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.File;
import java.io.FileNotFoundException;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Scanner;

public class Codeforce {
    public static void main(String[] args) {
        boolean debug = false;
        Scanner scanner = null;
        try {
            scanner = debug?new Scanner(new File("cf.txt")):new Scanner(System.in);
        } catch (FileNotFoundException e) {
            e.printStackTrace();
        }

        int n = Integer.parseInt(scanner.nextLine());
        int[] val = new int[4];
        for(int i = 1; i<=4 ; i++){
            int next = 1;
            for(int j = 0 ; j<n; j++){

                String str = scanner.nextLine();
                for(int k = 0 ; k<str.length();k++) {
                    int x = str.charAt(k) - '0';
                    if (x != next) {
                        val[i - 1]++;
                    }
                    next = (next == 1 ? 0 : 1);
                }

            }
            if(scanner.hasNextLine()){
                scanner.nextLine();
            }
        }

        ArrayList<Integer> list = new ArrayList<>();
        for(int x : val){
            list.add(x);
        }
        Collections.sort(list);
        int sum = 0 ;
        sum += list.get(0);
        sum += list.get(1);
        sum += (n*n-list.get(2)) ;
        sum += (n*n - list.get(3));
        System.out.println(sum);






    }
}
