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.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.StringTokenizer;

public class C {
static int convert (char [][]a,int x)
{
	int n=a.length;
	int ans=0;
	for(int i=0;i<n;i++)
		for(int j=0;j<n;j++)
		{
			if(a[i][j]-'0'!=x)
				ans++;
			x=1-x;
		}
	return ans;
}
	public static void main(String[] args) throws IOException {
		Scanner sc=new Scanner(System.in);
		PrintWriter pw=new PrintWriter(System.out);
		int n=sc.nextInt();
		int []ones=new int [4],zeroes=new int [4];
		for(int rep=0;rep<4;rep++)
		{
			char [][]a=new char[n][n];
			for(int i=0;i<n;i++)
				a[i]=sc.nextLine().toCharArray();
			sc.nextLine();
			ones[rep]=convert(a,1);
			zeroes[rep]=convert(a,0);
		}
		
		int other=0;
		for(int x:zeroes)
			other+=x;
		int ans=4*n*n;
		for(int i=0;i<4;i++)
			for(int j=i+1;j<4;j++)
			{
				int s=other;
				s+=ones[i]+ones[j];
				s=s-(zeroes[i]+zeroes[j]);
				ans=Math.min(ans, s);
			}
		
		
		pw.println(ans);
		pw.close();

	}
	static class Scanner
	{
		BufferedReader br;
		StringTokenizer st;
		public Scanner(InputStream s)
		{
			br=new BufferedReader(new InputStreamReader(s));
		}
		public String nextLine() throws IOException
		{
			return br.readLine();
		}
		public String next() throws IOException
		{
			while(st==null || !st.hasMoreTokens())
				st=new StringTokenizer(br.readLine());
			return st.nextToken();
		}
		public int nextInt() throws IOException
		{
			return Integer.parseInt(next());
			
		}
		public double nextDouble() throws IOException
		{
			return Double.parseDouble(next());
		}
		public boolean ready() throws IOException
		{
			return br.ready();
		}
		public long nextLong() throws IOException
		{
			return Long.parseLong(next());
		}
	}
}
