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.util.*;
public class C961 {
	public static void main(String[] args) {
		Scanner in = new Scanner(System.in);
		int n = in.nextInt(), wFix[] = new int[4], bFix[] = new int[4];
		char arr[][][] = new char[4][n][n];
		
		for(int i=0; i<4; i++)
			for(int j=0; j<n; j++)
				arr[i][j] = in.next().toCharArray();
		
		for(int i=0; i<4; i++)
		{
			wFix[i] = calc_w_fix(arr[i], n);
			bFix[i] = calc_b_fix(arr[i], n);
		}
		
		Arrays.sort(wFix);
		Arrays.sort(bFix);
		
		System.out.println(wFix[0] + wFix[1] + bFix[0] + bFix[1]);
	}
	
	public static int calc_w_fix(char arr[][], int n)
	{
		int count = 0;
		for(int i=0; i<n; i++)
			for(int j=0; j<n; j++)
				if(((i+j)%2 == 0 && arr[i][j] == '1') || ((i+j)%2 == 1 && arr[i][j] == '0'))
					count++;	
		
		return count;
	}
	
	public static int calc_b_fix(char arr[][], int n)
	{
		int count = 0;
		for(int i=0; i<n; i++)
			for(int j=0; j<n; j++)
				if(((i+j)%2 == 1 && arr[i][j] == '1') || ((i+j)%2 == 0 && arr[i][j] == '0'))
					count++;
			
		return count;
	}
}
