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.io.BufferedReader;
import java.io.Closeable;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.util.Arrays;
import java.util.LinkedList;
import java.util.Scanner;
import java.util.StringTokenizer;

public class Main {
	
	public static boolean dfs(final int deep, final int limit, final int n, boolean[][] board){
		//System.out.println(deep + " " + limit + " " + Arrays.deepToString(board));
		if(deep >= limit){
			for(int i = 0; i < n; i++){
				for(int j = 0; j < n; j++){
					if(!board[i][j]){ return false; }
				}
			}
			
			return true;
		}
		

		for(int row = 0; row < n; row++){
			for(int col = 0; col < n; col++){
				
				boolean[] prev_col = new boolean[n];
				boolean[] prev_row = new boolean[n];
				for(int i = 0; i < n; i++){
					prev_col[i] = board[i][col];
					prev_row[i] = board[row][i];
				}
				
				for(int i = 0; i < n; i++){
					board[i][col] = prev_row[i];
				}
				
				if(dfs(deep + 1, limit, n, board)){ return true; }
				
				for(int i = 0; i < n; i++){
					board[i][col] = prev_col[i];
				}
			}
		}
		
		return false;
	}
	
	public static void main(String[] args) throws IOException {
		final Scanner sc = new Scanner(System.in);
		
		final int n = sc.nextInt();
		
		if(n > 3){ return; }
		
		boolean[][] board = new boolean[n][n];
		for(int i = 0; i < n; i++){
			final char[] input = sc.next().toCharArray();
			
			for(int j = 0; j < n; j++){
				board[i][j] = input[j] == '#';
			}
		}
		
		boolean flg = false;
		for(int i = 0; i < n; i++){
			if(board[0][i] || board[i][0]){
				flg = true;
				break;
			}
		}
		
		if(flg){
			System.out.println(-1);
			return;
		}
		
		int count = 0;
		while(!dfs(0, count, n, board)){
			count++;
		}
		
		
		System.out.println(count);
	}
	
	public static class Scanner implements Closeable {
		private BufferedReader br;
		private StringTokenizer tok;
 
		public Scanner(InputStream is) throws IOException {
			br = new BufferedReader(new InputStreamReader(is));
		}
 
		private void getLine() throws IOException {
			while (!hasNext()) {
				tok = new StringTokenizer(br.readLine());
			}
		}
 
		private boolean hasNext() {
			return tok != null && tok.hasMoreTokens();
		}
 
		public String next() throws IOException {
			getLine();
			return tok.nextToken();
		}
 
		public int nextInt() throws IOException {
			return Integer.parseInt(next());
		}
 
		public long nextLong() throws IOException {
			return Long.parseLong(next());
		}
 
		public double nextDouble() throws IOException {
			return Double.parseDouble(next());
		}
		
		public int[] nextIntArray(int n) throws IOException {
			final int[] ret = new int[n];
			for(int i = 0; i < n; i++){
				ret[i] = this.nextInt();
			}
			return ret;
		}
		
		public long[] nextLongArray(int n) throws IOException {
			final long[] ret = new long[n];
			for(int i = 0; i < n; i++){
				ret[i] = this.nextLong();
			}
			return ret;
		}
 
		public void close() throws IOException {
			br.close();
		}
	}
}