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.*;
import java.util.*;
import java.math.BigInteger;

public class Test {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);

        int n=sc.nextInt();

        int[][] a1=new int[n][n];
        for(int i=0;i<n;i++){
            String s=sc.next();
            for(int j=0;j<n;j++) a1[i][j]=(s.charAt(j)=='0')?0:1;
        }
        //sc.nextLine();

        int[][] a2=new int[n][n];
        for(int i=0;i<n;i++){
            String s=sc.next();
            for(int j=0;j<n;j++) a2[i][j]=(s.charAt(j)=='0')?0:1;
        }
        //sc.nextLine();

        int[][] a3=new int[n][n];
        for(int i=0;i<n;i++){
            String s=sc.next();
            for(int j=0;j<n;j++) a3[i][j]=(s.charAt(j)=='0')?0:1;
        }
        //sc.nextLine();

        int[][] a4=new int[n][n];
        for(int i=0;i<n;i++){
            String s=sc.next();
            for(int j=0;j<n;j++) a4[i][j]=(s.charAt(j)=='0')?0:1;
        }
        //sc.nextLine();

        int ans=Integer.MAX_VALUE;
        String[] s=new String[6];
        s[0]="0011";
        s[1]="0101";
        s[2]="1001";
        s[3]="0110";
        s[4]="1010";
        s[5]="1100";

        for(int i=0;i<6;i++){
            int curr=find(a1,s[i].charAt(0))+find(a2,s[i].charAt(1))+find(a3,s[i].charAt(2))+find(a4,s[i].charAt(3));
            //System.out.println(curr);
            ans=Math.min(ans,curr);
        }

        System.out.println(ans);
    }

    static int find(int[][] a,char t){
        int ans=0;
        int n=a.length;

        if(t=='0'){
            for(int i=0;i<n;i++){
                for(int j=0;j<n;j++){
                    if(i%2==0){
                        if(j%2==0 && a[i][j]==1) ans++;
                        else if(j%2==1 && a[i][j]==0) ans++;
                    }
                    else{
                        if(j%2==0 && a[i][j]==0) ans++;
                        else if(j%2==1 && a[i][j]==1) ans++;
                    }
                }
            }
        }

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