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.Scanner;
public class C {

    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int n = in.nextInt();
        int[][] d = new int[4][2];
        for (int i = 0; i < 4; i++) {
            for (int j = 0; j < n; j++) {
                String s = in.next();
                for (int k = 0; k < n; k++) {
                    int cur = s.charAt(k)-'0';
                    if ((j+k) % 2 == cur) {
                        d[i][0]++;
                    } else {
                        d[i][1]++;
                    }
                }
            }
//            System.out.println(d[i][0]+" "+d[i][1]);
        }
        
        int min = Integer.MAX_VALUE;
        for (int i = 0; i < 3; i++) {
            for (int j = i+1; j < 4; j++) {
                int c1 = d[i][0]+d[j][0];
                int c2 = d[0][1]+d[1][1]+d[2][1]+d[3][1]-d[i][1]-d[j][1];
                int c = c1+c2;
                min = Math.min(min, c);
            }
        }
            
        System.out.println(min);
        
    }
}
