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.*;

public class Codeforces
{
    public static void main(String args[])throws Exception
    {
        BufferedReader bu=new BufferedReader(new InputStreamReader(System.in));
        StringBuilder sb=new StringBuilder();

        int i,j,k,l;
        ArrayList<int[]> a=new ArrayList<>();
        for(i=0;i<4;i++)
        for(j=0;j<4;j++)
        if(j!=i)
        for(k=0;k<4;k++)
        if(k!=i && k!=j)
        for(l=0;l<4;l++)
        if(l!=i && l!=j && l!=k) a.add(new int[]{i,j,k,l});

        int n=Integer.parseInt(bu.readLine());
        int g[][][]=new int[4][n][n];
        for(i=0;i<4;i++)
        {
            for(j=0;j<n;j++)
            {
                String s=bu.readLine();
                for(k=0;k<n;k++)
                g[i][j][k]=s.charAt(k)-'0';
            }
            if(i!=3) bu.readLine();
        }

        int ans=Integer.MAX_VALUE;
        for(int x[]:a)
        ans=Math.min(ans,moves(g,x));
        System.out.println(ans);
    }

    static int moves(int g[][][],int x[])
    {
        int n=g[0].length,a[][]=new int[2*n][2*n],i,j,k;
        for(i=0;i<4;i++)
        {
            int u=0,v=0;
            if(i==1 || i==3) v=n;
            if(i==2 || i==3) u=n;
            for(j=0;j<n;j++)
            for(k=0;k<n;k++)
            a[u+j][v+k]=g[x[i]][j][k];
        }

        int c[][]=new int[2][2];
        for(i=0;i<2*n;i++)
        for(j=0;j<2*n;j++)
        c[(i+j)%2][a[i][j]]++;

        return Math.min(c[0][0]+c[1][1],c[0][1]+c[1][0]);
    }
}
