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 com.company;

import java.util.Scanner;
import static java.lang.Math.min;

public class Main {
    public static void main(String[] args) {
        int n;
        Scanner sc = new Scanner(System.in);

        n = sc.nextInt();
        String s[][] = new String[4][n];

        for (int i = 0; i < 4; i++) {
            for(int j = 0; j < n; j++) {
                s[i][j] = sc.next();
            }
        }

        int cnt[][] = new int[4][2];

        for (int i = 0; i < 4; i++) {
            for(int c = 0; c < 2; c++) {
                for (int j = 0; j < n; j++) {
                    for (int k = 0; k < n; k++) {
                        if((int)s[i][j].charAt(k) - (int)'0' != (c + j*n + k) % 2 ){
                            cnt[i][c]++;
                        }
                    }
                }
//                System.out.println(cnt[i][c]);
            }
        }

        int res = 4*n*n;
        for(int i = 0; i < (1 << 4); i++) {
            if(Integer.bitCount(i) == 2) {
                int x = i, temp = 0, t = 0;
                while(t < 4) {
                    temp += cnt[t][x%2];
                    x /= 2;
                    t++;
                }
                res = min(res, temp);
            }
        }

        System.out.println(res);
    }
}
