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.Scanner;

public class CF3 {

	public static void main(String[] args) {
		Scanner scanner = new Scanner(System.in);
		int N = scanner.nextInt();
		int BOARDS = 4;
		String[][] board = new String[4][N];
		for (int i = 0; i < BOARDS; i++) {
			int j = 0;
			while (j < N) {
				String s = scanner.nextLine();
				if (s.length() == N) {
					board[i][j] = s;
					j++;
				}
			}
		}
		
		int N2 = N * N;

		int[] EVEN = new int[BOARDS];
		int[] ODD = 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 k = j * N + jj;
					char c = board[i][j].charAt(jj);
					if ((k%2==1 && c=='1') || (k%2==0 && c=='0'))
						ODD[i]++;
				}
			}
			EVEN[i] = N2-ODD[i];
		}
		
		int MIN = Integer.MAX_VALUE;
		
		MIN = Math.min(MIN, EVEN[0]+EVEN[1]+ODD[2]+ODD[3]);
		MIN = Math.min(MIN, EVEN[0]+EVEN[2]+ODD[1]+ODD[3]);
		MIN = Math.min(MIN, EVEN[0]+EVEN[3]+ODD[1]+ODD[2]);
		MIN = Math.min(MIN, EVEN[1]+EVEN[2]+ODD[0]+ODD[3]);
		MIN = Math.min(MIN, EVEN[1]+EVEN[3]+ODD[0]+ODD[2]);
		MIN = Math.min(MIN, EVEN[2]+EVEN[3]+ODD[0]+ODD[1]);

		System.out.println(MIN);
		
	}

}
