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.File;
import java.io.FileNotFoundException;
import java.io.FileReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Stack;
import java.util.StringTokenizer;

public class Ezz {



	static int a1[][],a2[][];
	static int diff(int a[][],int b[][]) {
		int q = 0;
		for (int i = 0 ; i < a.length ; ++i) {
			for (int j = 0 ; j < a[i].length ; ++j) {
				if (a[i][j] != b[i][j]) {
					++q;
				}
			}
		}
		return q;
	}
	public static void main(String[]args) throws Throwable {
		Scanner sc = new Scanner(System.in);
		PrintWriter out = new PrintWriter(System.out);
		int n  = sc.nextInt();
		int arr[][][] = new int[4][n][n];
		a1 = new int[n][n];
		a2 = new int[n][n];
		int cur = 1;
		for (int i = 0 ; i < n ; ++i) {
			for (int j = 0 ; j < n ; ++j) {
				a1[i][j] = cur;
				cur ^= 1;
			}
		}
		cur = 0;
		for (int i = 0 ; i < n ; ++i) {
			for (int j = 0 ; j < n ; ++j) {
				a2[i][j] = cur;
				cur ^= 1;
			}
		}
		for (int i = 0 ; i < 4 ; ++i) {
			for (int j = 0 ; j < n ; ++j) {
				String str = sc.next();
				for (int k = 0 ; k < n ; ++k) {
					arr[i][j][k] = str.charAt(k) - '0';
				}
			}
		}
		int best = 1 << 30;
		for (int msk = 0; msk < (1 << 4) ; ++msk) {
			if (Integer.bitCount(msk) != 2) {
				continue;
			}
			int cost = 0;
			for (int i = 0 ; i < 4 ; ++i) {
				if ((msk & (1 << i)) > 0) {
					cost += diff(arr[i],a1);
				} else {
					cost += diff(arr[i],a2);
				}
			}
			best = Math.min(best, cost);
		}
		out.println(best);
		out.flush();
		out.close();
	}
	static class Scanner {
		StringTokenizer st;
		BufferedReader br;

		public Scanner(InputStream s) {
			br = new BufferedReader(new InputStreamReader(s));
		}

		public Scanner(String s) throws FileNotFoundException {
			br = new BufferedReader(new FileReader(new File(s)));
		}

		public String next() throws IOException {
			while (st == null || !st.hasMoreTokens())
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}

		public int nextInt() throws IOException {
			return Integer.parseInt(next());
		}

		public long nextLong() throws IOException {
			return Long.parseLong(next());
		}

		public String nextLine() throws IOException {
			return br.readLine();
		}

		public double nextDouble() throws IOException {
			return Double.parseDouble(next());
		}

		public boolean ready() throws IOException {
			return br.ready();
		}
	}

}