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 Main {
    static int pt=0;
    static int[][] p;
    public static void main(String args[]) {
        Scanner in = new Scanner(new BufferedReader(new InputStreamReader(System.in)));
        PrintWriter out = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)), false);
        p = new int[24][4];
        permute(new int[]{1,2,3,4}, 0,3);
        // Permutations...
        // for(int[] t:p){
        //     for(int j:t){
        //         out.print(j+" ");
        //     }out.println();
        // }
        int n = in.nextInt();
        int a[][][] = new int[4][n][n];
        for(int i=0;i<4;i++){
            for(int j=0;j<n;j++){
                String s = in.next();
                for(int k=0;k<n;k++){
                    a[i][j][k] = s.charAt(k)=='0'?0:1;
                }
            }
        }
        int cost[] = new int[4];
        for(int i=0;i<4;i++){
            cost[i] = compute(a[i]);
        }
        // for(int i:cost) out.println("cst: "+i);
        int mn = Integer.MAX_VALUE;
        int cst=0;
        for(int[] i:p){
            cst=0;
            for(int j=0;j<2;j++){
                cst+=cost[i[j]-1];
            }
            for(int j=2;j<4;j++){
                cst+=(n*n-cost[i[j]-1]);
            }
            // out.println("C: "+cst);
            mn = Math.min(cst, mn);
        }
        out.println(mn);
        in.close();out.flush();out.close();
    }
    static int compute(int a[][]){
        int n = a.length;
        int cst = 0;
        int mark=1;
        for(int i=0;i<n;i++){
            for(int j=0;j<n;j++){
                if(a[i][j]!=mark) cst++;
                mark = 1 - mark;
            }
        }
        return cst;
    }
    static void permute(int[] ar, int l, int r){
        if(l==r){
            for(int i=0;i<4;i++) p[pt][i] = ar[i];
            ++pt;
        }else{
            int tmp=0;
            for(int i=l;i<=r;i++){
                tmp = ar[l];
                ar[l] = ar[i];
                ar[i] = tmp;
                permute(ar,l+1,r);
                tmp = ar[l];
                ar[l] = ar[i];
                ar[i] = tmp;
            }
        }
    }
}