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.*;
import java.util.Arrays;
import java.util.InputMismatchException;
import java.util.Scanner;

/*
        CODE WRITTEN BY RITWIK SHANKER
*/
public class C41
{
    public static void main(String[] args) throws Exception
    {
        InputReader in = new InputReader(System.in);
        OutputWriter out = new OutputWriter(System.out);
        Scanner scn=new Scanner(System.in);
        int n = in.readInt();
        //out.printLine(n);
        int chet[] = new int[4];
        for (int i = 0; i < 4; i++)
        {
            for (int j = 0; j < n; j++)
            {
                String s=in.readString();
                for (int k = 0; k < n; k++)
                {
                    char a =  s.charAt(k);
                    //out.printLine(a);
                    if (j % 2 == 0)
                    {
                        if (k % 2 == 0)
                        {
                            if (a == '1')
                            {
                                continue;
                            }
                            else
                            {
                                chet[i]++;
                            }
                        }
                        else
                        {
                            if (a == '0')
                            {
                                continue;
                            }
                            else
                            {
                                chet[i]++;
                            }
                        }
                    }
                    else
                    {
                        if (k % 2 == 0)
                        {
                            if (a == '0')
                            {
                                continue;
                            }
                            else
                            {
                                chet[i]++;
                            }
                        }
                        else
                        {
                            if (a == '1')
                            {
                                continue;
                            }
                            else
                            {
                                chet[i]++;
                            }
                        }
                    }
                }
            }
        }
        Arrays.sort(chet);
        long a = Long.MAX_VALUE;
        for (int i = 0; i < 4; i++)
        {
            for (int j = 0; j < 4; j++)
            {
                long answer;
                if (i != j)
                {
                    answer = chet[i] + chet[j];
                    for (int k = 0; k < 4; k++)
                    {
                        if (k != i && k != j)
                        {
                            answer += (n * n - chet[k]);
                        }
                    }
                    a = Math.min(a, answer);
                }
            }
        }
        out.printLine(a);
    }

    //FAST IO
    private static class InputReader
    {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private 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 readInt()
        {
            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 readString()
        {
            int c = read();
            while (isSpaceChar(c))
            {
                c = read();
            }
            StringBuilder res = new StringBuilder();
            do
            {
                res.appendCodePoint(c);
                c = read();
            } while (!isSpaceChar(c));
            return res.toString();
        }

        public double readDouble()
        {
            int c = read();
            while (isSpaceChar(c))
            {
                c = read();
            }
            int sgn = 1;
            if (c == '-')
            {
                sgn = -1;
                c = read();
            }
            double res = 0;
            while (!isSpaceChar(c) && c != '.')
            {
                if (c == 'e' || c == 'E')
                {
                    return res * Math.pow(10, readInt());
                }
                if (c < '0' || c > '9')
                {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            }
            if (c == '.')
            {
                c = read();
                double m = 1;
                while (!isSpaceChar(c))
                {
                    if (c == 'e' || c == 'E')
                    {
                        return res * Math.pow(10, readInt());
                    }
                    if (c < '0' || c > '9')
                    {
                        throw new InputMismatchException();
                    }
                    m /= 10;
                    res += (c - '0') * m;
                    c = read();
                }
            }
            return res * sgn;
        }

        public long readLong()
        {
            int c = read();
            while (isSpaceChar(c))
            {
                c = read();
            }
            int sgn = 1;
            if (c == '-')
            {
                sgn = -1;
                c = read();
            }
            long 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 boolean isSpaceChar(int c)
        {
            if (filter != null)
            {
                return filter.isSpaceChar(c);
            }
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public String next()
        {
            return readString();
        }

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

    private 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 print(Object... objects)
        {
            for (int i = 0; i < objects.length; i++)
            {
                if (i != 0)
                {
                    writer.print(' ');
                }
                writer.print(objects[i]);
            }
            writer.flush();
        }

        public void printLine(Object... objects)
        {
            print(objects);
            writer.println();
            writer.flush();
        }

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

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