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.*;
import java.util.*;

public class Chessboard {
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		PrintWriter pw = new PrintWriter(System.out);
		
		int n = Integer.parseInt(sc.nextLine());
		int[][] q1 = new int[n][n];
		for(int i = 0; i < n; i++) {
			String line = sc.nextLine();
			for(int j = 0; j < n; j++) {
				if(line.charAt(j) == '0')
					q1[i][j] = 0;
				else
					q1[i][j] = 1;
			}
		}
		sc.nextLine();
		int[][] q2 = new int[n][n];
		for(int i = 0; i < n; i++) {
			String line = sc.nextLine();
			for(int j = 0; j < n; j++) {
				if(line.charAt(j) == '0')
					q2[i][j] = 0;
				else
					q2[i][j] = 1;
			}
		}
		sc.nextLine();
		int[][] q3 = new int[n][n];
		for(int i = 0; i < n; i++) {
			String line = sc.nextLine();
			for(int j = 0; j < n; j++) {
				if(line.charAt(j) == '0')
					q3[i][j] = 0;
				else
					q3[i][j] = 1;
			}
		}
		sc.nextLine();
		int[][] q4 = new int[n][n];
		for(int i = 0; i < n; i++) {
			String line = sc.nextLine();
			for(int j = 0; j < n; j++) {
				if(line.charAt(j) == '0')
					q4[i][j] = 0;
				else
					q4[i][j] = 1;
			}
		}
		sc.close();
		
		int o1 = oddDiff(q1); int e1 = evenDiff(q1);
		int o2 = oddDiff(q2); int e2 = evenDiff(q2);
		int o3 = oddDiff(q3); int e3 = evenDiff(q3);
		int o4 = oddDiff(q4); int e4 = evenDiff(q4);
		
		int value = o1 + o2 + e3 + e4;
		value = Math.min(value,  o1 + e2 + o3 + e4);
		value = Math.min(value,  o1 + e2 + e3 + o4);
		value = Math.min(value,  e1 + o2 + o3 + e4);
		value = Math.min(value,  e1 + o2 + e3 + o4);
		value = Math.min(value,  e1 + e2 + o3 + o4);
		pw.println(value);
		pw.close();
	}
	
	public static int oddDiff(int[][] quadrant) {
		int total = 0;
		for(int i = 0; i < quadrant.length; i++) {
			for(int j = 0; j < quadrant.length; j++) {
				if((i + j) % 2 == 0) {
					if(quadrant[i][j] == 1)
						total++;
				}
				else
					if(quadrant[i][j] == 0)
						total++;
			}
		}
		return total;
	}
	
	public static int evenDiff(int[][] quadrant) {
		int total = 0;
		for(int i = 0; i < quadrant.length; i++) {
			for(int j = 0; j < quadrant.length; j++) {
				if((i + j) % 2 == 1) {
					if(quadrant[i][j] == 1)
						total++;
				}
				else
					if(quadrant[i][j] == 0)
						total++;
			}
		}
		return total;
	}
}