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.BufferedReader;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.Scanner;
import java.util.StringTokenizer;

public class P961C
{
	public static void main(String[] args)
	{
		Scanner scan = new Scanner(System.in);
		int n = scan.nextInt();
		int[][][] color = new int[4][n][n];
		for (int k = 0; k < 4; k++)
		{
			for (int i = 0; i < n; i++)
			{
				char[] row = scan.next().toCharArray();
				for (int j = 0; j < n; j++)
				{
					color[k][i][j] = row[j]-'0';
				}
			}
		}
		int min = 999999;
		for (int a = 0; a < 4; a++)
		{
			for (int b = 0; b < 4; b++)
			{
				if (b == a)
					continue;
				for (int c = 0; c < 4; c++)
				{
					if (c == a || c == b)
						continue;
					for (int d = 0; d < 4; d++)
					{
						if (d == a || d == b || d == c)
							continue;
						int ops = 0;
						ops += flips(color[a], 1);
						ops += flips(color[b], 0);
						ops += flips(color[c], 1);
						ops += flips(color[d], 0);
						min = Math.min(min, ops);
					}
				}
			}
		}
		System.out.println(min);
	}
	private static int flips(int[][] color, int start)
	{
		int f = 0;
		for (int i = 0; i < color.length; i++)
		{
			for (int j = 0; j < color[0].length; j++)
			{
				if (color[i][j] != (i+j+start) % 2)
					f++;
			}
		}
		return f;
	}
	static class FastScanner
	{
		BufferedReader br;
		StringTokenizer st;

		public FastScanner()
		{
			try
			{
				br = new BufferedReader(new InputStreamReader(System.in));
				st = new StringTokenizer(br.readLine());
			} catch (Exception e)
			{
				e.printStackTrace();
			}
		}

		public String next()
		{
			if (st.hasMoreTokens())
				return st.nextToken();
			try
			{
				st = new StringTokenizer(br.readLine());
			} catch (Exception e)
			{
				e.printStackTrace();
			}
			return st.nextToken();
		}

		public int nextInt()
		{
			return Integer.parseInt(next());
		}

		public long nextLong()
		{
			return Long.parseLong(next());
		}

		public String nextLine()
		{
			String line = "";
			try
			{
				line = br.readLine();
			} catch (Exception e)
			{
				e.printStackTrace();
			}
			return line;
		}
	}
}
