Magnus decided to play a classic chess game. Though what he saw in his locker shocked him! His favourite chessboard got broken into 4 pieces, each of size n by n, n is always odd. And what's even worse, some squares were of wrong color. j-th square of the i-th row of k-th piece of the board has color ak, i, j; 1 being black and 0 being white. 

Now Magnus wants to change color of some squares in such a way that he recolors minimum number of squares and obtained pieces form a valid chessboard. Every square has its color different to each of the neightbouring by side squares in a valid board. Its size should be 2n by 2n. You are allowed to move pieces but not allowed to rotate or flip them.

Input

The first line contains odd integer n (1 ≤ n ≤ 100) — the size of all pieces of the board. 

Then 4 segments follow, each describes one piece of the board. Each consists of n lines of n characters; j-th one of i-th line is equal to 1 if the square is black initially and 0 otherwise. Segments are separated by an empty line.

Output

Print one number — minimum number of squares Magnus should recolor to be able to obtain a valid chessboard.

Examples

Input

1
0

0

1

0


Output

1


Input

3
101
010
101

101
000
101

010
101
011

010
101
010


Output

2
import java.util.*;
import java.lang.*;
import java.io.*;

/*
 * 
 * Comments Here
 * 
 */
public class C41
{
	static BufferedReader br; 
	static BufferedWriter bw; 
	static StringTokenizer st;

	public static void main(String[] args) throws java.lang.Exception
	{
		/**/
		br = new BufferedReader(new InputStreamReader(System.in));
		bw = new BufferedWriter(new OutputStreamWriter(System.out));
    		//Uncomment to read from file
    		/*/
		File file = new File("2016/A.in");
		br = new BufferedReader(new FileReader(file));
		bw = new BufferedWriter(new OutputStreamWriter(System.out));
		/**/
		
		int n = Integer.parseInt(br.readLine());
		
		int[][] corrs = new int[4][2];
		
		for(int piece = 0; piece < 4; ++piece) {
			
			char[][] vals = new char[n][n];
			for(int row = 0; row < n; ++row) {
				vals[row] = br.readLine().toCharArray();
			}
			br.readLine();
			
			
			int count = 0;
			for(int i  =0; i < n; ++i) {
				for(int j = 0; j < n; ++j) {
					
					if(vals[i][j] == '0') {
						++corrs[piece][count%2];
					} else {
						++corrs[piece][(count+1)%2];
					}

					++count;
				}
			}
			
			
		}
		
		int best = Integer.MAX_VALUE;
		
		best = Math.min(best, corrs[0][0]+corrs[1][0]+corrs[2][1]+corrs[3][1]);
		best = Math.min(best, corrs[0][0]+corrs[1][1]+corrs[2][0]+corrs[3][1]);
		best = Math.min(best, corrs[0][0]+corrs[1][1]+corrs[2][1]+corrs[3][0]);
		best = Math.min(best, corrs[0][1]+corrs[1][0]+corrs[2][0]+corrs[3][1]);
		best = Math.min(best, corrs[0][1]+corrs[1][0]+corrs[2][1]+corrs[3][0]);
		best = Math.min(best, corrs[0][1]+corrs[1][1]+corrs[2][0]+corrs[3][0]);

		bw.write(best+"\n");
		
		
		
		br.close();
		bw.close();
	}
	

	
	
}

