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.OutputStream;
import java.io.PrintWriter;
import java.io.BufferedWriter;
import java.util.InputMismatchException;
import java.io.IOException;
import java.util.ArrayList;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.io.InputStream;

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

    static class TaskC {
        ArrayList<String> list = new ArrayList<>(24);

        public void solve(int testNumber, InputReader in, OutputWriter out) {
            int n = in.nextInt();
            int m = 2 * n;
            int[][][] a = new int[4][n][n];
            int[][] b = new int[m][m];

            for (int i = 0; i < 4; i++) {
                for (int j = 0; j < n; j++) {
                    String s = in.nextString();
                    for (int k = 0; k < n; k++) {
                        if (s.charAt(k) == '0')
                            a[i][j][k] = 0;
                        else
                            a[i][j][k] = 1;
                    }
                }
            }

            int[][] c = new int[m][m];
            int[][] d = new int[m][m];
            for (int i = 0; i < m; i++) {
                int st;
                if (i % 2 == 0) {
                    st = 0;
                } else {
                    st = 1;
                }
                for (int j = 0; j < m; j++) {
                    if (j % 2 == 0) {
                        c[i][j] = st;
                        d[i][j] = 1 - st;
                    } else {
                        c[i][j] = 1 - st;
                        d[i][j] = st;
                    }
                }
            }
        /*
        for (int i = 0; i < m; i++) {
            for (int j = 0; j < m; j++) {
                out.print(c[i][j]);
            }
            out.println();
        }
        out.println();
        for (int i = 0; i < m; i++) {
            for (int j = 0; j < m; j++) {
                out.print(d[i][j]);
            }
            out.println();
        }*/

            int min = Integer.MAX_VALUE;
            permutation("0123");
            for (int k = 0; k < 24; k++) {
                String s = list.get(k);

                for (int i = 0; i < n; i++) {
                    for (int j = 0; j < n; j++) {
                        b[i][j] = a[s.charAt(0) - '0'][i][j];
                    }
                }

                for (int i = 0; i < n; i++) {
                    for (int j = 0; j < n; j++) {
                        b[i][j + n] = a[s.charAt(1) - '0'][i][j];
                    }
                }

                for (int i = 0; i < n; i++) {
                    for (int j = 0; j < n; j++) {
                        b[i + n][j] = a[s.charAt(2) - '0'][i][j];
                    }
                }

                for (int i = 0; i < n; i++) {
                    for (int j = 0; j < n; j++) {
                        b[i + n][j + n] = a[s.charAt(3) - '0'][i][j];
                    }
                }

                int t = 0;
                int x = 0;
                int y = 0;
                for (int i = 0; i < m; i++) {
                    for (int j = 0; j < m; j++) {
                        if (b[i][j] != c[i][j]) {
                            x++;
                        }
                        if (b[i][j] != d[i][j]) {
                            y++;
                        }
                    }
                }
                t = Math.min(x, y);
                min = Math.min(min, t);
            }
            out.println(min);
        }

        void permutation(String str) {
            permutation("", str);
        }

        void permutation(String prefix, String str) {
            int n = str.length();
            if (n == 0) {
                list.add(prefix);
            } else {
                for (int i = 0; i < n; i++)
                    permutation(prefix + str.charAt(i), str.substring(0, i) + str.substring(i + 1, n));
            }
        }

    }

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private InputReader.SpaceCharFilter filter;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public int read() {
            if (numChars == -1) {
                throw new InputMismatchException();
            }
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0) {
                    return -1;
                }
            }
            return buf[curChar++];
        }

        public int nextInt() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public String nextString() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            StringBuilder res = new StringBuilder();
            do {
                if (Character.isValidCodePoint(c)) {
                    res.appendCodePoint(c);
                }
                c = read();
            } while (!isSpaceChar(c));
            return res.toString();
        }

        public boolean isSpaceChar(int c) {
            if (filter != null) {
                return filter.isSpaceChar(c);
            }
            return isWhitespace(c);
        }

        public static boolean isWhitespace(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);

        }

    }

    static class OutputWriter {
        private final PrintWriter writer;

        public OutputWriter(OutputStream outputStream) {
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
        }

        public OutputWriter(Writer writer) {
            this.writer = new PrintWriter(writer);
        }

        public void close() {
            writer.close();
        }

        public void println(int i) {
            writer.println(i);
        }

    }
}

