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.Scanner;

public class C {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int N = sc.nextInt();
        int[][] dosk1 = new int[N][N];
        int[][] dosk2 = new int[N][N];
        int[][] dosk3 = new int[N][N];
        int[][] dosk4 = new int[N][N];

        int w1 =  0;
        int w2 =  0;
        int w3 =  0;
        int w4 =  0;
        int b1 =  0;
        int b2 =  0;
        int b3 =  0;
        int b4 =  0;

        sc.nextLine();
        for(int i = 0; i < N; i++){
            String line = sc.nextLine();
            for(int j = 0; j< N; j++){
                dosk1[i][j] = Character.getNumericValue(line.charAt(j));
            }
        }
        sc.nextLine();
        for(int i = 0; i < N; i++){
            String line = sc.nextLine();
            for(int j = 0; j< N; j++){
                dosk2[i][j] = Character.getNumericValue(line.charAt(j));
            }
        }
        sc.nextLine();
        for(int i = 0; i < N; i++){
            String line = sc.nextLine();
            for(int j = 0; j< N; j++){
                dosk3[i][j] = Character.getNumericValue(line.charAt(j));
            }
        }
        sc.nextLine();
        for(int i = 0; i < N; i++){
            String line = sc.nextLine();
            for(int j = 0; j< N; j++){
                dosk4[i][j] = Character.getNumericValue(line.charAt(j));
            }
        }

        int count1 = 0;
        for(int i = 0; i < N; i++){
            for(int j = 0; j< N; j++){
                if(dosk1[i][j] != count1%2){
                    w1++;
                }else{
                    b1++;
                }
                count1++;
            }
        }

        count1 = 0;
        for(int i = 0; i < N; i++){
            for(int j = 0; j< N; j++){
                if(dosk2[i][j] != count1%2){
                    w2++;
                }else{
                    b2++;
                }
                count1++;
            }
        }

        count1 = 0;
        for(int i = 0; i < N; i++){
            for(int j = 0; j< N; j++){
                if(dosk3[i][j] != count1%2){
                    w3++;
                }else{
                    b3++;
                }
                count1++;
            }
        }

        count1 = 0;
        for(int i = 0; i < N; i++){
            for(int j = 0; j< N; j++){
                if(dosk4[i][j] != count1%2){
                    w4++;
                }else{
                    b4++;
                }
                count1++;
            }
        }

        int res1 = w1 + w3 + b2 + b4;
        int res2 = w1 + w2 + b3 + b4;
        int res3 = w1 + w4 + b3 + b2;

        int res4 = b1 + b3 + w2 + w4;
        int res5 = b1 + b2 + w3 + w4;
        int res6 = b1 + b4 + w3 + w2;

        int res = Math.min(res1, res2);
        res = Math.min(res, res3);
        res = Math.min(res, res4);
        res = Math.min(res, res5);
        res = Math.min(res, res6);

        System.out.println(res);

    }
}
