COCI '11 Contest 1 #2 Matrix

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Points: 7 (partial)
Time limit: 1.0s
Memory limit: 32M

Problem type

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 N \times N 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.

Input Specification

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

The following N lines each contain N integers in the range [-1\,000, 1\,000], the elements of the matrix.

Output Specification

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

Sample Input 1

2
1 -2
4 5

Sample Output 1

4

Sample Input 2

3
1 2 3
4 5 6
7 8 9

Sample Output 2

0

Sample Input 3

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

Sample Output 3

5

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