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 codeforcesQuestions;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.*;
public class cdf3a
{
	static void merge(int arr[], int l, int m, int r) 
    { 
        int n1 = m - l + 1; 
        int n2 = r - m; 
        int L[] = new int [n1]; 
        int R[] = new int [n2]; 
        for (int i=0; i<n1; ++i) 
            L[i] = arr[l + i]; 
        for (int j=0; j<n2; ++j) 
            R[j] = arr[m + 1+ j]; 
        int i = 0, j = 0; 
        int k = l; 
        while (i < n1 && j < n2) 
        { 
            if (L[i] <= R[j]) 
            { 
                arr[k] = L[i]; 
                i++; 
            } 
            else
            { 
                arr[k] = R[j]; 
                j++; 
            } 
            k++; 
        } 
        while (i < n1) 
        { 
            arr[k] = L[i]; 
            i++; 
            k++; 
        } 
        while (j < n2) 
        { 
            arr[k] = R[j]; 
            j++; 
            k++; 
        } 
    } 
    static void sort(int arr[], int l, int r) 
    { 
        if (l < r) 
        { 
            int m = (l+r)/2; 
            sort(arr, l, m); 
            sort(arr , m+1, r); 
            merge(arr, l, m, r); 
        } 
    } 
    public static int lowerBound(int[] array, int length, int value) 
	{
        int low = 0;
        int high = length;
        while (low < high) 
        {
            final int mid = (low + high) / 2;
            //checks if the value is less than middle element of the array
            if (value <= array[mid]) 
            {
                high = mid;
            } 
            else 
            {
                low = mid + 1;
            }
        }
        return low;
    }
	public static int upperBound(int[] array, int length, int value) 
	{
        int low = 0;
        int high = length;
        while (low < high) {
            final int mid = (low + high) / 2;
            if (value >= array[mid]) {
                low = mid + 1;
            } else {
                high = mid;
            }
        }
        return low;
    }
    static int gcd(int a, int b) 
    { 
      if (b == 0) 
        return a; 
      return gcd(b, a % b);  
    } 
    static long power(long n,long m)
    {
    	if(m==0)
    		return 1;
    	long ans=1;
    	while(m>0)
    	{
    		ans=ans*n;
    		m--;
    	}
    	return ans;
    }
    static int BinarySearch(int arr[], int x) 
    { 
        int l = 0, r = arr.length - 1; 
        while (l <= r) { 
            int m = l + (r - l) / 2; 
            if (arr[m] == x) 
                return m; 
            if (arr[m] < x) 
                l = m + 1; 
            else
                r = m - 1; 
        } 
        return -1; 
    } 
	public static void main(String args[])throws Exception
	{
		BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
		int cas=1;//Integer.parseInt(br.readLine());
		ArrayList <String> arrli=new ArrayList<String>();
	    for(int i=1;i<=cas;i++)
	    {
	        String s=br.readLine();
	        String t=br.readLine();
	        int x1=(int)s.charAt(0)-97;
	        int y1=(int)s.charAt(1)-48;
	        int x2=(int)t.charAt(0)-97;
	        int y2=(int)t.charAt(1)-48;
	        int ans=0;
	        //System.out.println(x1+" "+y1+" "+x2+" "+y2);
	        while(true)
	        {
	        	if(x1==x2&&y1==y2)
	        		break;
	        	ans++;
	        	if(x1==x2&&y1<y2)
	        	{
	        		y1++;
	        		arrli.add("U");
	        	}
	        	else if(x1==x2&&y1>y2)
	        	{
	        		y1--;
	        		arrli.add("D");
	        	}
	        	else if(y1==y2&&x1>x2)
	        	{
	        		x1--;
	        		arrli.add("L");
	        	}
	        	else if(y1==y2&&x1<x2)
	        	{
	        		x1++;
	        		arrli.add("R");
	        	}
	        	else if(y1<y2&&x1<x2)
	        	{
	        		y1++;
	        		x1++;
	        		arrli.add("RU");
	        	}
	        	else if(y1>y2&&x1<x2)
	        	{
	        		y1--;
	        		x1++;
	        		arrli.add("RD");
	        	}
	        	else if(y1<y2&&x1>x2)
	        	{
	        		y1++;
	        		x1--;
	        		arrli.add("LU");
	        	}
	        	else if(y1>y2&&x1>x2)
	        	{
	        		y1--;
	        		x1--;
	        		arrli.add("LD");
	        	}
	        	
	        	//System.out.println(x1+" "+y1+" "+x2+" "+y2);
	        }
	        System.out.println(ans);
	        for(int j=0;j<ans;j++)
	        	System.out.println(arrli.get(j));
	    }
	}
}