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.*;
 
public class Main {
	static final int maxn = 110;
	static final int dead = 0x7f7f7f7f;
 
	public static void main(String[] args) {
		Scanner in = new Scanner(System.in);
		int[] cout=new int[5];
		int n=in.nextInt();
		String temp;
		for(int i=1;i<=4;i++){
			for(int j=1;j<=n;j++) {
				temp=in.next();
				for(int k=0;k<=n-1;k++) {
					if(temp.charAt(k)=='0'&&((j-1)*n+k+1)%2==1)
						cout[i]++;
					else if(temp.charAt(k)=='1'&&((j-1)*n+k+1)%2==0)
						cout[i]++;
				}
			}
		}
		int mi=dead;
		int sum=cout[1]+cout[2]+cout[3]+cout[4];
		for(int i=1;i<4;i++) {
			for(int j=i+1;j<=4;j++) {
				mi=Math.min(sum-cout[i]-cout[j]+n*n-cout[i]+n*n-cout[j], mi);
			}
		}
		System.out.println(mi);
	}
}