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