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 C41 {
    public static void main(String[] args) {
        MyScanner sc = new MyScanner();
        PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out));
        int n = sc.nextInt();
        int [][][] a = new int[4][n][n];
        for (int g = 0; g< 4; g++) {
            for (int i = 0; i < n; i++) {
                String s = sc.next();
                for (int j = 0; j < n; j++) a[g][i][j] = s.charAt(j) - '0';
            }
        }
        long best = Integer.MAX_VALUE;
        for (int i = 0; i < 4; i++) {
            for (int j = 0; j < 4; j++) {
                if (i == j) continue;
                for (int k = 0; k < 4; k++) {
                    if (j == k || k == i) continue;
                    for (int m = 0; m < 4; m++) {
                        if (m == j || m ==k || m == i) continue;
                        int [] map = new int[]{i, j, k, m};

                        for (int type = 0; type <= 1; type++) {
                            int ct = 0;
                            for (int r = 0; r < n; r++) {
                                for (int c = 0; c < n; c++) {
                                    int here = ((r + c) % 2 == 0 ? type : 1 - type);
                                    if (a[map[0]][r][c] != here) ct++;
                                }
                            }
                            for (int r = 0; r < n; r++) {
                                for (int c = 0; c < n; c++) {
                                    int here = ((r + c) % 2 == 0 ? 1 - type : type);
                                    if (a[map[1]][r][c] != here) ct++;
                                }
                            }
                            for (int r = 0; r < n; r++) {
                                for (int c = 0; c < n; c++) {
                                    int here = ((r + c) % 2 == 0 ? 1 - type : type);
                                    if (a[map[2]][r][c] != here) ct++;
                                }
                            }
                            for (int r = 0; r < n; r++) {
                                for (int c = 0; c < n; c++) {
                                    int here = ((r + c) % 2 == 0 ? type : 1 - type);
                                    if (a[map[3]][r][c] != here) ct++;
                                }
                            }
                            best = Math.min(best, ct);
                        }
                    }
                }
            }
        }
        out.println(best);
        out.close();
    }


    //-----------MyScanner class for faster input----------
    public static class MyScanner {
        BufferedReader br;
        StringTokenizer st;

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

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

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

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

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

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }


    }

}