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

/**
 * @author: Mehul Raheja
 */

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

public class C{

    /*
        Runtime = O()
     */
    static int N, M, K;
    static String s;
    static StringTokenizer st;
    static int[] d;
    
    public static void main(String[] args) throws Exception {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in)); 
        int N = Integer.parseInt(br.readLine());
        
        int[][][] d = new int[N][N][4];
        
        for (int i = 0; i < 4; i++) {
           
            for (int j = 0; j < N; j++) {
                 String s = br.readLine();
                 for (int k = 0; k < N; k++) {
                    d[j][k][i] = Integer.parseInt(s.charAt(k) + "");
                }
            }
            
            if(i < 3){
                br.readLine();
            }
        }
        
        int[] c1 = new int[4];
        int[] c2 = new int[4];
        
        for (int i = 0; i < 4; i++) {
            int cur = 0;
            for (int j = 0; j < N*N; j++) {
                int a = j/N;
                int b = j%N;
               // System.out.println(d[a][b][i]);
                if(d[a][b][i] != cur){
                    c1[i]++;
                }
                cur ^= 1;
            }
        }
        
        for (int i = 0; i < 4; i++) {
            int cur = 1;
            for (int j = 0; j < N*N; j++) {
                int a = j/N;
                int b = j%N;
                if(d[a][b][i] != cur){
                    c2[i]++;
                }
                cur ^= 1;
            }
        }
        
//        System.out.println(Arrays.toString(c1));
//        System.out.println(Arrays.toString(c2));
        int ans = 1<<30;
        int tot = 0;
        for (int i = 0; i < 4; i++) {
            tot += c2[i];
        }
        for (int i = 0; i < 4; i++) {
            for (int j = 0; j < 4; j++) {
                if(i == j){
                    continue;
                }
                
                int cur = c1[i] + c1[j] - c2[i] - c2[j] + tot;
                ans = Math.min(ans,cur);
            }
        }
        
        System.out.println(ans);
        
        
    }    
}
