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.*;
import java.io.*;

public class Solution2 {
    private final int BLACK = 1;
    private final int WHITE = 0;

    private void solve() throws IOException {
        int[][] permutations = { { 1, 2, 3, 4},  { 1, 2, 4, 3}, { 1, 3, 2, 4}, { 1, 3, 4, 2}, { 1, 4, 2, 3}, { 1, 4, 3, 2},
                {2, 1, 3, 4}, {2, 1, 4, 3}, {2, 3, 1, 4}, {2, 3, 4, 1}, {2, 4, 1, 3}, {2, 4, 3, 1},
                {3, 1, 2, 4}, {3, 1, 4, 2}, {3, 2, 1, 4}, {3, 2, 4, 1}, {3, 4, 1, 2}, {3, 4, 2, 1},
                {4, 1, 2, 3}, {4, 1, 3, 2}, {4, 2, 1, 3}, {4, 2, 3, 1}, {4, 3, 1, 2}, {4, 3, 2, 1}
        };
        int n = in.nextInt();
        int[][][] parts = new int[4][n][n];
        for (int i = 0; i < 4; i++) {
            for (int j = 0; j < n; j++) {
                String s = in.next();
                for (int k = 0; k < n; k++) {
                    if (s.charAt(k) == '1') {
                        parts[i][j][k] = BLACK;
                    }
                    else {
                        parts[i][j][k] = WHITE;
                    }
                }
            }
        }
        int ans = Integer.MAX_VALUE;
        for (int i = 0; i < 2; i++) {
            for (int[] permutation : permutations) {
                int recolour = 0;
                int j = 0;
                for (int k : permutation) {
                    int color = (j == 0 || j == 3) ? i : (n % 2 == 1) ? (i + 1) % 2 : i;
                    for (int l = 0; l < n; l++) {
                        for (int m = 0; m < n; m++) {
                            if (parts[k - 1][l][m] == (l + m + (color + 1) % 2) % 2) {
                                recolour++;
                            }
                        }
                    }
                    j++;
                }
                ans = Math.min(ans, recolour);
            }
        }
        System.out.println(ans);
    }

    private PrintWriter out;
    private MyScanner in;

    private void run() throws IOException {
        in = new MyScanner();
        out = new PrintWriter(System.out);
        solve();
        in.close();
        out.close();
    }

    private class MyScanner {
        private BufferedReader br;
        private StringTokenizer st;

        public MyScanner() throws IOException {
            this.br = new BufferedReader(new InputStreamReader(System.in));
        }

        public MyScanner(String fileTitle) throws IOException {
            this.br = new BufferedReader(new FileReader(fileTitle));
        }

        public String nextLine() throws IOException {
            String s = br.readLine();
            return s == null ? "-1" : s;
        }

        public String next() throws IOException {
            while (st == null || !st.hasMoreTokens()) {
                String s = br.readLine();
                if (s == null) {
                    return "-1";
                }
                st = new StringTokenizer(s);
            }
            return st.nextToken();
        }

        public Integer nextInt() throws IOException {
            return Integer.parseInt(this.next());
        }

        public Long nextLong() throws IOException {
            return Long.parseLong(this.next());
        }

        public Double nextDouble() throws IOException {
            return Double.parseDouble(this.next());
        }

        public void close() throws IOException {
            this.br.close();
        }
    }

    public static void main(String[] args) throws IOException {
        Locale.setDefault(Locale.US);
        new Solution2().run();
    }
}
