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.Arrays;
import java.util.Scanner;

public class Solution {
    private static int minColoring(int n, int[][][] boards) {
        int[][] defects = new int[2][4];
        for (int board = 0; board < 4; board++)
            for (int i = 0; i < n; i++)
                for (int j = 0; j < n; j++)
                    defects[((i ^ j) & 1) ^ boards[board][i][j]][board]++;
        int total = 0;
        int[] diff = new int[4];
        for (int board = 0; board < 4; board++) {
            total += defects[0][board];
            diff[board] = defects[1][board] - defects[0][board];
        }
        Arrays.sort(diff);
        total += diff[0] + diff[1];
        return total;
    }

    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int n = in.nextInt();
        int[][][] boards = new int[4][n][n];
        for (int board = 0; board < 4; board++) {
            for (int i = 0; i < n; i++) {
                String s = in.next();
                for (int j = 0; j < n; j++) boards[board][i][j] = s.charAt(j) - '0';
            }
        }
        int result = minColoring(n, boards);
        System.out.println(result);
    }
}
