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 Solution {
	public static void main(String[] args){
		Solution solution = new Solution();
		solution.solve();
	}

	private void solve() {
		Scanner in = new Scanner(System.in);

		int n = in.nextInt();
		String[][] chess = new String[4][n];
		int[][] r = new int[4][2];

		int total1 = 0;

		for (int i = 0; i < 4; ++i){
			for (int  j = 0; j < n; ++j){
				chess[i][j] = in.next();
			}

			for (int j = 0; j < n; ++j){
				for (int k = 0; k < n; ++k){
					int c = chess[i][j].charAt(k) - '0';
					r[i][0] += (j + k) % 2 == 0 ? c : 1 - c;
					r[i][1] += (j + k) % 2 == 0 ? 1 - c : c;
				}
			}

			total1 += r[i][1];
		}

		int min = 40001;
		for (int i = 0; i < 3; ++i){
			for (int j = i + 1; j < 4; ++j){
				min = Math.min(min, r[i][0] + r[j][0] + total1 - r[i][1] - r[j][1]);
			}
		}
		System.out.println(min);
	}
}
