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.io.PrintWriter;
import java.util.ArrayList;

public class CF_428_DIV2_C {
		
	private static int adjustPiece(char[][][] pieces, char start, int index) {
		int count = 0;
		
		int n = pieces[index].length;
		char rev = start == '1' ? '0' : '1';
		boolean sw = false;
		for (int i = 0; i < n; i++) {
			for (int j = 0; j < n; j++) {
				if ((!sw || pieces[index][i][j] != start) && (sw || pieces[index][i][j] != rev)) {
					count++;
				}
				sw = !sw;
			}
		}
		
		return count;
	}
	
	private static int min = Integer.MAX_VALUE;
	
	private static void g(int step, char start, char[][][] pieces, int cost, boolean[] visited) {
		if (step == 4) {
			min = Math.min(min, cost);
		} else {
			for (int i = 0; i < 4; i++) {
				if (!visited[i]) {
					visited[i] = true;
					
					if (step == 0 || step == 3) {
						g(step + 1, start, pieces, cost + adjustPiece(pieces, start, i), visited);
					} else {
						g(step + 1, start, pieces, cost + adjustPiece(pieces, start == '1' ? '0' : '1', i), visited);
					}
					
					visited[i] = false;
				}
			}
		}
	}
	
	public static void main(String[] args) throws IOException {
		BufferedReader input = new BufferedReader (new InputStreamReader(System.in));
		PrintWriter pw = new PrintWriter(System.out, true);
		
		int n = Integer.parseInt(input.readLine());
		
		char[][][] pieces = new char[4][n][n];
		String line;
		for (int k = 0; k < 4; k++) {
			if (k != 0) line = input.readLine();
			for (int i = 0; i < n; i++) {
				line = input.readLine();
				for (int j = 0; j < n; j++) {
					pieces[k][i][j] = line.charAt(j);
				}
			}
		}
		g(0, '0', pieces, 0, new boolean[4]);
		g(0, '1', pieces, 0, new boolean[4]);
		
		System.out.println(min);
		input.close();
		pw.close();
	}
}
