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 Main {
    public static void main(String args[]) {
        InputReader in = new InputReader(System.in);
        PrintWriter out = new PrintWriter(System.out);
        Task solver = new Task();
        solver.solve(in, out);
        out.close();
    }

    static class Task {
        char[][] f;
        char[][][] c;
        int[] a;
        boolean[] used;
        int n;
        int ans = (int) 1e9;

        public void solve(InputReader in, PrintWriter out) {
            n = in.nextInt();
            used = new boolean[4];
            a = new int[4];
            c = new char[4][n][n];
            f = new char[2 * n][2 * n];

            for (int num = 0; num < 4; ++num) {
                for (int i = 0; i < n; ++i) {
                    String t = in.next();
                    for (int j = 0; j < n; ++j) {
                        c[num][i][j] = t.charAt(j);
                    }
                }
            }
            rec(0);
            out.println(ans);
        }

        private void rec(int l) {
            if (l == 4) {
                updateAns();
                return;
            }
            for (int p = 0; p < 4; ++p) {
                if (!used[p]) {
                    a[l] = p;
                    used[p] = true;
                    rec(l + 1);
                    used[p] = false;
                }
            }
        }

        private void updateAns() {
            int iAdd = 0;
            int jAdd = 0;
            for (int t = 0; t < 4; ++t) {
                int num = a[t];
                for (int i = 0; i < n; ++i) {
                    for (int j = 0; j < n; ++j) {
                        f[i + iAdd][j + jAdd] = c[num][i][j];
                    }
                }
                if (t == 0) jAdd += n;
                if (t == 1) { iAdd += n; jAdd = 0; }
                if (t == 2) jAdd += n;
            }
            int cnt = 0;
            for (int i = 0; i < 2 * n; ++i) {
                for (int j = 0; j < 2 * n; ++j) {
                    char x = (char) ((i + j) % 2 + '0');
                    if (x != f[i][j]) ++cnt;
                }
            }
            ans = Math.min(ans, Math.min(cnt, 4 * n * n - cnt));
        }
    }

    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }
    }
}