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.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Scanner;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author Swatantra
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        Scanner in = new Scanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskC solver = new TaskC();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskC {
        public void solve(int testNumber, Scanner in, PrintWriter out) {

            int n = Integer.parseInt(in.nextLine());
            String wb[][] = new String[4][n];
            int i, j, p, k;

            //in.nextLine();
            for (i = 0; i < 4; i++) {

                for (j = 0; j < n; j++) {
                    // System.out.println("n="+n);
                    wb[i][j] = in.nextLine();
                    //System.out.println("w="+wb[i][j]);
                }
                if (i != 3) in.nextLine();
            }

            int cb[][][] = new int[2][n][n];
            int color = 0;
            for (i = 0; i < n; i++) {
                for (j = 0; j < n; j++) {

                    cb[0][i][j] = color;
                    cb[1][i][j] = 1 - color;
                    color = 1 - color;
                }
            }

            int res = Integer.MAX_VALUE;

            for (i = 3; i <= 16; i++) {

                int myc = Integer.MAX_VALUE;
                if (Integer.bitCount(i) == 2) {


                    myc = 0;
                    for (j = 0; j < 4; j++) {

                        int bp = ((1 << j) & i) != 0 ? 1 : 0;

                        for (p = 0; p < n; p++) {

                            for (k = 0; k < n; k++) {

                                // System.out.println("bp="+bp+" p="+p+"k="+k);
                                if (cb[bp][p][k] != (wb[j][p].charAt(k) - '0')) {

                                    myc++;
                                }
                            }
                        }
                    }
                }
                res = Math.min(res, myc);
            }

            out.println(res);
        }

    }
}

