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
//package codeforces;

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

public class Chessboard961 {
	public static void main(String[] args) {
		Scanner scan = new Scanner(System.in);
		PrintWriter out = new PrintWriter(System.out);
		
		new Chessboard961().solve(scan, out);
		
		scan.close();
		out.close();
	}

	ArrayList<int[]> perms = new ArrayList<>();
	int[] P = {0,1,2,3};
	
	private void solve(Scanner scan, PrintWriter out) {
		//System.out.println(('1'-'0'));
		int n = scan.nextInt();
		int[][][] boards = new int[4][n][n];
		for(int a=0; a<4; a++) {
			for(int i=0; i<n; i++) {
				String num = scan.next();
				for(int j=0; j<n; j++) {
					boards[a][i][j] = num.charAt(j)-'0';
					//num/=10;
					//System.out.print(boards[a][i][j] + " ");
				}
				//System.out.println();
			}
			scan.nextLine();
		}
		
		permute(0, new boolean[4], new int[4]);
		//System.out.println(perms);
		int minCount = Integer.MAX_VALUE;
		for(int perm=0; perm<perms.size(); perm++) {
			int[][] chessboard = new int[2*n][2*n];
			for(int piece=0; piece<4; piece++) {
				int chessPiece = perms.get(perm)[piece];
				int k=(piece>=2)?n:0;
				int l=(piece == 1 || piece==3)?n:0;
				
				//System.out.println("piece"+piece);
				for(int i=0+k; i<n+k; i++) {
					for(int j=0+l; j<n+l; j++) {
						//System.out.println("ChessPiece "+chessPiece+" i "+i+" j "+j);
						chessboard[i][j] = boards[chessPiece][i-k][j-l];
					}
				}
				
			}
			for(int black=0; black<=1; black++) {		
				int count = 0;
				for(int i=0; i<2*n; i++) {
					for(int j=0; j<2*n; j++) {
						//System.out.print(chessboard[i][j]);
						if((i+j)%2==0) {
							if(chessboard[i][j]==black) {
								count++;
							}
						} else {
							if(chessboard[i][j]!=black) {
								count++;
							}
						}
					}
					//System.out.println();
				}
				//System.out.println();
				if(count < minCount) {
					minCount = count;
				}
			}
		}
		out.println(minCount);
	}
	private void permute(int size, boolean[] used, int[] perm) {
		if(size==4) {
			int[] copy = new int[4];
			for(int i=0; i<4; i++) {
				copy[i]=perm[i];
			}
			perms.add(copy);
			return;
		}
		for(int i=0; i<4; i++) {
			if(!used[i]) {
				perm[size] = P[i];
				used[i] = true;
				permute(size+1, used, perm);
				used[i] = false;
			}
		}
	}
}
