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.Scanner;

/**
 * Created by thaim on 18/04/04.
 */
public class SolutionC {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);

        int n = sc.nextInt();
        sc.nextLine();
        String[][] line = new String[4][n];
        for (int i=0; i<4; i++) {
            if (i!=0) {
                sc.nextLine();
            }
            for (int j=0; j<n; j++) {
                line[i][j] = sc.nextLine();
            }
        }

        System.out.println(solve(n, line));
    }

    private static int solve(int n, String[][] line) {
        int[][] dist = new int[4][2];
        char[] req = {'0', '1'};

        for (int color=0; color<2; color++) {
            for (int i=0; i<4; i++) {
                for (int j=0; j<n; j++) {
                    for (int k=0; k<n; k++) {
                        if (line[i][j].charAt(k) != req[(j+k+color)%2]) {
                            dist[i][color]++;
                            //System.err.print("color: " + color + ", board: " + i + " line: " + j + ", pos: " + k + " = " + line[i][j].charAt(k));
                            //System.err.println(" => " + req[(j+k+color)%2]);
                        }
                    }
                }
//                System.err.println("board: " + i + " with color:" + color + " dist = " + dist[i][color]);
            }
        }

        int minDist = Integer.MAX_VALUE;
        int[] select = {3, 5, 6, 9, 10, 12};
        for (int i=0; i<select.length; i++) {
            int tmp = 0;
            for (int j=0; j<4; j++) {
                tmp += dist[j][(select[i]>>j)%2];
            }
            minDist = Math.min(minDist,tmp);
        }

        return minDist;
    }
}
