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Условие:

7.Knight Game

Chess is the oldest game, but it is still popular these days. For this task we will use only one chess piece – the Knight.

The knight moves to the nearest square but not on the same row, column, or diagonal. (This can be thought of as moving two squares horizontally, then one square vertically, or moving one square horizontally then two squares vertically— i.e. in an "L" pattern.) 

The knight game is played on a board with dimensions N x N and a lot of chess knights 0 <= K <= N2.

You will receive a board with K for knights and '0' for empty cells. Your task is to remove a minimum of the knights, so there will be no knights left that can attack another knight.

Input

On the first line, you will receive the N size of the board

On the next N lines, you will receive strings with Ks and 0s.

Output

Print a single integer with the minimum number of knights that needs to be removed

Constraints

• Size of the board will be 0 < N < 30
• Time limit: 0.3 sec. Memory limit: 16 MB.

Examples