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:
"""
Codeforces
3A - Shortest path of the king
http://codeforces.com/problemset/problem/3/A

Héctor González Belver
../06/2018
"""

import sys
import heapq

ORD_A = ord('a')

DIRECTIONS4 = { 'L':(-1, 0), 'D':(0, 1), 'R':(1, 0), 'U':(0, -1) }
DIRECTIONS8 = dict(DIRECTIONS4) 
DIRECTIONS8.update({'LD':(-1, 1), 'RD':(1, 1), 'RU':(1, -1), 'LU':(-1, -1) })

class Grid():
    def __init__(self, width, height, allow_diagonals=False):
        self.width = width
        self.height = height
        self.allow_diagonals = allow_diagonals

    def neighbors(self, node):
        results = []
        x, y = node
        directions = DIRECTIONS8 if self.allow_diagonals else DIRECTIONS4  
        for k, (dx, dy) in directions.items():
            nx, ny = x + dx, y + dy
            if 0 <= nx < self.width and 0 <= ny < self.height:
                results.append(((nx,ny),k))
        return results 

class PriorityQueue:
    def __init__(self):
        self.heap = []
    
    def empty(self):
        return len(self.heap) == 0
    
    def add(self, item, cost):
        heapq.heappush(self.heap, (cost, item))
    
    def pop(self):
        return heapq.heappop(self.heap)[1]

def reconstruct_path(came_from, start, goal):
    current = goal
    path = []
    moves = []
    while current != start:
        path.append(current)
        moves.append(came_from[current][1])
        current = came_from[current][0]
    path.append(start) 
    path.reverse()
    moves.reverse()
    return path, moves

def diagonal_distance_h(goal, node, D, D2):
    #Admissible heuristic if diagonal movements are allowed
    #Compute the number of steps you take if you can’t take a diagonal,
    #then subtract the steps you save by using the diagonal
    #There are min(dx, dy) diagonal steps, and each one costs D2 
    #but saves you 2*D non-diagonal steps.
    dx = abs(goal[0] - node[0])
    dy = abs(goal[1] - node[1])
    return D * (dx + dy) + (D2 - 2 * D) * min(dx, dy) 

def Chebyshev_distance_h(goal, node):
    #It is also known as chessboard distance
    #Diagonal distance when D = 1 and D2 = 1
    return diagonal_distance_h(goal, node, 1, 1)


def greedy_best_first_search(grid, start, goal, costfn):
    #Explores in promising directions
    #Grid whithout obstacles
    frontier = PriorityQueue()
    frontier.add(start, 0)
    came_from = {}
    came_from[start] = None
    
    while not frontier.empty():
        current = frontier.pop()
        
        if current == goal:
            break
        
        for child, move in grid.neighbors(current):
            if child not in came_from:
                frontier.add(child, costfn(goal, child))
                came_from[child] = (current, move)
    
    return came_from

def convert_chess_coordinates(coord):
    return (ord(coord[0]) - ORD_A, 8 - int(coord[1]))

def main():
    start = convert_chess_coordinates(sys.stdin.readline().strip())
    goal = convert_chess_coordinates(sys.stdin.readline().strip())

    chess = Grid(8,8, allow_diagonals=True)

    moves = reconstruct_path(greedy_best_first_search(chess,start,goal,Chebyshev_distance_h), start, goal)[1]

    sys.stdout.write(str(len(moves)) + '\n')
    sys.stdout.write('\n'.join(moves) + '\n')

if __name__ == '__main__': 
  main()