Problem: The king is left alone on the chessboard. In spite of this loneliness, he doesn't lose heart, because he has business of national importance. For example, he has to pay an official visit to square t. As the king is not in habit of wasting his time, he wants to get from his current position s to square t in the least number of moves. Help him to do this.

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In one move the king can get to the square that has a common side or a common vertex with the square the king is currently in (generally there are 8 different squares he can move to).

Input

The first line contains the chessboard coordinates of square s, the second line — of square t.

Chessboard coordinates consist of two characters, the first one is a lowercase Latin letter (from a to h), the second one is a digit from 1 to 8.

Output

In the first line print n — minimum number of the king's moves. Then in n lines print the moves themselves. Each move is described with one of the 8: L, R, U, D, LU, LD, RU or RD. 

L, R, U, D stand respectively for moves left, right, up and down (according to the picture), and 2-letter combinations stand for diagonal moves. If the answer is not unique, print any of them. 

Examples

Input

a8
h1


Output

7
RD
RD
RD
RD
RD
RD
RD

Solution (in JAVA):

Solution:

import java.util.*;
import java.io.*;

public class Codeforces {

    
    static Node path[][] = new Node[8][8];
    
    public static void main(String[] args) throws IOException {
        Reader.init(System.in);
        String start = Reader.next();
        String end = Reader.next();
        int s1 = start.charAt(0) - 'a', s2 = start.charAt(1) - '1';
        int e1 = end.charAt(0) - 'a', e2 = end.charAt(1) - '1';
        
        ArrayList<String> ans = new ArrayList();
        int c = 0;
        Node ref = BFS(s1, s2, e1, e2);
        
        while(!ref.s.equals("start")){
            ans.add(ref.s);
            ref = path[ref.r][ref.c];
        }
        System.out.println(ans.size());
        for(int i = ans.size() -1; i > -1; i--)
            System.out.println(ans.get(i));
    }
    //L, R, U, D, LU, LD, RU or RD
    static int dirR[] = {1, 0, -1, 0, 1, -1, 1, -1};
    static int dirC[] = {0, 1, 0, -1, 1, -1, -1, 1};
    static String s[] = {"R", "U", "L", "D", "RU", "LD", "RD", "LU"};
    
    static Node BFS(int r, int c, int rt, int ct){
        Queue<Node> q = new LinkedList();
        boolean visited[][] = new boolean[8][8];
        
        q.add(new Node(r, c, "start"));
        int depth = 0;
        
        if(r == rt && c == ct)
            return q.peek();
        
        Node ref;
        while(!q.isEmpty()){
            int size = q.size();
            
            for(int i = 0; i < size; i++){
                ref = q.poll();
                
                for(int j = 0; j < 8; j++){
                    int x = ref.r + dirR[j], y = ref.c + dirC[j];
                    
                    if(!valid(x, y) || visited[x][y])
                        continue;
              
                    visited[x][y] = true;
                    q.add(new Node(x, y, s[j]));
                    path[x][y] = ref;
                    
                    if(visited[rt][ct])
                        return new Node(x, y, s[j]);
                }
            }
            depth++;
        }
        
        return null;
    }
    
    static boolean valid(int r, int c){
        return r < 8 && c < 8 && r > -1 && c >-1;
    }
}

class Node{

    int r;
    int c;
    String s;

    

    public Node(int a, int b, String x) {
        s = x;
        r = a;
        c = b;
    }

}

class Reader {

    static BufferedReader reader;
    static StringTokenizer tokenizer;

    /**
     * call this method to initialize reader for InputStream
     */
    public static int pars(String x) {
        int num = 0;
        int i = 0;
        if (x.charAt(0) == '-') {
            i = 1;
        }
        for (; i < x.length(); i++) {
            num = num * 10 + (x.charAt(i) - '0');
        }

        if (x.charAt(0) == '-') {
            return -num;
        }

        return num;
    }

    static void init(InputStream input) {
        reader = new BufferedReader(
                new InputStreamReader(input));
        tokenizer = new StringTokenizer("");
    }

    static void init(FileReader input) {
        reader = new BufferedReader(input);
        tokenizer = new StringTokenizer("");
    }

    /**
     * get next word
     */
    static String next() throws IOException {
        while (!tokenizer.hasMoreTokens()) {
            //TODO add check for eof if necessary
            tokenizer = new StringTokenizer(
                    reader.readLine());
        }
        return tokenizer.nextToken();
    }

    static int nextInt() throws IOException {
        return pars(next());
    }

    static byte nextByte() throws IOException {

        return Byte.parseByte(next());
    }

    static long nextLong() throws IOException {
        return Long.parseLong(next());
    }

    static double nextDouble() throws IOException {
        return Double.parseDouble(next());
    }
}