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 codeforces {
    public static void main(String[] args){
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int[] arr = new int[8];
        char c='0';
        int ans=0;
        for (int k=0;k<4;k++) {
            for (int i = 0; i < n; i++) {
                String t = sc.next();
                for (int j = 0; j < n; j++) {
                    if (t.charAt(j) == c) {
                        ans++;
                    }
                    if (c == '0') c = '1';
                    else c = '0';
                }
            }
            arr[k]=ans;
            arr[k+4]=n*n-ans;
            ans=0;
            c='0';
        }
        ans = Math.min(arr[0]+arr[1]+arr[6]+arr[7],arr[0]+arr[2]+arr[5]+arr[7]);
        ans = Math.min(ans,arr[0]+arr[3]+arr[5]+arr[6]);
        ans = Math.min(ans,arr[1]+arr[2]+arr[4]+arr[7]);
        ans = Math.min(ans,arr[1]+arr[3]+arr[4]+arr[6]);
        ans = Math.min(ans,arr[2]+arr[3]+arr[4]+arr[5]);
        System.out.print(ans);
    }
}
