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.*;
import java.io.*;
public class Solution{
    
    
    public static void main(String[] args){
        Scanner sc = new Scanner(new BufferedReader(new InputStreamReader(System.in)));
        int n = sc.nextInt();
        char x;
        String s = new String();
        int[][] t = new int[2][4];
        for(int i=0;i<4;i++){
            for(int j=0;j<n;j++){
                s = sc.next();
                for(int k=0;k<n;k++){
                    x = s.charAt(k);
                    if(j%2==k%2){
                        if(x=='1') t[1][i]++;
                        else t[0][i]++;
                    }else{
                        if(x=='1') t[0][i]++;
                        else t[1][i]++;
                    }
                }
            }
        }
        int m=0;
        int min = n*n*4+1;
        for(int i=0;i<4;i++){
            for(int j=0;j<4;j++){
                if(j==i) continue;
                for(int k=0;k<4;k++){
                    if(k==j||k==i) continue;
                    for(int d=0;d<4;d++){
                        if(d==i||d==j||d==k) continue;
                        m = t[0][i] + t[0][j] + t[1][k] + t[1][d];
                        if(min>m) min = m;
                    }
                }
            }
        }
        System.out.println(min);
    }
}















