Description

Input an n * n matrix. If two different points A(x1, y1), B (x2, y2) satisfy x1 + x2 = n + 1, y1 + y2 = n + 1, and the number at positions A and B are the same, then we say the pair (A, B) is called a symmetric pair. Find the number of symmetric pairs. In this problem, both x and y start with 1.

Input
The first line has an integer n

Then n rows, with n integers between 0 and 100 per row

Output

An integer that represents the answer.

Examples

Input 1

5
3 3 3 4 1
2 0 0 3 1
0 3 1 4 1
3 4 3 3 1
1 0 3 3 1

Output 1

3
Examples Explanation
There are 3 pairs:
(1,2) and (5,4)
(1,3) and (5,3)
(1,5) and (5,1)

Constraint
1<=n<=500