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.Arrays;
public class chess2 {
    public static void print2(char diff[][]){
        for(int i=0;i<diff.length;i++){
            for(int j=0;j<diff[0].length;j++)
                System.out.print(diff[i][j]);
            System.out.println();
        }
    }
    
    public static void print(int diff[][]){
        for(int i=0;i<diff.length;i++){
            for(int j=0;j<diff[0].length;j++)
                System.out.print(diff[i][j]);
            System.out.println();
        }
    }
    
    public static void computeDiff(char piece[][],char board[][], long n, int diff[][], int itr){
        for(int i=0;i<n;i++){
            for(int j=0;j<n;j++){
                //System.out.println("Comparing "+piece[i][j]+" and "+board[i][j]);
                if(piece[i][j]==board[i][j])
                    diff[1][itr]++;
                else
                    diff[0][itr]++;
            }
        }
    }
    public static void main(String[] args) throws IOException, FileNotFoundException
    {
        // TODO Auto-generated method stub
        //BufferedReader b = new BufferedReader(new FileReader("C:\\Users\\mohit.18\\Desktop\\Graph\\chessInput.txt"));
        BufferedReader b = new BufferedReader(new InputStreamReader(System.in));
        long n = Long.parseLong(b.readLine());
        char a[][] = new char[(int)n][(int)n];
        for(long i=0;i<n;i++)
        {
            String g = b.readLine();
            if(g.equalsIgnoreCase(""))
            {
                i--;
                continue;
            }
            for(long j=0;j<n;j++)
            {
                a[(int)i][(int)j] = g.charAt((int)j);
            }
        }
        char c[][] = new char[(int)n][(int)n];
        for(long i=0;i<n;i++)
        {
            String g = b.readLine();
            if(g.equalsIgnoreCase(""))
            {
                i--;
                continue;
            }
            for(long j=0;j<n;j++)
            {
                c[(int)i][(int)j] = g.charAt((int)j);
            }
        }
        char d[][] = new char[(int)n][(int)n];
        for(long i=0;i<n;i++)
        {
            String g = b.readLine();
            if(g.equalsIgnoreCase(""))
            {
                i--;
                continue;
            }
            for(long j=0;j<n;j++)
            {
                d[(int)i][(int)j] = g.charAt((int)j);
            }
        }
        char e[][] = new char[(int)n][(int)n];
        for(long i=0;i<n;i++)
        {
            String g = b.readLine();
            if(g.equalsIgnoreCase(""))
            {
                i--;
                continue;
            }
            for(long j=0;j<n;j++)
            {
                e[(int)i][(int)j] = g.charAt((int)j);
            }
        }
        int diff[][] = new int[2][4];
        char board[][] = new char[(int)n][(int)n];
        int num = 1;
        for(int i=0;i<n;i++){
            for(int j=0;j<n;j++){
                board[i][j] = (char) (num+'0');
                if(num==0)
                    num++;
                else num--;
            }
        }
        /*print2(a);
        print2(c);
        print2(d);
        print2(e);
        print2(board);*/
        computeDiff(a,board,n,diff,0);
        computeDiff(c,board,n,diff,1);
        computeDiff(d,board,n,diff,2);
        computeDiff(e,board,n,diff,3);
        //print(diff);
        Arrays.sort(diff[0]);
        Arrays.sort(diff[1]);
        //print(diff);
        System.out.println(diff[0][0] + diff[0][1] + diff[1][0] + diff[1][1]);
    }

}
