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.util.stream.IntStream;
import java.util.Arrays;
import java.io.BufferedWriter;
import java.util.InputMismatchException;
import java.io.IOException;
import java.util.stream.Collectors;
import java.util.ArrayList;
import java.util.List;
import java.util.stream.Stream;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author dmytro.prytula prituladima@gmail.com
 */
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);
        LSHahmatnayaDoska solver = new LSHahmatnayaDoska();
        solver.solve(1, in, out);
        out.close();
    }

    static class LSHahmatnayaDoska {
        int n;
        int ans = 0;
        int INF = Integer.MAX_VALUE;
        int[] a;
        List<List<Integer>> perm = new ArrayList<>();

        public void solve(int testNumber, InputReader in, OutputWriter out) {
            n = in.nextInt();
            int[][][] M = new int[4][n][n];
            for (int k = 0; k < 4; k++) {
                for (int i = 0; i < n; i++) {
                    for (int j = 0; j < n; j++) {
                        M[k][i][j] += in.readCharacter() == '1' ? 1 : 0;
                    }
                }
            }
            a = new int[]{0, 1, 2, 3};
            permute(a, 0, a.length - 1);
            ans = INF;
            for (List<Integer> order : perm) {
                int cur = 0;
                for (int i1 = 0; i1 < order.size(); i1++) {
                    int k = order.get(i1);
                    for (int i = 0; i < n; i++) {
                        for (int j = 0; j < n; j++) {
                            if (i1 == 0 || i1 == 2) {
                                if ((i + j) % 2 == 0 && M[k][i][j] == 0)
                                    cur++;
                                if ((i + j) % 2 == 1 && M[k][i][j] == 1)
                                    cur++;
                            } else {
                                if ((i + j) % 2 == 0 && M[k][i][j] == 1)
                                    cur++;
                                if ((i + j) % 2 == 1 && M[k][i][j] == 0)
                                    cur++;
                            }
                        }
                    }
                }


                ans = Math.min(ans, cur);
            }

            out.printLine(ans);
        }

        void permute(int[] a, int l, int r) {
            int i;
            if (l == r)
                perm.add(Arrays.stream(a).boxed().collect(Collectors.toList()));
            else {
                for (i = l; i <= r; i++) {
                    swap(a, l, i);
                    permute(a, l + 1, r);
                    swap(a, l, i); //backtrack
                }
            }
        }

        void swap(int[] a, int i, int j) {
            int temp;
            temp = a[i];
            a[i] = a[j];
            a[j] = temp;
        }

    }

    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 OutputWriter printLine(int i) {
            writer.println(i);
            return this;
        }

    }

    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;
        }

        private 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;
        }

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

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

        public char readCharacter() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            return (char) c;
        }

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

        }

    }
}

