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 black[] = new int[4];
        int white[] = new int[4];
        for (int k = 0; k < 4; k++) {
            for (int i = 0; i < n; i++) {
                String s = in.next();
                for (int j = 0; j < n; j++) {
                    int buf = s.charAt(j);
                    if ((i + j) % 2 == 0) {
                        white[k] += buf;
                        black[k] += (1 - buf);
                    } else {
                        white[k] += (1 - buf);
                        black[k] += buf;
                    }
                }
            }
        }
        System.out.println(min(white[0] + white[1] + black[2] + black[3], white[0] + white[2] + black[1] + black[3],white[0] + white[3] + black[1] + black[2],
                white[1] + white[2] + black[0] + black[3],white[1] + white[3] + black[0] + black[2],white[2] + white[3] + black[0] + black[1]));
    }
    static int min(int a, int b, int c, int d, int e, int f){
        return Math.min(a, Math.min(b, Math.min(c, Math.min(d, Math.min(e, f)))));
    }
}
