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.IOException;
import java.io.InputStream;
import java.util.InputMismatchException;

public class A {
	public static int getScore(int[][] mat, int N, boolean parity){
		int total = 0;
		for(int i = 0; i<N; i++){
			for(int j = 0; j<N; j++){
				if(parity && (i + j) % 2 == mat[i][j]) total++;
				if(!parity && (i + j) % 2 != mat[i][j]) total++;
			}
		}
		return total;
	}
	
	public static void main(String[] args) {
		FastScannerA sc = new FastScannerA(System.in);

		int N = sc.nextInt();
		
		int[][][] arr = new int[4][N][N];
		for(int k = 0; k < 4; k++){
			for(int i = 0; i < N; i++){
				String line = sc.next();
				for(int j = 0; j < N; j++){
					arr[k][i][j] = line.charAt(j) - '0';
				}
			}
		}
		
		int[][] table = new int[2][4];
		for(int i = 0; i < 4; i++) table[0][i] = getScore(arr[i], N, true);
		for(int i = 0; i < 4; i++) table[1][i] = getScore(arr[i], N, false);
		
//		for(int i = 0; i<2; i++){
//			for(int j = 0; j<4; j++){
//				System.out.print(table[i][j] + " ");
//			}
//			System.out.println();
//		}
		
		// calculate result
		int[] sums = new int[6];
		sums[0] = table[0][0] + table[0][1] + table[1][2] + table[1][3];
		sums[1] = table[0][0] + table[1][1] + table[0][2] + table[1][3];
		sums[2] = table[0][0] + table[1][1] + table[1][2] + table[0][3];
		sums[3] = table[1][0] + table[0][1] + table[1][2] + table[0][3];
		sums[4] = table[1][0] + table[0][1] + table[0][2] + table[1][3];
		sums[5] = table[1][0] + table[1][1] + table[0][2] + table[0][3];
		
		int min = Integer.MAX_VALUE;
		for(int i = 0; i < 6; i++) min = Math.min(min, sums[i]);
		System.out.println(min);
	}
}

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

    public FastScannerA(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 next()
    {
        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 String nextLine()
    {
        int c = read();
        StringBuilder res = new StringBuilder();
        do
        {
            res.appendCodePoint(c);
            c = read();
        } while (!isLineEndChar(c));
        return res.toString();
    }    
    
    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 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 boolean isSpaceChar(int c)
    {
        if (filter != null)
            return filter.isSpaceChar(c);
        return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
    }
    
    public boolean isLineEndChar(int c)
    {
        if (filter != null)
            return filter.isSpaceChar(c);
        return c == '\n' || c == '\r' || c == -1;
    }

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