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HIIT Open 2018

Start:2018-05-26 11:00:00
End:2018-05-26 16:00:00
 

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CSES - HIIT Open 2018 - Grid

Grid

Time limit:1.00 s
Memory limit:512 MB

There is an $n \times n$ grid whose each square is initially white. On each move you can paint one row or column black.

Your task is to create a given target grid using the minimum number of moves.

Input

The first input line has an integer $n$: the size of the grid.

After this, there are $n$ lines of $n$ characters that describe the target grid. Each color is 0 (white) or 1 (black).

Output

Print the minimum number of moves needed. If the task is impossible, print $-1$.

Constraints
Example 1

Input:
3
001
111
001


Output:
2

Example 2

Input:
3
101
111
001


Output:
-1