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
/* package codechef; // don't place package name! */

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

/* Name of the class has to be "Main" only if the class is public. */
public class Codechef
{
	public static void main (String[] args) throws java.lang.Exception
	{
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		int[][] diff = new int[4][2];
		for(int k=0; k<4; k++)
		{
		    for(int i=0; i<n; i++)
		    {
		        String s = sc.next();
		        for(int j=0; j<n; j++)
		        {
		            if(((i+j)%2)!=Integer.parseInt(s.substring(j,j+1)))
		            diff[k][0]++;
		            if((1-(i+j)%2)!=Integer.parseInt(s.substring(j,j+1)))
		            diff[k][1]++;
		        }
		    }
		}
		int min = (int)Math.min(diff[0][0]+diff[1][0]+diff[2][1]+diff[3][1], Math.min(diff[0][0]+diff[1][1]+diff[2][0]+diff[3][1], Math.min(diff[0][0]+diff[1][1]+diff[2][1]+diff[3][0], Math.min(diff[0][1]+diff[1][0]+diff[2][0]+diff[3][1], Math.min(diff[0][1]+diff[1][0]+diff[2][1]+diff[3][0], diff[0][1]+diff[1][1]+diff[2][0]+diff[3][0])))));
		System.out.println(min);
	}
}
