# HIIT Open 2018

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

CSES - HIIT Open 2018 - GridCSES - 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
• $1 \le n \le 1000$
Example 1

Input:
3 001 111 001

Output:
2

Example 2

Input:
3 101 111 001

Output:
-1