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

In order to leave the matrix, Nikki 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.

Input

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.

Output

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

Example

Input
2
1 -2
4 5

Output
4

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

Output
5