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:
// package atcoder.other2017.mujin2017;

import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.InputMismatchException;

public class Main {
    static final int INF = 100000;

    public static void main(String[] args) {
        InputReader in = new InputReader(System.in);
        PrintWriter out = new PrintWriter(System.out);

        int n = in.nextInt();
        int[][] basetbl = new int[n][n];
        for (int i = 0; i < n ; i++) {
            char[] row = in.nextToken().toCharArray();
            for (int j = 0; j < n ; j++) {
                basetbl[i][j] = row[j] == '.' ? 0 : 1;
            }
        }
        int ret = solve2(basetbl);
        out.println(ret >= INF ? -1 : ret);
        out.flush();
    }


    static int solve2(int[][] basetbl) {
        int n = basetbl.length;

        boolean hasOne = false;
        for (int i = 0; i < n ; i++) {
            for (int j = 0; j < n ; j++) {
                hasOne |= basetbl[i][j] == 1;
            }
        }
        if (!hasOne) {
            return INF;
        }

        int[] tr = new int[n];
        for (int i = 0; i < n ; i++) {
            int[][] tbl = clone2(basetbl);
            int time = 0;
            if (tbl[i][i] == 0) {
                boolean hasSub = false;
                for (int j = 0; j < n ; j++) {
                    if (tbl[j][i] == 1) {
                        hasSub = true;
                    }
                }
                if (!hasSub) {
                    for (int j = 0; j < n; j++) {
                        int cnt = 0;
                        for (int k = 0; k < n; k++) {
                            cnt += tbl[j][k];
                        }
                        if (cnt >= 1) {
                            int[] tmp = tbl[j].clone();
                            for (int k = 0; k < n; k++) {
                                tbl[k][i] = tmp[k];
                            }
                            time++;
                            break;
                        }
                    }
                }
                for (int j = 0; j < n ; j++) {
                    if (tbl[j][i] == 1) {
                        int[] tmp = tbl[j].clone();
                        for (int k = 0; k < n ; k++) {
                            tbl[k][i] = tmp[k];
                        }
                        time++;
                        break;
                    }
                }
            }
            int[] tmp = tbl[i].clone();
            for (int j = 0; j < n ; j++) {
                if (tbl[i][j] == 0) {
                    for (int k = 0; k < n ; k++) {
                        tbl[k][j] = tmp[k];
                    }
                    time++;
                }
            }
            for (int j = 0; j < n ; j++) {
                int cnt = 0;
                for (int k = 0; k < n ; k++) {
                    cnt += tbl[k][j];
                }
                time += cnt < n ? 1 : 0;
            }
            tr[i] = time;
        }
        int ret = INF;
        for (int i = 0; i < n ; i++) {
            ret = Math.min(ret, tr[i]);
        }
        return ret;
    }

    static int[][] clone2(int[][] a) {
        int[][] b = new int[a.length][];
        for (int i = 0; i < a.length; i++) {
            b[i] = a[i].clone();
        }
        return b;
    }

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        private int[] nextInts(int n) {
            int[] ret = new int[n];
            for (int i = 0; i < n; i++) {
                ret[i] = nextInt();
            }
            return ret;
        }

        private int[][] nextIntTable(int n, int m) {
            int[][] ret = new int[n][m];
            for (int i = 0; i < n; i++) {
                for (int j = 0; j < m; j++) {
                    ret[i][j] = nextInt();
                }
            }
            return ret;
        }

        private long[] nextLongs(int n) {
            long[] ret = new long[n];
            for (int i = 0; i < n; i++) {
                ret[i] = nextLong();
            }
            return ret;
        }

        private long[][] nextLongTable(int n, int m) {
            long[][] ret = new long[n][m];
            for (int i = 0; i < n; i++) {
                for (int j = 0; j < m; j++) {
                    ret[i][j] = nextLong();
                }
            }
            return ret;
        }

        private double[] nextDoubles(int n) {
            double[] ret = new double[n];
            for (int i = 0; i < n; i++) {
                ret[i] = nextDouble();
            }
            return ret;
        }

        private int next() {
            if (numChars == -1)
                throw new InputMismatchException();
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }

        public char nextChar() {
            int c = next();
            while (isSpaceChar(c))
                c = next();
            if ('a' <= c && c <= 'z') {
                return (char) c;
            }
            if ('A' <= c && c <= 'Z') {
                return (char) c;
            }
            throw new InputMismatchException();
        }

        public String nextToken() {
            int c = next();
            while (isSpaceChar(c))
                c = next();
            StringBuilder res = new StringBuilder();
            do {
                res.append((char) c);
                c = next();
            } while (!isSpaceChar(c));
            return res.toString();
        }

        public int nextInt() {
            int c = next();
            while (isSpaceChar(c))
                c = next();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = next();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c-'0';
                c = next();
            } while (!isSpaceChar(c));
            return res*sgn;
        }

        public long nextLong() {
            int c = next();
            while (isSpaceChar(c))
                c = next();
            long sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = next();
            }
            long res = 0;
            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c-'0';
                c = next();
            } while (!isSpaceChar(c));
            return res*sgn;
        }

        public double nextDouble() {
            return Double.valueOf(nextToken());
        }

        public boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);
        }
    }

    static void debug(Object... o) {
        System.err.println(Arrays.deepToString(o));
    }
}