Jumppy likes to jump! One day Jumppy went to a park. Jumppy can jump all over the park. The park can be thought of as a square grid with square cells of side length 1. The contents of the grid is either 0 (zero) or X. There are certain things which Jumppy likes. They are:

• Jumppy likes rectangles.
• Jumppy likes X.

Therefore Jumppy will jump only in the rectangles consisting of X. A rectangle is defined as follows:

1. The whole rectangular region should contain only X.
2. The rectangle should be surrounded with 0 or the boundary of the grid.
3. The diagonally adjacent cell (see the definition) of the corner of the rectangle may be X or 0. (Refer to the first example).

Diagonally adjacent cell: Suppose the given cell has coordinates (p, q) then its diagonally adjacent cells would have coordinates (p+1, q+1), (p+1, q-1), (p-1, q+1), (p-1, q-1).

Now Jumppy is curious how many rectangles are there in the park. Help Jumppy find the number of rectangle.

Input

An integer n denoting the size of the grid. Then n lines follow each containing a string of n characters describing the square grid. All the characters will be either 0 or X.

Output

Output the number of rectangles in the given grid.

Constraints

0 < n <= 1000

Examples:

Input:
4
XX00
XX00
00XX
00XX

Output:
2

Input:
5
00000
0XXX0
0XXX0
0XXX0
00X00

Output:
0

Input:
5
00000
0XXX0
0X0X0
0XXX0
00000

Output:
0

Input:
3
X0X
0X0
X0X

Output:
5

Explanation

Case 1: As can be seen there are two rectangles as highlighted.

Case 2: The grid contains no rectangles because it violates the second condition of the definition.

Case 3: The grid contains no rectangles because it violates the first condition of the definition.

Case 4: The individual X in this case can be considered as rectangles.