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) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        int N = Integer.parseInt(br.readLine());
        char[][][]grid = new char[4][N][N];

        int[][]moves = new int[4][2];

        for (int i = 0; i < 4; i++) {
            for (int j = 0; j < N; j++) {
                grid[i][j] = br.readLine().toCharArray();
                for (int k = 0; k < N; k++) {
                    if((j+k)%2==0) {
                        if (grid[i][j][k]=='0')
                            moves[i][1]++;
                        else
                            moves[i][0]++;
                    }
                    else{
                        if(grid[i][j][k]=='0')
                            moves[i][0]++;
                        else
                            moves[i][1]++;
                    }
                }

            }
            if(i!=3)
                br.readLine();
        }

       // for (int i = 0; i < 4; i++) {
        //    System.out.println(moves[i][0]+" "+moves[i][1]);
       // }

        int ans = Integer.MAX_VALUE;
        for (int i = 0; i < 4; i++) {
            for (int j = 0; j < 4; j++) {
                if(j==i)
                    continue;
                int t = moves[i][1]+moves[j][1];
                for (int k = 0; k < 4; k++) {
                    if(k!=i&&k!=j)
                        t+=moves[k][0];
                }
                ans = Math.min(ans,t);
            }
        }
        System.out.println(ans);



    }
}
