Problem: Bessie the cow and her best friend Elsie each received a sliding puzzle on Pi Day. Their puzzles consist of a 2 × 2 grid and three tiles labeled 'A', 'B', and 'C'. The three tiles sit on top of the grid, leaving one grid cell empty. To make a move, Bessie or Elsie can slide a tile adjacent to the empty cell into the empty cell as shown below:

<image>

In order to determine if they are truly Best Friends For Life (BFFLs), Bessie and Elsie would like to know if there exists a sequence of moves that takes their puzzles to the same configuration (moves can be performed in both puzzles). Two puzzles are considered to be in the same configuration if each tile is on top of the same grid cell in both puzzles. Since the tiles are labeled with letters, rotations and reflections are not allowed.

Input

The first two lines of the input consist of a 2 × 2 grid describing the initial configuration of Bessie's puzzle. The next two lines contain a 2 × 2 grid describing the initial configuration of Elsie's puzzle. The positions of the tiles are labeled 'A', 'B', and 'C', while the empty cell is labeled 'X'. It's guaranteed that both puzzles contain exactly one tile with each letter and exactly one empty position.

Output

Output "YES"(without quotes) if the puzzles can reach the same configuration (and Bessie and Elsie are truly BFFLs). Otherwise, print "NO" (without quotes).

Examples

Input

AB
XC
XB
AC


Output

YES


Input

AB
XC
AC
BX


Output

NO

Note

The solution to the first sample is described by the image. All Bessie needs to do is slide her 'A' tile down.

In the second sample, the two puzzles can never be in the same configuration. Perhaps Bessie and Elsie are not meant to be friends after all...

Solution (in JAVA):

Solution:
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.stream.IntStream;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashMap;
import java.util.HashSet;
import java.util.LinkedHashMap;
import java.util.LinkedList;
import java.util.List;
import java.math.BigInteger;
import java.util.Map;
import java.util.Map.Entry;
import java.util.Scanner;
import java.util.StringTokenizer;
import java.util.TreeMap;

public class Dragons {
	 
    static class Pair {
        long a;
        long b;
        public Pair(long a, long b){
            this.a=a;
            this.b=b;
        }
    }
	static ArrayList<Integer>[]adjList;
	static boolean[] color;
	static boolean visited[];
	
	public static void main(String[] args) throws IOException {
Scanner sc=new Scanner(System.in);
String a=sc.nextLine();
String b=sc.nextLine();
StringBuilder input1 = new StringBuilder();
input1.append(b);
b=input1.reverse().toString();
String c=sc.nextLine();
String d=sc.nextLine();
StringBuilder input2 = new StringBuilder();
input2.append(d);
d=input2.reverse().toString();
StringBuilder sb=new StringBuilder();
StringBuilder ab=new StringBuilder();
String y="";
for(int i=0;i<4;i++) {
	if(i<=1) {
	if(a.charAt(i)!='X') {
		sb.append(a.charAt(i));
	}}else if(i>1) {
		if(b.charAt(i-2)!='X') {
		sb.append(b.charAt(i-2));}
	}
}
for(int i=0;i<4;i++) {
	if(i<=1) {
	if(c.charAt(i)!='X') {
		ab.append(c.charAt(i));
	}}else if(i>1) {
		if(d.charAt(i-2)!='X') {
		ab.append(d.charAt(i-2));}
	}
}

y=y+sb.toString()+" ";
char t=sb.charAt(0);
sb.deleteCharAt(0);
sb.append(t);
y=y+sb.toString()+" ";
t=sb.charAt(0);
sb.deleteCharAt(0);
sb.append(t);
y=y+sb.toString();

if(y.contains(ab.toString())) {
	System.out.println("YES");
}else {
	System.out.println("NO");
}
	}
	static boolean isInteger(double N)
	{
	 
	    // Convert float value
	    // of N to integer
	    long X = (long)N;
	    double temp2 = N - X;
	 
	    // If N is not equivalent
	    // to any integer
	    if (temp2 > 0)
	    {
	        return false;
	    }
	    return true;
	}
	static long isrecursive(long p) {
		if(p==0) {
			return 0;
		}else if(p%2==0) {
			return isrecursive(p/2);
		}else {
			return isrecursive(p/2)+1;
		}
		
	}
	static int islucky(int r) {
		String temp = Integer.toString(r);
		int[] newGuess = new int[temp.length()];
		int tu=0;
		for (int i = 0; i < temp.length(); i++)
		{
		    newGuess[i] = temp.charAt(i) - '0';
		    if(newGuess[i]==4 || newGuess[i]==7) {
		    	tu=tu*10+newGuess[i];
		    }
		}
		return tu;
	}
	static int distance(long l,long m) {
		return (int) (Math.pow(l,2)+Math.pow(m,2));
	}
	static int findSmallest(int N)
	{
	  
	    // Base case
	    if (N == 0)
	        return 2;
	    if (N == 1)
	        return 1;
	  
	    int prime = N, counter = 0;
	    boolean found = false;
	  
	    // Loop continuously until isPrime returns
	    // true for a number greater than n
	    while (!found) {
	        if (isPrime(prime))
	            found = true;
	        else {
	  
	            // If the number is not a prime, then
	            // increment the number by 1 and the
	            // counter which stores the number
	            // to be added
	            prime++;
	            counter++;
	        }
	    }
	  
	    return counter;
	}
	static boolean isPrime(int n)
	{
	    // Base cases
	    if (n <= 1)
	        return false;
	    if (n <= 3)
	        return true;
	  
	    // This is checked so that we can skip
	    // middle five numbers in below loop
	    if (n % 2 == 0 || n % 3 == 0)
	        return false;
	  
	    // For all the remaining numbers, check if
	    // any number is a factor if the number
	    // or not
	    for (int i = 5; i * i <= n; i = i + 6)
	        if (n % i == 0 || n % (i + 2) == 0)
	            return false;
	  
	    // If none of the above numbers are the
	    // factors for the number, then the
	    // given number is prime
	    return true;
	}
	
	
		static int mod(int a, int m)
		{
		    return (a%m + m) % m;
		}
		
	static long getSum(long y)
    {
       long sum = 0;
 
        while (y != 0) {
            sum = sum + y % 10;
            y = y / 10;
        }
 
        return sum;
    }
	static boolean detect(int arr[],int x) {
		long sum=0;
		for(int i=0;i<arr.length;i++) {
			sum+=arr[i];
			if(sum==x) {
				return true;
			}
			
		}
		return false;
	}
	
    static class Node {
        String s;
        int val;
 
        public Node(String a, int v) {
            val = v;
            s = a;
        }
    }
	  
	 public static HashMap<String, Integer> sortByValue(HashMap<String, Integer> hm)
	    {
	        // Create a list from elements of HashMap
	        List<Map.Entry<String, Integer> > list =
	               new LinkedList<Map.Entry<String, Integer> >(hm.entrySet());
	 
	        // Sort the list
	        Collections.sort(list, new Comparator<Map.Entry<String, Integer> >() {
	            public int compare(Map.Entry<String, Integer> o1,
	                               Map.Entry<String, Integer> o2)
	            {
	                return -(o1.getValue()).compareTo(o2.getValue());
	            }
	        });
	         
	        // put data from sorted list to hashmap
	        HashMap<String, Integer> temp = new LinkedHashMap<String, Integer>();
	        for (Map.Entry<String, Integer> aa : list) {
	            temp.put(aa.getKey(), aa.getValue());
	        }
	        return temp;
	    }
	
 
static class FastScanner {
		BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st=new StringTokenizer("");
		String next() {
			while (!st.hasMoreTokens())
				try {
					st=new StringTokenizer(br.readLine());
				} catch (IOException e) {
					e.printStackTrace();
				}
			return st.nextToken();
		}
		
		int nextInt() {
			return Integer.parseInt(next());
		}
		int[] readArray(int n) {
			int[] a=new int[n];
			for (int i=0; i<n; i++) a[i]=nextInt();
			return a;
		}
		long nextLong() {
			return Long.parseLong(next());
		}
	}
	
	
static void reduceFraction(int x, int y) 
{ 
    int d; 
    d = gcd(x, y); 
  
    x = x / d; 
    y = y / d; 
  if(x>0 && y<0) {
	  x=-x;
	  y=-y;
  }
    System.out.println( x + "/" + y); 
} 
	
	static int gcd(int a, int b) {
		return a%b == 0 ? b : gcd(b,a%b);
	}
	
	static boolean[] sieve(int n) {
		
		boolean isPrime[] = new boolean[n+1];
		for(int i = 2; i <= n; i++) {
			if(isPrime[i]) continue;
			for(int j = 2*i; j <= n; j+=i) {
				isPrime[j] = true;
			}
		
		}
		return isPrime;
		
	}
}