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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.lang.reflect.Array;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;

public class Main {

    public static void main(String[] args) throws IOException{
	// write your code here
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

        int n = Integer.valueOf(br.readLine().split(" ")[0]);

        Helper helper = new Helper();

        String [][][] str = new String[4][n][n];

        for (int i = 0; i < 3; i ++){
            for (int j = 0; j < n; j ++){
                str[i][j] = br.readLine().split("");
            }
            br.readLine();
        }

        for (int j = 0; j < n; j ++){
            str[3][j] = br.readLine().split("");
        }

        int [] ans = new int[4];

        for (int i = 0; i < 4; i ++){
            ans[i] = helper.getMist(str[i], n);
        }

        Arrays.sort(ans);

        int summ = ans[0] + ans[1] + 2 * n * n - ans[2] - ans[3];
        System.out.println(summ);

    }
}

class Helper {

    public int getMist(String[][] a, int n){

        int mist = 0;
        for (int i = 0; i < n; i ++){
            for (int j = 0; j < n; j ++){
                if ((i + j) % 2 == 0 && Integer.valueOf(a[i][j]) == 1){
                    mist += 1;
                }
                else if ((i + j) % 2 == 1 && Integer.valueOf(a[i][j]) == 0){
                    mist += 1;
                }
            }
        }
        return mist;
    }


}
