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.FileNotFoundException;
import java.io.FileReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.io.UnsupportedEncodingException;
import java.util.StringTokenizer;

public class Main {

    public static void main(String[] args) throws UnsupportedEncodingException, IOException, Exception {
        Reader.init(System.in);
        StringBuilder out = new StringBuilder();
        int n = Reader.nextInt();
        String str;
        boolean b[][][] = new boolean[4][n][n];
        for(int k = 0, i, j; k < 4; k++)
            for(i = 0; i < n; i++) {
                str = Reader.next();
                for(j = 0; j < n; j++)
                    b[k][i][j] = str.charAt(j) == '1';
            }
        int[][] min = new int[4][2];
        for(int i = 0; i < 4; i++) {
            min[i][0] = calc(b[i], false);
            min[i][1] = calc(b[i], true);
        }
        int mn = Integer.MAX_VALUE;
        for(int i = 0, j, k, l; i < 4; i++)
            for(j = 0; j < 4; j++)
                for(k = 0; k < 4; k++)
                    for(l = 0; l < 4; l++)
                        if(check(i, j, k, l))
                            mn = Math.min(mn, min[i][0] + min[j][0] + min[k][1] + min[l][1]);
        out.append(mn).append('\n');
        PrintWriter pw = new PrintWriter(System.out);
        pw.print(out);
        pw.close();
    }
    
    static boolean check(int i, int j, int k, int l) {
        return i != j && i != k && i != l && j != k && j != l && k != l;
    }
    
    static int calc(boolean[][] b, boolean s) {
        int cnt = 0;
        for(int i = 0, j; i < b.length; i++)
            for(j = 0; j < b[i].length; j++) {
                if(b[i][j] != s)
                    cnt++;
                s = !s;
            }
        return cnt;
    }

}

class Reader {

    static BufferedReader reader;
    static StringTokenizer tokenizer;

    static void init(InputStream input) throws UnsupportedEncodingException {
        reader = new BufferedReader(
                new InputStreamReader(input, "UTF-8"));
        tokenizer = new StringTokenizer("");
    }

    static void init(String url) throws FileNotFoundException {
        reader = new BufferedReader(new FileReader(url));
        tokenizer = new StringTokenizer("");
    }

    static String next() throws IOException {
        while (!tokenizer.hasMoreTokens()) {
            //TODO add check for eof if necessary
            tokenizer = new StringTokenizer(
                    reader.readLine());
        }
        return tokenizer.nextToken();
    }

    static String nextLine() throws IOException {
        return reader.readLine();
    }

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

    static double nextDouble() throws IOException {
        return Double.parseDouble(next());
    }

    static long nextLong() throws IOException {
        return Long.parseLong(next());
    }
}