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.Scanner;
import java.util.Arrays;
import java.math.*;
import java.util.Collections;
public class codeforce{
    public static void main(String[] args){
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int[] nb0 = new int[4];
        int[] nb1 = new int[4];
        String[][] s = new String[4][n];
        for(int k=0;k<4;k++){
            for(int i=0;i<n;i++){
                s[k][i] = sc.next();
            }
        }
        for(int k=0;k<4;k++){
            boolean ok = true;
            nb0[k] = 0;
            nb1[k] = 0;
            for(int i=0;i<n;i++){
                for(int j=0;j<n;j++){
                    if(ok){
                        ok = false;
                        if(s[k][i].charAt(j)!='0') nb0[k]++;
                        else nb1[k]++;
                    }
                    else{
                        ok = true;
                        if(s[k][i].charAt(j)=='0') nb0[k]++;
                        else nb1[k]++;
                    }
                }
            }
        }
        int max;
        max = nb0[0] + nb0[1] +nb1[2] + nb1[3];
        int test;
        for(int k=0;k<3;k++){
            for(int kk=k+1;kk<4;kk++){
                if(k==0&&kk==1) continue;
                test = nb0[k]+nb0[kk];
                for(int i=0;i<4;i++){
                    if(i!=k && i!=kk) test += nb1[i];
                }
                if(max>test) max = test;
            }
        }
        
        System.out.println(max);
       
        
    }
    

    
}