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.

<image>

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:
//package codeforces.contest_beta_round3;

import java.io.BufferedOutputStream;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Comparator;
import java.util.List;
import java.util.Objects;
import java.util.Random;
import java.util.StringTokenizer;

public class A {

  static MyScanner scanner = new MyScanner();
  static PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out));
  static final int MOD = 1000000007;
  static final boolean oj = System.getProperty("ONLINE_JUDGE") != null;
  static final int[][] d4 = new int[][]{{-1, 0}, {0, -1}, {1, 0}, {0, 1}};
  static final int[][] d8 = new int[][]{{-1, -1}, {-1, 0}, {-1, 1}, {0, -1}, {0, 1}, {1, -1}, {1, 0}, {1, 1}};
  static final int N = 0;

  public static void main(String[] args) {
    int tc = 1;
    for(int t=0; t<tc; t++) {
      String s1 = scanner.next();
      String s2 = scanner.next();
      char[] cs1 = s1.toCharArray();
      char[] cs2 = s2.toCharArray();
      List<String> res = new ArrayList<>();
      while(cs1[0] != cs2[0] || cs1[1] != cs2[1]) {
        if(cs1[0] == cs2[0]) {
          if(cs1[1] < cs2[1]) {
            res.add("U");
            cs1[1]++;
          } else {
            res.add("D");
            cs1[1]--;
          }
        } else if(cs1[1] == cs2[1]) {
          if(cs1[0] < cs2[0]) {
            res.add("R");
            cs1[0]++;
          } else {
            res.add("L");
            cs1[0]--;
          }
        } else {
          if(cs1[0] < cs2[0] && cs1[1] < cs2[1]) {
            cs1[0]++;
            cs1[1]++;
            res.add("RU");
          } else if(cs1[0] < cs2[0] && cs1[1] > cs2[1]) {
            cs1[0]++;
            cs1[1]--;
            res.add("RD");
          } else if(cs1[0] > cs2[0] && cs1[1] < cs2[1]) {
            cs1[0]--;
            cs1[1]++;
            res.add("LU");
          } else {
            cs1[0]--;
            cs1[1]--;
            res.add("LD");
          }
        }
      }
      out.println(res.size());
      for(String s : res) {
        out.println(s);
      }
    }

    out.close();
  }

  private static int[] getIntArr(int n) {
    int[] a = new int[n];
    for(int i=0; i<n; i++) {
      a[i] = scanner.nextInt();
    }
    return a;
  }

  private static long[] getLongArr(int n) {
    long[] a = new long[n];
    for(int i=0; i<n; i++) {
      a[i] = scanner.nextLong();
    }
    return a;
  }

  public static void print(Object o) {
    if(!oj) {
      out.println(o);
    }
  }

  //Find the GCD of two numbers
  public static long gcd(long a, long b) {
    if (a < b) return gcd(b,a);
    if (b == 0)
      return a;
    else
      return gcd(b,a%b);
  }

  private static long[] fac = new long[N+1];
  private static long[] invfac = new long[N+1];

  private static long fac(int n){
    if(n == 0) return fac[0] = 1;
    else if(fac[n] > 0) return fac[n];
    else return fac[n] = n * fac(n-1) % MOD;
  }

  private static long invfac(int n){
    if(invfac[n] > 0) return invfac[n];
    else return invfac[n] = inv(fac[n]);
  }

  private static long choose(int n, int k){
    return fac(n) * invfac(k) % MOD * invfac(n-k) % MOD;
  }

  private static long inv(long a){
    return (gcdex(a, MOD).key + MOD) % MOD;
  }

  private static Pair<Long, Long> gcdex(long a, long b){
    if(b > a) return gcdex(b, a).invert();
    else if(b == 0) return new Pair<>(1L, 0L);
    else{
      Pair<Long, Long> p = gcdex(b, a % b);
      return new Pair<>(p.key, p.key - p.value*(a/b));
    }
  }

  //Fast exponentiation (x^y mod m)
  public static long power(long x, long y, long m) {
    if (y < 0) return 0L;
    long ans = 1;
    x %= m;
    while (y > 0) {
      if(y % 2 == 1)
        ans = (ans * x) % m;
      y /= 2;
      x = (x * x) % m;
    }
    return ans;
  }

  public static int[] shuffle(int[] array) {
    Random rgen = new Random();
    for (int i = 0; i < array.length; i++) {
      int randomPosition = rgen.nextInt(array.length);
      int temp = array[i];
      array[i] = array[randomPosition];
      array[randomPosition] = temp;
    }
    return array;
  }

  public static long[] shuffle(long[] array) {
    Random rgen = new Random();
    for (int i = 0; i < array.length; i++) {
      int randomPosition = rgen.nextInt(array.length);
      long temp = array[i];
      array[i] = array[randomPosition];
      array[randomPosition] = temp;
    }
    return array;
  }

  public static int[][] shuffle(int[][] array) {
    Random rgen = new Random();
    for (int i = 0; i < array.length; i++) {
      int randomPosition = rgen.nextInt(array.length);
      int[] temp = array[i];
      array[i] = array[randomPosition];
      array[randomPosition] = temp;
    }
    return array;
  }

  public static int[][] sort(int[][] array) {
    //Sort an array (immune to quicksort TLE)

    Arrays.sort(array, new Comparator<int[]>() {
      @Override
      public int compare(int[] a, int[] b) {
        return a[1]-b[1]; //ascending order
      }
    });
    return array;
  }

  public static long[][] sort(long[][] array) {
    //Sort an array (immune to quicksort TLE)
    Random rgen = new Random();
    for (int i = 0; i < array.length; i++) {
      int randomPosition = rgen.nextInt(array.length);
      long[] temp = array[i];
      array[i] = array[randomPosition];
      array[randomPosition] = temp;
    }
    Arrays.sort(array, new Comparator<long[]>() {
      @Override
      public int compare(long[] a, long[] b) {
        if (a[0] < b[0])
          return -1;
        else if (a[0] > b[0])
          return 1;
        else
          return 0;
      }
    });
    return array;
  }

  static class MyScanner {
    private BufferedReader br;
    private StringTokenizer st;

    MyScanner() {
      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();
    }

    int nextInt() {
      return Integer.parseInt(next());
    }

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

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

    String nextLine(){
      String str = "";
      try {
        str = br.readLine();
      } catch (IOException e) {
        e.printStackTrace();
      }
      return str;
    }
  }

  static class Pair<K,V> {

    public K key;
    public V value;

    public Pair(K key, V value) {
      this.key = key;
      this.value = value;
    }

    @Override
    public String toString() {
      return key + ":" + value;
    }

    @Override
    public int hashCode() {
      return key.hashCode() * 13 + (value == null ? 0 : value.hashCode());
    }

    @Override
    public boolean equals(Object o) {
      if (this == o) return true;
      if (o instanceof Pair) {
        Pair pair = (Pair) o;
        return Objects.equals(key, pair.key) && Objects.equals(value, pair.value);
      }
      return false;
    }

    public Pair<V, K> invert() {
      return new Pair<>(value, key);
    }
  }

  static class Triple<A, B, C> {
    public A a;
    public B b;
    public C c;

    public Triple(A a, B b, C c) {
      this.a = a;
      this.b = b;
      this.c = c;
    }

    @Override
    public String toString() {
      return a + ":" + b + ":" + c;
    }

    @Override
    public int hashCode() {
      return (a == null ? 0 : a.hashCode()) * 13 + (b == null ? 0 : b.hashCode()) * 41 + (c == null ? 0 : c.hashCode());
    }

    @Override
    public boolean equals(Object o) {
      if (this == o) return true;
      if (o instanceof Triple) {
        Triple triple = (Triple) o;
        return Objects.equals(a, triple.a) && Objects.equals(b, triple.b) && Objects.equals(c, triple.c);
      }
      return false;
    }
  }
}