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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.StringTokenizer;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        ProblemCChessboard solver = new ProblemCChessboard();
        solver.solve(1, in, out);
        out.close();
    }

    static class ProblemCChessboard {
        int n;
        int[][] choices;
        final int oo = (int) 1e9;

        int dp(int ind, int choice1, int choice2) {
            if (ind == 4) return choice1 == choice2 ? 0 : oo;
            int a = choices[0][ind] + dp(ind + 1, choice1 + 1, choice2);
            int b = choices[1][ind] + dp(ind + 1, choice1, choice2 + 1);
            return Math.min(a, b);
        }

        public void solve(int testNumber, InputReader in, PrintWriter out) {
            n = in.nextInt();
            choices = new int[2][4];
            boolean[][][] grids = new boolean[2][n][n];
            for (int i = 0; i < 2; ++i) {
                boolean[][] grid = new boolean[n][n];
                boolean parity = i % 2 == 0;
                for (int a = 0; a < n; ++a) {
                    for (int b = 0; b < n; ++b) {
                        grid[a][b] = parity;
                        parity = !parity;
                    }
                }
                grids[i] = grid;
            }
            for (int i = 0; i < 4; ++i) {
                boolean[][] grid = new boolean[n][n];
                for (int a = 0; a < n; ++a) {
                    String line = in.next();
                    for (int b = 0; b < n; ++b) {
                        grid[a][b] = line.charAt(b) == '1';
                    }
                }
                int choice1 = 0;
                for (int a = 0; a < n; ++a) {
                    for (int b = 0; b < n; ++b) {
                        if (grid[a][b] != grids[0][a][b]) ++choice1;
                    }
                }
                int choice2 = 0;
                for (int a = 0; a < n; ++a) {
                    for (int b = 0; b < n; ++b) {
                        if (grid[a][b] != grids[1][a][b]) ++choice2;
                    }
                }
                choices[0][i] = choice1;
                choices[1][i] = choice2;
            }
            out.println(dp(0, 0, 0));
        }

    }

    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());
        }

    }
}

