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 PYTHON3):

Solution:
#####################################################################################
# - Programming Credits - atifcppprogrammer 3/6/19.
#####################################################################################
# Importing Modules.
import operator as op
#####################################################################################
# Class Definition.
class ShortestPathComputer:
    # Method to print Path for our king.
    def print_path(self):
        print(len(self.path))
        for i in range(len(self.path)):
            print(self.path[i])
    # Method to generate shortest path for our king.
    def generate_shortest_path(self):
        curr_coords = self.init_coords
        while self.manhattan_distance(curr_coords,self.final_coords)!=0:
            next = self.next_neighbour(curr_coords)
            curr_coords = self.relative_coords(curr_coords,next)
            self.path.append(next)
        return self
    # Method to decide which neighbour to jump to next in a greedy manner.
    def next_neighbour(self,coords):
        neighbours = self.list_neighbours(coords)
        min_neighbour,min_dist = 'U',ShortestPathComputer.MAX_MANHATTAN_DISTANCE
        for neighbour in neighbours:
            neighbour_coords = self.relative_coords(coords,neighbour)
            new_dist = self.manhattan_distance(neighbour_coords,self.final_coords)
            if new_dist<=min_dist:
                min_dist = new_dist;min_neighbour = neighbour
        return min_neighbour
    # Method to return list of Neighbours for given square.
    def list_neighbours(self,coords):
        neighbours = []
        values = list(ShortestPathComputer.relative.values())
        keys   = list(ShortestPathComputer.relative.keys())
        neighbours = []
        # Finding Legitimate neighbours.
        for i in range(ShortestPathComputer.MAX_NEIGHBOURS):
            key,value = keys[i],values[i]
            if self.coords_are_legit(self.relative_coords(coords,key)):
                neighbours.append(key)
        return neighbours
    # Method to compute new coordinates relative to given coordinates.
    def relative_coords(self,coords,marker):
        rel_coords = ShortestPathComputer.relative[marker]
        return tuple(map(op.add,coords,rel_coords))
    # Method to determine if coords are legitimate.
    def coords_are_legit(self,coords):
        return 0<=coords[0]<8 and 0<=coords[1]<8
    # Method to compute Manhattan Distance between given Squares.
    def manhattan_distance(self,coordsA,coordsB):
        return abs(coordsA[0]-coordsB[0])+abs(coordsA[1]-coordsB[1])
    # Method to parse square location given in chess notation.
    def parse_chess_square(self,square):
        i,j = tuple(square)
        return ShortestPathComputer.parseRow[j],ShortestPathComputer.parseCol[i]
    # Constructor.
    def __init__(self,squareA,squareB):
        # Parsing First Square.
        self.init_coords  = self.parse_chess_square(squareA)
        # Parsing Second Square.
        self.final_coords = self.parse_chess_square(squareB)
        # Path of the King to be computed.
        self.path = []
    # Defining Class Variables.
    MAX_NEIGHBOURS,MAX_MANHATTAN_DISTANCE = 8,14
    # For Parsing.
    parseCol = {'a':0,'b':1,'c':2,'d':3,'e':4,'f':5,'g':6,'h':7}
    parseRow = {'1':7,'2':6,'3':5,'4':4,'5':3,'6':2,'7':1,'8':0}
    # For Manhattan Distances.
    relative = {'U':(-1,0),'D':(1,0),'L':(0,-1),'R':(0,1),
        'RU':(-1,1),'RD':(1,1),'LU':(-1,-1),'LD':(1,-1)}
#####################################################################################
# Driver Program.
path_finder = ShortestPathComputer(input(),input())
path_finder.generate_shortest_path().print_path()
#####################################################################################