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.*;
import java.io.*;
import java.math.*;
 
public class A
{
    static int color_10(char arr[][], int n){
        int ret = 0;
        int prev = 0;

        for(int i = 0; i < n; i++){
            for(int j = 0; j < n; j++){
                int curr = arr[i][j] - '0';
                if(curr != 1 - prev)
                    ret++;

                prev = 1 - prev;
            }
        }

        return ret;
    }

    static int color_01(char arr[][], int n){
        int ret = 0;
        int prev = 1;

        for(int i = 0; i < n; i++){
            for(int j = 0; j < n; j++){
                int curr = arr[i][j] - '0';
                if(curr != 1 - prev)
                    ret++;

                prev = 1 - prev;
            }
        }

        return ret;
    }

    public static void process(int test_number)throws IOException
    {
        int n = ni();
        char arr[][][] = new char[4][n][];

        for(int i = 1; i <= 4; i++){
            for(int j = 1; j <= n; j++)
                arr[i- 1][j - 1] = nln().toCharArray();
            nln();
        }

        int res = oo;
        
        for(int i = 0; i < 4; i++){
            for(int j = i + 1; j < 4; j++){
                int recolor = color_10(arr[i], n) + color_10(arr[j], n);

                for(int k = 0; k < 4; k++)
                    if(k != i && k != j)
                        recolor += color_01(arr[k], n);

                res = Math.min(res, recolor);
            }
        }
        pn(res);
    }
     
    static int oo = 98765;
    static final long mod = (long)1e9+7l;
    
    static FastReader sc;
    static PrintWriter out;
    public static void main(String[]args)throws IOException
    {
        out = new PrintWriter(System.out);
        sc = new FastReader();
 
        long s = System.currentTimeMillis();
        int t = 1;
        //t = ni();
        for(int i = 1; i <= t; i++)
            process(i);
 
        out.flush();
        System.err.println(System.currentTimeMillis()-s+"ms");
    }

    static void trace(Object... o){ System.err.println(Arrays.deepToString(o)); };
    static void pn(Object o){ out.println(o); }
    static void p(Object o){ out.print(o); }
    static int ni()throws IOException{ return Integer.parseInt(sc.next()); }
    static long nl()throws IOException{ return Long.parseLong(sc.next()); }
    static double nd()throws IOException{ return Double.parseDouble(sc.next()); }
    static String nln()throws IOException{ return sc.nextLine(); }
    static long gcd(long a, long b)throws IOException{ return (b==0)?a:gcd(b,a%b);}
    static int gcd(int a, int b)throws IOException{ return (b==0)?a:gcd(b,a%b); }
    static int bit(long n)throws IOException{ return (n==0)?0:(1+bit(n&(n-1))); }
    
    static class FastReader{ 
        BufferedReader br; 
        StringTokenizer st; 
  
        public FastReader(){ 
            br = new BufferedReader(new InputStreamReader(System.in)); 
        } 
  
        String next(){ 
            while (st == null || !st.hasMoreElements()){ 
                try{ st = new StringTokenizer(br.readLine()); } catch (IOException  e){ e.printStackTrace(); } 
            } 
            return st.nextToken(); 
        } 
  
        String nextLine(){ 
            String str = ""; 
            try{ str = br.readLine(); } catch (IOException e) { e.printStackTrace(); } 
            return str; 
        } 
    } 
}
