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.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import static java.lang.Math.*;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Stack;
import java.util.StringTokenizer;

/*
 * To change this template, choose Tools | Templates
 * and open the template in the editor.
 */
/**
 *
 * @author Trung Pham
 */
public class A {

    public static int[] x = {0, 1, 0, -1, -1, 1, -1, 1};
    public static int[] y = {1, 0, -1, 0, 1, -1, -1, 1};

    public static void main(String[] args) {
        Scanner in = new Scanner();
        PrintWriter out = new PrintWriter(System.out);
        String cur = in.next();
        String to = in.next();
        int[][] map = new int[8][8];
        for (int[] val : map) {
            Arrays.fill(val, -1);
        }
        int curX = cur.charAt(0) - 'a';
        int curY = 7 - (cur.charAt(1) - '1');
        int nexX = to.charAt(0) - 'a';
        int nexY = 7 - (to.charAt(1) - '1');
        map[curX][curY] = -2;
        ArrayList<Point> q = new ArrayList();
        q.add(new Point(curX, curY));
        while (!q.isEmpty()) {
            Point temp = q.remove(0);
            for (int i = 0; i < 8; i++) {
                int tempX = temp.x + x[i];
                int tempY = temp.y + y[i];
                if (tempX >= 0 && tempX < 8 && tempY >= 0 && tempY < 8 && map[tempX][tempY] == -1) {
                    map[tempX][tempY] = i;
                    q.add(new Point(tempX, tempY));
                }
            }
        }
        Stack<String> stack = new Stack();
        while (map[nexX][nexY] != -2) {
            int val = map[nexX][nexY];
            //  System.out.println(val + " " + nexX + " " + nexY);
            nexX -= x[val];
            nexY -= y[val];
            if (val == 0) {
                stack.push("D");
            } else if (val == 1) {
                stack.push("R");
            } else if (val == 2) {
                stack.push("U");
            } else if (val == 3) {
                stack.add("L");
            } else if (val == 4) {
                stack.push("LD");
            } else if (val == 5) {
                stack.push("RU");
            } else if (val == 6) {
                stack.push("LU");
            } else if (val == 7) {
                stack.push("RD");
            }
        }
        //System.out.println("HE HE");
        out.println(stack.size());
        while (!stack.isEmpty()) {
            out.println(stack.pop());
        }
        out.close();
    }

    static int gcd(int a, int b) {
        if (b == 0) {
            return a;
        } else {
            return gcd(b, a % b);
        }
    }

    static int pow(int a, int b) {
        if (b == 0) {
            return 1;
        }
        if (b == 1) {
            return a;
        }
        int val = pow(a, b / 2);
        if (b % 2 == 0) {

            return val * val;
        } else {
            return val * val * a;
        }
    }

//    static Point intersect(Point a, Point b, Point c) {
//        double D = cross(a, b);
//        if (D != 0) {
//            return new Point(cross(c, b) / D, cross(a, c) / D);
//        }
//        return null;
//    }
//
//    static Point convert(Point a, double angle) {
//        double x = a.x * cos(angle) - a.y * sin(angle);
//        double y = a.x * sin(angle) + a.y * cos(angle);
//        return new Point(x, y);
//    }
    static Point minus(Point a, Point b) {
        return new Point(a.x - b.x, a.y - b.y);
    }

    static Point add(Point a, Point b) {
        return new Point(a.x + b.x, a.y + b.y);
    }

    static double cross(Point a, Point b) {
        return a.x * b.y - a.y * b.x;
    }

    static class Point {

        int x, y;

        Point(int x, int y) {
            this.x = x;
            this.y = y;
        }

        @Override
        public String toString() {
            return "Point: " + x + " " + y;
        }
    }

    static class Scanner {

        BufferedReader br;
        StringTokenizer st;

        public Scanner() {
            //System.setOut(new PrintStream(new BufferedOutputStream(System.out), true));
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        public String next() {


            while (st == null || !st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (Exception e) {
                    throw new RuntimeException();
                }
            }
            return st.nextToken();
        }

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

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

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

        public String nextLine() {
            st = null;
            try {
                return br.readLine();
            } catch (Exception e) {
                throw new RuntimeException();
            }
        }

        public boolean endLine() {
            try {
                String next = br.readLine();
                while (next != null && next.trim().isEmpty()) {
                    next = br.readLine();
                }
                if (next == null) {
                    return true;
                }
                st = new StringTokenizer(next);
                return st.hasMoreTokens();
            } catch (Exception e) {
                throw new RuntimeException();
            }
        }
    }
}