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.util.ArrayList;
import java.util.List;
import java.util.Scanner;

public class ChessBoard {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = Integer.parseInt(sc.nextLine());
        List<List<Integer>> boards = new ArrayList<>();
        for (int i = 0; i < 4; i++) {
            List<Integer> board = new ArrayList<>();
            for (int j = 0; j < n; j++) {
                String line = sc.nextLine();
                for (int k = 0; k < n; k++) {
                    board.add(line.charAt(k) == '1' ? 1 : 0);
                }
            }
            if (i < 3) sc.nextLine();
            boards.add(board);
        }

        List<Integer> changes = new ArrayList<>();
        for (List<Integer> board : boards) {
            int numToChangeToBe1 = 0;
            for (int i = 0; i < board.size(); i++) {
                if (i % 2 == 0 && board.get(i) == 0) {
                    numToChangeToBe1++;
                }
                if (i % 2 == 1 && board.get(i) == 1) {
                    numToChangeToBe1++;
                }
            }
            int numToChangeToBe0 = 0;
            for (int i = 0; i < board.size(); i++) {
                if (i % 2 == 0 && board.get(i) == 1) {
                    numToChangeToBe0++;
                }
                if (i % 2 == 1 && board.get(i) == 0) {
                    numToChangeToBe0++;
                }
            }
            changes.add(numToChangeToBe1);
            changes.add(numToChangeToBe0);
        }


        int min = Integer.MAX_VALUE;
        int aBlack = changes.get(0);
        int aWhite = changes.get(1);
        int bBlack = changes.get(2);
        int bWhite = changes.get(3);
        int cBlack = changes.get(4);
        int cWhite = changes.get(5);
        int dBlack = changes.get(6);
        int dWhite = changes.get(7);
        // a, b black, c, d white
        min = Math.min(min, aBlack + bBlack + cWhite + dWhite);
        // a, c black
        min = Math.min(min, aBlack + cBlack + bWhite + dWhite);
        // a, d black
        min = Math.min(min, aBlack + dBlack + cWhite + bWhite);
        // now whites
        min = Math.min(min, aWhite + bWhite + cBlack + dBlack);
        min = Math.min(min, aWhite + cWhite + bBlack + dBlack);
        min = Math.min(min, aWhite + dWhite + cBlack + bBlack);
        System.out.println(min);
    }
}
