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 PYTHON3):

Solution:
# -*- coding: utf-8 -*-
"""
Created on Mon May 11 15:03:20 2020

@author: alexi
"""


class Node():
    
    def __init__(self, parent = None, position = None):
        self.parent = parent
        self.position = position
        self.g = 0
        self.h = 0
        self.f = 0
        
    def __eq__(self, other):
        return self.position == other.position
    
def heuristic(A, B):
    return abs(A[0]-B[0]) + abs(A[1]-B[1])

def Astar(maze, start, end):
    
    start_node = Node(None, start)
    start_node.g = 0
    start_node.h = heuristic(start, end)
    start_node.f = start_node.g + start_node.h
    
    end_node = Node(None, end)
    end_node.g = heuristic(start, end)
    end_node.h = 0
    end_node.f = end_node.g + end_node.h

    open_list = []
    closed_list = []
    
    open_list.append(start_node)
    
    while True:
        
        if len(open_list) == 0:
            return -1
        
        current_node = open_list[0]
        current_index = 0
        
        for index, item in enumerate(open_list):
            if item.f < current_node.f:
                current_node = item
                current_index = index
        
        open_list.pop(current_index)
        closed_list.append(current_node)
        
        if current_node == end_node:
            path = []
            current = current_node
            while current is not None:
                path.append(current.position)
                current = current.parent
            
            return path[::-1]
        else:
            
            children = []
            
            for new_position in [(0, -1),(0, 1),(1, 0),(-1, 0),(-1, -1),(-1, 1),(1, -1),(1, 1)]:
                
                node_position = (current_node.position[0] + new_position[0], current_node.position[1] + new_position[1])
                
                if node_position[0] > (len(maze)-1) or node_position[0] < 0 or node_position[1] > (len(maze[len(maze)-1])-1) or node_position[1] < 0:
                    continue
                
                if maze[node_position[0]][node_position[1]] != 0:
                    continue
                
                new_node = Node(current_node, node_position)
                new_node.g = current_node.g + 1
                new_node.h = heuristic(new_node.position, end)
                new_node.f = new_node.g + new_node.h
                
                children.append(new_node)
                
            visited = False
            
            for child in children:
                for open_child in open_list:
                    if child.position == open_child.position:
                        if child.f < open_child.f:
                            open_child = child
                        visited = True
                
                for closed_child in closed_list:
                    if child.position == closed_child.position:
                        if child.f < closed_child.f:
                            closed_child = child
                        visited = True
                
                if visited:
                    visited = False
                else:
                    open_list.append(child)
                
                


def move_the_king():


    maze = [[0, 0, 0, 0, 0, 0, 0, 0],
            [0, 0, 0, 0, 0, 0, 0, 0],
            [0, 0, 0, 0, 0, 0, 0, 0],
            [0, 0, 0, 0, 0, 0, 0, 0],
            [0, 0, 0, 0, 0, 0, 0, 0],
            [0, 0, 0, 0, 0, 0, 0, 0],
            [0, 0, 0, 0, 0, 0, 0, 0],
            [0, 0, 0, 0, 0, 0, 0, 0],
          ]
    
    
    dic_letters = {'a':0,'b':1,'c':2,'d':3,'e':4,'f':5,'g':6,'h':7}
    dic_numbers = {8:0,7:1,6:2,5:3,4:4,3:5,2:6,1:7}
    dic_move = {(1,0):'D',(-1,0):'U',(0,1):'R',(0,-1):'L',(-1, -1):'LU',(-1, 1):'RU',(1, -1):'LD',(1, 1):'RD'}
    
    start = input()
    end = input()
    
    actual_start = (dic_numbers[int(start[1])],dic_letters[start[0]])
    actual_end = (dic_numbers[int(end[1])],dic_letters[end[0]])
    
    path = Astar(maze, actual_start, actual_end)
    print(len(path)-1)
    
    for i in range(1, len(path)):
        temp = (path[i][0] - path[i-1][0], path[i][1] - path[i-1][1])
        print(dic_move[temp])
    
    
    
move_the_king()