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A bishop is a piece in the board game of chess. The bishop has no restrictions
in distance for each move, but is limited to diagonal movement, forward and
backward.
Consider a chessboard of size NxN.
Your must find the maximum number of bishops that can be placed on the
chessboard, such that no pair of bishops can attack each other. Some cells
are damaged. Bishops cannot be placed on these cells, but they can attack
through them.
Input
The first line contains one integer N (1 ≤ N ≤ 100) - size
of the chessboard. The following N lines describe the chessboard. Each
line contains N symbols. '.' is entire cell, '#' is damaged.
Output
Output a single integer - the number of bishops that can be placed on the
chessboard under the given restrictions.
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