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.IOException;
import java.io.InputStream;
import java.util.Arrays;
import java.util.NoSuchElementException;


public class Main {
  public static void main(String[] args) {
    FastScanner sc = new FastScanner();
    int N = sc.nextInt();
    char[][] map = new char[N][];
    for (int i = 0; i < N; i++) {
      map[i] = sc.next().toCharArray();
    }


    int ret = solve(map);
    System.out.println(ret);

//    int N =3;
//     char[][] map = new char[N][N];
//     while (true) {
//     for (int i = 0; i < N; i ++) {
//     for (int j = 0; j < N; j ++) {
//     map[i][j] = Math.random() < 0.5 ? '#' : '.';
//     }
//     }
//    
//     for (char[] line : map) {
//     System.out.println(line);
//     }
//     System.out.println();
//     if (solve(map) != solve2(map)) {
//     System.out.println("NG");
//     break;
//     }
//     }
  }


  public static int solve2(char[][] map) {
    int ret = dfs(map, 0);
    if (ret == Integer.MAX_VALUE) {
      return -1;
    }
    return ret;
  }

  public static int dfs(char[][] map, int depth) {
    if (depth >= 7) {
      return Integer.MAX_VALUE;
    }

    int N = map.length;
    boolean flg = true;
    loop: for (int i = 0; i < N; i++) {
      for (int j = 0; j < N; j++) {
        if (map[i][j] == '.') {
          flg = false;
          break loop;
        }
      }
    }
    if (flg) {
      if (depth == 2) {
        return depth;
      }
      return depth;
    }

    int ret = Integer.MAX_VALUE;

    for (int i = 0; i < N; i++) {
      for (int j = 0; j < N; j++) {
        char[] bak = new char[N];
        char[] to = new char[N];
        for (int k = 0; k < N; k++) {
          bak[k] = map[k][j];
          to[k] = map[i][k];
        }
        for (int k = 0; k < N; k++) {
          map[k][j] = to[k];
        }
        ret = Math.min(ret, dfs(map, depth + 1));
        for (int k = 0; k < N; k++) {
          map[k][j] = bak[k];
        }
      }
    }
    return ret;
  }

  public static int solve(char[][] map) {
    int N = map.length;
    boolean flg = false;
    loop: for (int i = 0; i < N; i++) {
      for (int j = 0; j < N; j++) {
        if (map[i][j] == '#') {
          flg = true;
          break loop;
        }
      }
    }
    if (!flg) {
      return -1;
    }

    int[] colCount = new int[N];
    int[] rowCount = new int[N];
    for (int i = 0; i < N; i++) {
      for (int j = 0; j < N; j++) {
        if (map[i][j] == '#') {
          colCount[j]++;
          rowCount[i]++;
        }
      }
    }

    int[] lineScore = new int[N];
    for (int i = 0; i < N; i++) {
      for (int j = 0; j < N; j++) {
        if (map[i][j] == '.') {
          if (colCount[i] > 0) {
            lineScore[i]++;
          } else {
            lineScore[i] += 2;
            colCount[i] ++;
          }
        }
      }
    }

    int ret = Arrays.stream(lineScore).min().getAsInt();

    for (int i = 0; i < N; i++) {
      if (colCount[i] != N) {
        ret++;
      }
    }
    return ret;
  }

}


class FastScanner {
  public static String debug = null;

  private final InputStream in = System.in;
  private int ptr = 0;
  private int buflen = 0;
  private byte[] buffer = new byte[1024];
  private boolean eos = false;

  private boolean hasNextByte() {
    if (ptr < buflen) {
      return true;
    } else {
      ptr = 0;
      try {
        if (debug != null) {
          buflen = debug.length();
          buffer = debug.getBytes();
          debug = "";
          eos = true;
        } else {
          buflen = in.read(buffer);
        }
      } catch (IOException e) {
        e.printStackTrace();
      }
      if (buflen < 0) {
        eos = true;
        return false;
      } else if (buflen == 0) {
        return false;
      }
    }
    return true;
  }

  private int readByte() {
    if (hasNextByte())
      return buffer[ptr++];
    else
      return -1;
  }

  private static boolean isPrintableChar(int c) {
    return 33 <= c && c <= 126;
  }

  private void skipUnprintable() {
    while (hasNextByte() && !isPrintableChar(buffer[ptr]))
      ptr++;
  }

  public boolean isEOS() {
    return this.eos;
  }

  public boolean hasNext() {
    skipUnprintable();
    return hasNextByte();
  }

  public String next() {
    if (!hasNext())
      throw new NoSuchElementException();
    StringBuilder sb = new StringBuilder();
    int b = readByte();
    while (isPrintableChar(b)) {
      sb.appendCodePoint(b);
      b = readByte();
    }
    return sb.toString();
  }

  public long nextLong() {
    if (!hasNext())
      throw new NoSuchElementException();
    long n = 0;
    boolean minus = false;
    int b = readByte();
    if (b == '-') {
      minus = true;
      b = readByte();
    }
    if (b < '0' || '9' < b) {
      throw new NumberFormatException();
    }
    while (true) {
      if ('0' <= b && b <= '9') {
        n *= 10;
        n += b - '0';
      } else if (b == -1 || !isPrintableChar(b)) {
        return minus ? -n : n;
      } else {
        throw new NumberFormatException();
      }
      b = readByte();
    }
  }

  public int nextInt() {
    return (int) nextLong();
  }

  public long[] nextLongList(int n) {
    return nextLongTable(1, n)[0];
  }

  public int[] nextIntList(int n) {
    return nextIntTable(1, n)[0];
  }

  public 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;
  }

  public 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;
  }
}