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.*;
import java.math.*;
import java.lang.*;
 
import static java.lang.Math.*;

public class Main implements Runnable {
    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private SpaceCharFilter filter;
        private BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

        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 String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            }
            catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
        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 long nextLong() {
            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 double nextDouble() {
            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, nextInt());
                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, nextInt());
                    if (c < '0' || c > '9')
                        throw new InputMismatchException();
                    m /= 10;
                    res += (c - '0') * m;
                    c = read();
                }
            }
            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 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);
        }
    }
    public static void main(String args[]) throws Exception {
        new Thread(null, new Main(),"Main",1<<26).start();
    }
    public void run() {
        InputReader sc = new InputReader(System.in);
        PrintWriter w = new PrintWriter(System.out);

        int n = sc.nextInt();
        
        int cost[][] = new int[4][2];

        int checkMat[][][] = new int[2][n][n];

        for(int i = 0; i < n; ++i) {
            for(int j = 0; j < n; ++j) {
                if(i == 0 && j == 0)
                    checkMat[0][i][j] = 0;
                else if(j == 0)
                    checkMat[0][i][j] = checkMat[0][i - 1][j] ^ 1;
                else
                    checkMat[0][i][j] = checkMat[0][i][j - 1] ^ 1;
            }
        }
        for(int i = 0; i < n; ++i) {
            for(int j = 0; j < n; ++j) {
                if(i == 0 && j == 0)
                    checkMat[1][i][j] = 1;
                else if(j == 0)
                    checkMat[1][i][j] = checkMat[1][i - 1][j] ^ 1;
                else
                    checkMat[1][i][j] = checkMat[1][i][j - 1] ^ 1;
            }
        }

        for(int i = 0; i < 4; ++i) {
            char mat2[][] = new char[n][n];
            int mat[][] = new int[n][n];
            for(int k = 0; k < n; ++k) {
                mat2[k] = sc.next().toCharArray();
                for(int j = 0; j < n; ++j) {
                    if(mat2[k][j] == '1')
                        mat[k][j] = 1;
                    if(mat[k][j] != checkMat[0][k][j])
                        cost[i][0]++;
                    if(mat[k][j] != checkMat[1][k][j])
                        cost[i][1]++;
                }
            }
        }

        int ans = Integer.MAX_VALUE;
        for(int i = 0; i < 4; ++i) {
            for(int j = 0; j < 4; ++j) {
                for(int k = 0; k < 4; ++k) {
                    for(int l = 0; l < 4; ++l) {
                        HashMap<Integer, Integer> map = new HashMap<>();
                        map.put(i, 1);
                        map.put(j, 1);
                        map.put(k, 1);
                        map.put(l, 1);
                        if(map.size() != 4)
                            continue;
                        int cans = cost[i][0] + cost[j][0] + cost[k][1] + cost[l][1];
                        ans = min(ans, cans);
                    }
                }
            }
        }

        w.print(ans);

        w.close();      
    }
}