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.*;
import java.util.LinkedList;
import java.util.Queue;
import java.util.StringTokenizer;

public class Main {
    private final InputReader in;
    private final PrintWriter out;

    public Main(final InputReader in, final PrintWriter out) {
        this.in = in;
        this.out = out;
    }

    private static PrintWriter getOutput(final String filename) throws IOException {
        if (filename == null || filename.isEmpty()) {
            return new PrintWriter(new OutputStreamWriter(System.out));
        } else {
            return new PrintWriter(new FileWriter(filename + ".out"));
        }
    }

    public static void main(final String[] args) throws NumberFormatException, IOException {
        final String filename = "";
        final long time = System.currentTimeMillis();
        try (final InputReader in = new InputReader(filename); final PrintWriter out = getOutput(filename)) {
            new Main(in, out).solve();
        }
//        System.err.println("Running time: " + (System.currentTimeMillis() - time));
    }

    private Queue<Character> t(final char[] line1, final char[] line2) {
        final Queue<Character> q = new LinkedList<>();
        if (line1[0] != 'X') q.offer(line1[0]);
        if (line1[1] != 'X') q.offer(line1[1]);
        if (line2[1] != 'X') q.offer(line2[1]);
        if (line2[0] != 'X') q.offer(line2[0]);
        while (q.peek() != 'A') q.add(q.remove());
        return q;
    }

    private void solve() throws IOException {
        final Queue<Character> q1 = t(in.readLine().toCharArray(), in.readLine().toCharArray());
        final Queue<Character> q2 = t(in.readLine().toCharArray(), in.readLine().toCharArray());
        out.println(q1.equals(q2) ? "YES" : "NO");
    }

    private void assertTrue(final boolean t) {
        if (!t) throw new RuntimeException();
    }
}

class InputReader implements Closeable {
    private StringTokenizer st;
    private final BufferedReader in;

    public InputReader(final String filename) throws IOException {
        if (filename == null || filename.isEmpty())
            in = new BufferedReader(new InputStreamReader(System.in));
        else
            in = new BufferedReader(new FileReader(filename + ".in"));
    }

    public boolean hasNextToken() throws IOException {
        while (st == null || !st.hasMoreTokens()) {
            String line = in.readLine();
            if (line == null)
                return false;
            st = new StringTokenizer(line);
        }
        return true;
    }

    public String nextToken() throws IOException {
        while (st == null || !st.hasMoreTokens()) {
            String line = in.readLine();
            if (line == null)
                return null;
            st = new StringTokenizer(line);
        }
        return st.nextToken();
    }

    public String readLine() throws IOException {
        return in.readLine();
    }

    public int nextInt() throws NumberFormatException, IOException {
        return Integer.parseInt(nextToken());
    }

    public long nextLong() throws NumberFormatException, IOException {
        return Long.parseLong(nextToken());
    }

    public double nextDouble() throws NumberFormatException, IOException {
        return Double.parseDouble(nextToken());
    }

    @Override
    public void close() throws IOException {
        in.close();
    }
}