrix

13  2 s   128 MB  


As we all know, we live inside the matrix that is divided into N rows and N columns. An integer is written into each one of the NxN cells of the matrix.

In order to leave the matrix, we must find the most beautiful square (square-shaped sub-matrix) contained in the matrix.

If we denote by A the sum of all integers on the main diagonal of some square, and by B the sum of the other diagonal, then the beauty of that square is A - B.

Note: The main diagonal of a square is the diagonal that runs from the top left corner to the bottom right corner.


The first line of input contains the positive integer N (2 ≤ N ≤ 400), the size of the matrix.

The following N lines each contain N integers in the range [-1000, 1000], the elements of the matrix.


The only line of output must contain the maximum beauty of a square found in the matrix.

Sample Input

Sample Output

1 -2
4 5

Sample Input 2

1 2 3
4 5 6
7 8 9

Sample Output 2


Sample Input 3

-3 4 5
7 9 -2
1 0 -6

Sample Output 3