Problem: There is a square-shaped grid with N vertical rows and N horizontal columns. We will denote the square at the i-th row from the top and the j-th column from the left as (i,\ j).

Initially, each square is either white or black. The initial color of the grid is given to you as characters a_{ij}, arranged in a square shape. If the square (i,\ j) is white, a_{ij} is `.`. If it is black, a_{ij} is `#`.

You are developing a robot that repaints the grid. It can repeatedly perform the following operation:

* Select two integers i, j (1 ≤ i,\ j ≤ N). Memorize the colors of the squares (i,\ 1), (i,\ 2), ..., (i,\ N) as c_1, c_2, ..., c_N, respectively. Then, repaint the squares (1,\ j), (2,\ j), ..., (N,\ j) with the colors c_1, c_2, ..., c_N, respectively.



Your objective is to turn all the squares black. Determine whether it is possible, and find the minimum necessary number of operations to achieve it if the answer is positive.

Constraints

* 2 ≤ N ≤ 500
* a_{ij} is either `.` or `#`.

Input

The input is given from Standard Input in the following format:


N
a_{11}...a_{1N}
:
a_{N1}...a_{NN}


Output

If it is possible to turn all the squares black, print the minimum necessary number of operations to achieve the objective. If it is impossible, print `-1` instead.

Examples

Input

2
#.
.#


Output

3


Input

2
.
.#


Output

3


Input

2
..
..


Output

-1


Input

2


Output

0


Input

3
.#.

.#.


Output

2


Input

3
...
.#.
...


Output

5

Solution (in JAVA):

Solution:
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.StringTokenizer;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskB solver = new TaskB();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskB {
        public void solve(int testNumber, InputReader in, PrintWriter out) {
            int n = in.nextInt();
            String[] a = new String[n];
            for (int i = 0; i < n; ++i) {
                a[i] = in.next();
            }
            boolean[] emptyRow = new boolean[n];
            for (int row = 0; row < n; ++row) {
                emptyRow[row] = true;
                for (int col = 0; col < n; ++col) {
                    if (a[row].charAt(col) == '#') emptyRow[row] = false;
                }
            }
            int untilBlackRow = Integer.MAX_VALUE;
            for (int blackRow = 0; blackRow < n; ++blackRow) {
                int whites = 0;
                for (int col = 0; col < n; ++col) if (a[blackRow].charAt(col) == '.') ++whites;
                if (whites == 0) {
                    untilBlackRow = Math.min(untilBlackRow, 0);
                    continue;
                }
                boolean anyFiller = false;
                for (int row = 0; row < n; ++row) if (a[row].charAt(blackRow) == '#') anyFiller = true;
                if (anyFiller) {
                    untilBlackRow = Math.min(untilBlackRow, whites);
                    continue;
                }
                int extra = a[blackRow].charAt(blackRow) == '#' ? 1 : 0;
                for (int row = 0; row < n; ++row)
                    if (!emptyRow[row]) {
                        untilBlackRow = Math.min(untilBlackRow, 1 + whites + extra);
                    }
            }
            if (untilBlackRow == Integer.MAX_VALUE) {
                out.println(-1);
                return;
            }
            int res = untilBlackRow;
            for (int col = 0; col < n; ++col) {
                boolean hasWhites = false;
                for (int row = 0; row < n; ++row) {
                    if (a[row].charAt(col) == '.') hasWhites = true;
                }
                if (hasWhites) ++res;
            }
            out.println(res);
        }

    }

    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

    }
}