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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.util.*;

public class contest {

    public static void main(String args[]) throws IOException {
        ContestReader reader = new ContestReader(System.in);
        int n  = reader.nextInt();
        int ans = 0;
        int[] temp = new int[4];
        int[][][] desk = new int[4][n][n];
        String line;
        for (int q = 0; q<4; q++) {
            for (int i = 0; i<n; i++) {
                line = reader.next();
                for (int j = 0; j < n; j++) {
                    desk[q][i][j] = Character.digit(line.charAt(j), 10);
                }
            }
            temp[q] = evaluateMain(desk[q]);
        }
        Arrays.sort(temp);
        ans = temp[0]+temp[1]+(n*n-temp[2])+(n*n-temp[3]);
        System.out.println(ans);
    }

    static int evaluateMain(int[][] matrix) {
        int res = 0;
        for (int i = 0; i<matrix.length; i++)
            for (int j = 0; j<matrix.length; j++)
                if (matrix[i][j]!=((i+j)%2))
                    res++;
        return res;
    }


}



class ContestReader {
    static BufferedReader reader;
    static StringTokenizer tokenizer;

    static void init(InputStream input) {
        reader = new BufferedReader(
                new InputStreamReader(input));
        tokenizer = new StringTokenizer("");
    }

    ContestReader(InputStream inpt) {
        init(inpt);
    }

    static String next() throws IOException {
        while (!tokenizer.hasMoreTokens()) {
            tokenizer = new StringTokenizer(
                    reader.readLine());
        }
        return tokenizer.nextToken();
    }

    static int nextInt() throws IOException {
        return Integer.parseInt(next());
    }
}