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
/**
 * http://codeforces.com/problemset/problem/961/C (Chessboard)
 * @author Alan Yan
 *
 */
import java.util.*;
public class Task961C {
	public static void main(String[] args) { 
		Scanner sc = new Scanner(System.in);
		int n = Integer.parseInt(sc.nextLine());
		int ret = Integer.MAX_VALUE;
		int[][][] boards = new int[4][n][n];
		int[][][] models = new int[2][n][n];
		int[][] numChanges = new int[4][2];
		for(int i = 0; i < 4; i++) {
			for(int j = 0; j < n; j++) { 
				String taco = sc.nextLine();
				for(int k = 0; k < n; k++) {
					boards[i][j][k] = (int) (taco.charAt(k) - '0');
				}
			}
			if(i < 3)
				sc.nextLine();
		}
		//create models
		for(int i = 0; i < n; i++) 
		for(int j = 0; j < n; j++) 
			models[(i+j)%2][i][j] = 1;
		
		//create numChanges
		for(int i = 0; i < 4; i++) 
		for(int j = 0 ; j < 2; j++) 
		for(int a = 0; a < n; a++) 
		for(int b = 0; b < n; b++) 
		if(models[j][a][b] != boards[i][a][b])
			numChanges[i][j]++;
		
		//choosing which to be of model2
		int temp = numChanges[0][0] + numChanges[1][0] + numChanges[2][0] + numChanges[3][0];
		for(int i = 0; i < 3; i++) { 
			for(int j = i+1; j < 4; j++) { 
				int x = temp - numChanges[i][0] + numChanges[i][1] - numChanges[j][0] + numChanges[j][1];
				ret = Math.min(x, ret);
			}
		}
		
		System.out.print(ret);
		sc.close();
	}
}
