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
//package uva;

import java.util.*;
import java.io.*;

public class Uva {
    public static void main(String arg[])throws IOException{
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        int n = Integer.parseInt(br.readLine());
        boolean a[][] = new boolean[4][n*n];
        for(int x=0;x<4;x++){
            for(int i=0;i<n;i++){
                String s = br.readLine();
                for(int j=0;j<s.length();j++){
                    if(s.charAt(j)=='1'){
                        a[x][i*n+j] = true;
                    }
                }
            }
            if(x<3){
                br.readLine();
            }
        }
        int ans[][] = new int[2][4];
        for(int i=0;i<2;i++){
            for(int j=0;j<4;j++){
                int count = 0;
                for(int k=0;k<n*n;k++){
                    if(a[j][k]&&(k+i)%2==1){
                        count++;
                    }else if(!a[j][k]&&(k+i)%2==0){
                        count++;
                    }
                }
                ans[i][j] = count;
            }
        }
        int a1 = ans[1][0]+ans[1][1]+ans[0][2]+ans[0][3];
        int a2 = ans[1][0]+ans[0][1]+ans[1][2]+ans[0][3];
        int a3 = ans[1][0]+ans[0][1]+ans[0][2]+ans[1][3];
        int a4 = ans[0][0]+ans[1][1]+ans[1][2]+ans[0][3];
        int a5 = ans[0][0]+ans[1][1]+ans[0][2]+ans[1][3];
        int a6 = ans[0][0]+ans[0][1]+ans[1][2]+ans[1][3];

        int min1 = Math.min(a1,a2);
        int min2 = Math.min(a3,a4);
        int min3 = Math.min(a5,a6);
        int min4 = Math.min(min1,min2);
        min4 = Math.min(min4,min3);
        System.out.println(min4);
    }
    
}