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.*;

import static java.lang.Math.*;

public class Edu41B {
    public static void main(String[] args) {
        FastScanner sc = new FastScanner();
        StringBuilder sb = new StringBuilder();
        int n = sc.nextInt();
        boolean[][][] boards = new boolean[4][n][n];
        for (int k = 0; k < 4; k++) {
            for (int row = 0; row < n; row++) {
                char[] line = sc.next().toCharArray();
                for (int col = 0; col < n; col++) {
                    if (line[col] == '1') {
                        boards[k][row][col] = true;
                    }
                }
            }
        }
        int[][] changes = new int[2][4]; //Color, board
        for (int k = 0; k < 4; k++) {
            //blacks on corners:
            for (int i = 0; i < n * n; i++) {
                if (boards[k][i/n][i%n] == (i%2 == 0)) {
                    changes[0][k]++;
                }
            }
            for (int i = 0; i < n * n; i++) {
                if (boards[k][i/n][i%n] == (i%2 == 1)) {
                    changes[1][k]++;
                }
            }
        }
        int min = Integer.MAX_VALUE/4;
        for (int i = 0; i < 4; i++) {
            for (int j = 0; j < 4; j++ ) {
                if (i != j) {
                    int change = 0;
                    for (int k = 0; k < 4; k++) {
                        if (k == j || k == i) {
                            change += changes[0][k];
                        } else {
                            change += changes[1][k];
                        }
                    }
                    min = min(min, change);
                }
            }
        }
        sb.append(min);


        System.out.print(sb);
    }

    public static class FastScanner {
        BufferedReader br;
        StringTokenizer st;

        public FastScanner(Reader in) {
            br = new BufferedReader(in);
        }

        public FastScanner() {
            this(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 readNextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }

        int[] readIntArray(int n) {
            int[] a = new int[n];
            for (int idx = 0; idx < n; idx++) {
                a[idx] = nextInt();
            }
            return a;
        }

        long[] readLongArray(int n) {
            long[] a = new long[n];
            for (int idx = 0; idx < n; idx++) {
                a[idx] = nextLong();
            }
            return a;
        }
    }
}
