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.InputStreamReader;
import java.util.Scanner;
import java.util.StringTokenizer;

//UPSOLVE

public class Chessboard {

	public static void main(String[] args) throws IOException {
        Scanner sc = new Scanner(System.in);
		
		
		int n = sc.nextInt();
		int boards = 4;
		
		String[][] chessBoard = new String[4][n];
		
		for (int i = 0; i < boards; i++) {

			int j = 0;
			while (j < n) {
				String s = sc.next();
				if (s.length() == n) {
					chessBoard[i][j] = s;
					j++;
				}
			
			}
		}
		
		int n1 = n * n;

		int[] evens = new int[boards];
		int[] odds = new int[boards];

		for (int i = 0; i < boards; i++) {
			for (int j = 0; j < n; j++) {
				for (int jj = 0; jj < n; jj++) {
					int temp = j * n + jj;
					char c = chessBoard[i][j].charAt(jj);
					if ((temp % 2 == 1 && c == '1') || (temp % 2 == 0 && c == '0')){
						odds[i]++;
					}
				}
			}
			evens[i] = n1 - odds[i];
		}
		
		int start = Integer.MAX_VALUE;
		 
		int step1 = Math.min(start, evens[0] + evens[1] + odds[2] + odds[3]);
		int step2 = Math.min(step1, evens[0] + evens[2] + odds[1] + odds[3]);
		int step3 = Math.min(step2, evens[0] + evens[3] + odds[1] + odds[2]);
		int step4 = Math.min(step3, evens[1] + evens[2] + odds[0] + odds[3]);
		int step5 = Math.min(step4, evens[1] + evens[3] + odds[0] + odds[2]);
		int answer = Math.min(step5, evens[2] + evens[3] + odds[0] + odds[1]);

		System.out.println(answer);

	}

}
