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 Question {

	public static void main(String[] args) throws IOException {
		Scanner sc = new Scanner(System.in);
		PrintWriter out = new PrintWriter(System.out);

		int n = sc.nextInt();

		boolean[][] arrOne = new boolean[n][n];
		boolean[][] arrTwo = new boolean[n][n];
		boolean here = true;

		for (int i = 0; i < n; i++) {
			for (int j = 0; j < n; j++) {
				arrOne[i][j] = here;
				arrTwo[i][j] = !here;
				here = !here;
			}
		}

		boolean[][][] grids = new boolean[4][n][n];

		for (int k = 0; k < 4; k++) {
			for (int i = 0; i < n; i++) {
				String input = sc.next();
				for (int m = 0; m < n; m++)
					grids[k][i][m] = input.charAt(m) == '1';

			}
		}
		ArrayList<Integer> arrMin = new ArrayList<>();
		for (int k = 0; k < 4; k++) {
			int resOne = 0;
			int resTwo = 0;
			for (int i = 0; i < n; i++) {
				for (int j = 0; j < n; j++) {
					if (grids[k][i][j] != arrOne[i][j]) {
						resOne++;
					}
					if (grids[k][i][j] != arrTwo[i][j]) {
						resTwo++;
					}
				}
			}
			arrMin.add(resOne);
			arrMin.add(resTwo);

		}
		int a = arrMin.get(0) + arrMin.get(2) + arrMin.get(5) + arrMin.get(7);
		int b = arrMin.get(1) + arrMin.get(3) + arrMin.get(4) + arrMin.get(6);
		int c = arrMin.get(0) + arrMin.get(3) + arrMin.get(5) + arrMin.get(6);
		int d = arrMin.get(1) + arrMin.get(2) + arrMin.get(4) + arrMin.get(7);
		int e = arrMin.get(1) + arrMin.get(2) + arrMin.get(6) + arrMin.get(5);
		int f = arrMin.get(0) + arrMin.get(3) + arrMin.get(4) + arrMin.get(7);
		
		int z = Math.min(Math.min(c, d),Math.min(e, f));

		out.println(Math.min(z, Math.min(a, b)));

		out.flush();

	}

	static class Scanner {
		StringTokenizer st;
		BufferedReader br;

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

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

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

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

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

		public char nextChar() throws IOException {
			return next().charAt(0);
		}

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

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

		public void waitForInput() {
			for (long i = 0; i < 3e9; i++)
				;
		}
	}

}

class Pair implements Comparable<Pair> {
	int a;
	int b;

	public Pair(int a, int b) {
		this.a = a;
		this.b = b;
	}

	@Override
	public int compareTo(Pair o) {
		// TODO Auto-generated method stub
		return this.a - o.a;
	}
}
