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:
import java.awt.*;
import java.util.*;
import java.io.*;

public class Main {

    static class Parser
    {
        final private int BUFFER_SIZE = 1 << 16;

        private DataInputStream din;
        private byte[] buffer;
        private int bufferPointer, bytesRead;

        public Parser(InputStream in)
        {
            din = new DataInputStream(in);
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

        public long nextLong() throws Exception
        {
            long ret = 0;
            byte c = read();
            while (c <= ' ') c = read();
            boolean neg = c == '-';
            if (neg) c = read();
            do
            {
                ret = ret * 10 + c - '0';
                c = read();
            } while (c > ' ');
            if (neg) return -ret;
            return ret;
        }

        //reads in the next string
        public String next() throws Exception
        {
            StringBuilder ret =  new StringBuilder();
            byte c = read();
            while (c <= ' ') c = read();
            do
            {
                ret = ret.append((char)c);
                c = read();
            } while (c > ' ');
            return ret.toString();
        }

        public int nextInt() throws Exception
        {
            int ret = 0;
            byte c = read();
            while (c <= ' ') c = read();
            boolean neg = c == '-';
            if (neg) c = read();
            do
            {
                ret = ret * 10 + c - '0';
                c = read();
            } while (c > ' ');
            if (neg) return -ret;
            return ret;
        }

        private void fillBuffer() throws Exception
        {
            bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
            if (bytesRead == -1) buffer[0] = -1;
        }

        private byte read() throws Exception
        {
            if (bufferPointer == bytesRead) fillBuffer();
            return buffer[bufferPointer++];
        }
    }
    static class OutputWriter
    {
        private PrintWriter writer;

        public OutputWriter(OutputStream stream)
        {
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(
                    stream)));
        }

        public OutputWriter(Writer writer)
        {
            this.writer = new PrintWriter(writer);
        }

        public void println(int x)
        {
            writer.println(x);
        }

        public void print(int x)
        {
            writer.print(x);
        }

        public void println(char x)
        {
            writer.println(x);
        }

        public void print(char x)
        {
            writer.print(x);
        }

        public void println(int array[], int size)
        {
            for (int i = 0; i < size; i++)
                println(array[i]);
        }

        public void print(int array[], int size)
        {
            for (int i = 0; i < size; i++)
                print(array[i] + " ");
        }

        public void println(long x)
        {
            writer.println(x);
        }

        public void print(long x)
        {
            writer.print(x);
        }

        public void println(long array[], int size)
        {
            for (int i = 0; i < size; i++)
                println(array[i]);
        }

        public void print(long array[], int size)
        {
            for (int i = 0; i < size; i++)
                print(array[i]);
        }

        public void println(float num)
        {
            writer.println(num);
        }

        public void print(float num)
        {
            writer.print(num);
        }

        public void println(double num)
        {
            writer.println(num);
        }

        public void print(double num)
        {
            writer.print(num);
        }

        public void println(String s)
        {
            writer.println(s);
        }

        public void print(String s)
        {
            writer.print(s);
        }

        public void println()
        {
            writer.println();
        }

        public void printSpace()
        {
            writer.print(" ");
        }

        public void printf(String format, Object args)
        {
            writer.printf(format, args);
        }

        public void flush()
        {
            writer.flush();
        }

        public void close()
        {
            writer.close();
        }

    }
    static class Graph {
        private int V;
        private LinkedList<Integer> adj[];

        Graph(int v) {
            V = v;
            adj = new LinkedList[v];
            for (int i = 0; i < v; ++i)
                adj[i] = new LinkedList();
        }

        void addEdge(int v, int w) {
            adj[v].add(w);
        }
        void BFS(int s) {
            boolean visited[] = new boolean[V];
            LinkedList<Integer> queue = new LinkedList<Integer>();
            visited[s] = true;
            queue.add(s);

            while (queue.size() != 0) {
                s = queue.poll();
                System.out.print(s + " ");
                Iterator<Integer> i = adj[s].listIterator();
                while (i.hasNext()) {
                    int n = i.next();
                    if (!visited[n]) {
                        visited[n] = true;
                        queue.add(n);
                    }
                }
            }
        }
    }
    static class Point{
        int x;
        int y;
        int dist;
        String ans;
        Point(int x,int y,int dist,String ans){
            this.x=x;
            this.y=y;
            this.dist=dist;
            this.ans=ans;
        }
    }
    public static void main(String args[]) throws Exception {
        Parser s = new Parser(System.in);
        OutputWriter out = new OutputWriter(System.out);

        String moves[]={"U","RU","R","RD","D","LD","L","LU"};

            boolean Visited[][]=new boolean[8][8];
            int[] xValues = {-1, -1, 0, 1, 1, 1, 0, -1};
            int[] yValues = {0, 1, 1, 1, 0, -1, -1, -1};
            Queue<Point> q =new LinkedList<>();
            String start = s.next();
            String end = s.next();

            int y1 = start.charAt(0) - 'a';
            int x1 = 7-(Integer.parseInt(start.substring(1))-1);

            int y2 = end.charAt(0) - 'a';
            int x2 = 7-(Integer.parseInt(end.substring(1))-1);
            q.add(new Point(x1,y1,0,""));
            Point curr=null;
            while(!q.isEmpty()){
                curr=q.remove();
                if(curr.x==x2&&curr.y==y2){
                    break;
                }
                for(int i=0;i<8;i++){
                    int xval=curr.x+xValues[i];
                    int yval=curr.y+yValues[i];
                    if(xval<8&&yval<8&&xval>=0&&yval>=0&&!Visited[xval][yval]){
                        Visited[xval][yval]=true;
                        q.add(new Point(xval,yval,curr.dist+1,(curr.ans+i)));}
                }

            }
            out.println(curr.dist);
            String val=curr.ans;
            for(int i=0;i<val.length();i++){
                int j=val.charAt(i)-48;
                out.println(moves[j]);
            }
        out.close();
    }
}