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.*;

/**
 * Created by Admin on 2018-01-16.
 */
public class Main {
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
       /* int iloscSłow = in.nextInt(),iloscGrup = in.nextInt(),iloscKoncowychSlow = in.nextInt();
        String [] słowa = new String[iloscSłow];
        HashMap <String,Integer> SlowoCena = new HashMap<String,Integer>();
        for (int i = 0; i < iloscSłow; i++) {
            String slowo = in.next();
            słowa [i] = slowo;
        }
        int [] ceny = new int[iloscSłow];
        for (int i = 0; i < iloscSłow; i++) {
            int cena = in.nextInt();
            ceny[i] = cena;
        }
        */
        int n = in.nextInt();
        String[] a = new String[4];
        Arrays.fill(a, "");
        for (int i = 0; i < 4; ++i) {
            for (int j = 0; j < n; ++j) {
                a[i] += in.next();
            }
        }
        char[][] o = new char[2][n * n];
        for (int i = 0; i < n * n; ++i) o[0][i] = i % 2 == 0 ? '1' : '0';
        for (int i = 0; i < n * n; ++i) o[1][i] = i % 2 == 0 ? '0' : '1';
        int[][] best = new int[4][2];
        for (int i = 0; i < 4; ++i) {
            for (int j = 0; j < 2; ++j) {
                int cnt = 0;
                for (int k = 0; k < n * n; ++k) {
                    if (a[i].charAt(k) != o[j][k]) ++cnt;
                }
                best[i][j] = cnt;
            }
        }
        int res = Integer.MAX_VALUE;
        res = Math.min(res, best[0][0] + best[1][0] + best[2][1] + best[3][1]);
        res = Math.min(res, best[0][1] + best[1][1] + best[2][0] + best[3][0]);
        res = Math.min(res, best[0][1] + best[1][0] + best[2][1] + best[3][0]);
        res = Math.min(res, best[0][0] + best[1][1] + best[2][0] + best[3][1]);
        res = Math.min(res, best[0][0] + best[1][1] + best[2][1] + best[3][0]);
        res = Math.min(res, best[0][1] + best[1][0] + best[2][0] + best[3][1]);
        System.out.println(res);
    }
}