Problem:
Score : 1300 points

Problem Statement

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 #.

Partial Score

In a test set worth 300 points, N ≤ 3.

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.

Sample Input 1

2
#.
.#

Sample Output 1

3

For example, perform the operation as follows:

Select i = 1, j = 2.

Select i = 1, j = 1.

Select i = 1, j = 2.

The transition of the colors of the squares is shown in the figure below:

Sample Input 2

2
..
..

Sample Output 2

-1

Sample Input 3

2
##
##

Sample Output 3

0

Sample Input 4

3
.#.
###
.#.

Sample Output 4

2

Sample Input 5

3
...
.#.
...

Sample Output 5

5

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.util.*;

public class Main {

    public static void main(String[] args) {

        Scanner scanner = new Scanner(System.in);
        int dimension = scanner.nextInt();

        boolean[][] matrix = new boolean[dimension][dimension];

        boolean allWhite = true;
        boolean allBlack = true;

        int[][] filledCells = new int[dimension][2];

        for (int i = 0; i < dimension; i++) {
            String line = scanner.next();
            filledCells[i][0] = i;
            for (int j = 0; j < dimension; j++) {

                char current = line.charAt(j);
                if (current == '#') {
                    matrix[i][j] = true;
                    filledCells[i][1]++;
                    allWhite = false;
                } else {
                    allBlack = false;
                }
            }
        }

        if (allBlack) {
            System.out.println(0);
            return;
        }
        if (allWhite) {
            System.out.println(-1);
            return;
        }

        boolean hasFillRow = false;

        for (int i = 0; i < dimension; i++) {
            int j = 0;
            boolean isRowFill = matrix[i][j];

            while (isRowFill) {
                if (j == dimension - 1) break;
                isRowFill &= matrix[i][++j];
            }
            if (isRowFill) {
                hasFillRow = true;
                break;
            }
        }

        int countOfFillColumn = 0;

        for (int i = 0; i < dimension; i++) {
            int j = 0;
            boolean isColumnFill = matrix[j][i];

            while (isColumnFill) {
                if (j == dimension - 1) break;
                isColumnFill &= matrix[j++][i];
            }
            if (isColumnFill) {
                countOfFillColumn++;
            }
        }

        if (hasFillRow) {
            System.out.println(dimension - countOfFillColumn);
            return;
        }

        Arrays.sort(filledCells, new Comparator<int[]>() {
            @Override
            public int compare(int[] o1, int[] o2) {
                return Integer.compare(o2[1], o1[1]);
            }
        });

        int minPrice = Integer.MAX_VALUE;

        boolean hasGoodVariant = false;

        for (int i = 0; i < dimension; i++) { // Строка с найбольшим кол-вом закрашенных

            boolean isRowValid = true;

            for (int j = 0; j < dimension; j++) { // Элемент в строке с найбильшим кол-вом закаршенных
                if (!matrix[filledCells[i][0]][j]) {

                    boolean isEmptyCellFillable = false;

                    for (int k = 0; k < dimension; k++) {
                        if (matrix[k][filledCells[i][0]]) {
                            isEmptyCellFillable = true;
                            break;
                        }
                    }

                    if (!isEmptyCellFillable) {
                        isRowValid = false;
                        break;
                    }
                }
            }

            if (isRowValid) {
                hasGoodVariant = true;
                minPrice = Math.min((2 * dimension - filledCells[i][1]) - countOfFillColumn, minPrice);
                break;
            }
        }

        if (hasGoodVariant) {
            System.out.println(minPrice);
        } else {
            System.out.println(2 * dimension);
        }

    }

}