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:
#! python3


def get_num_pos(pos):
    cols = ['a', 'b', 'c', 'd', 'e', 'f', 'g', 'h']
    rows = ['1', '2', '3', '4', '5', '6', '7', '8']
    col, row = pos[0], pos[1]
    return [cols.index(col), rows.index(row)]

slanting_mv = {(1, 1): 'RU',  (-1, 1): 'LU',  (1, -1): 'RD',  (-1, -1): 'LD'}
parallel_mv =  {(1, 0): 'R', (0, 1): 'U', (-1, 0): 'L', (0, -1): 'D'}

start_npos = get_num_pos(input())
dest_npos = get_num_pos(input())

diff_npos = [ dest_npos[i] - start_npos[i] for i in range(len(dest_npos))]
x, y = diff_npos

slanting_mv_num = min(abs(x), abs(y))
parallel_mv_num = max(abs(x), abs(y)) - slanting_mv_num

sloss_cmd = []
sloss_val = []
for smv, cmd in slanting_mv.items():
    sloss_cmd.append(smv)
    sloss_val.append(abs(x - smv[0]*slanting_mv_num) + abs(y - smv[1]*slanting_mv_num))
min_sloss_val = min(sloss_val)
min_sloss_cmd = sloss_cmd[sloss_val.index(min_sloss_val)]
cmd_list = [slanting_mv[min_sloss_cmd] for i in range(slanting_mv_num)]

x -= min_sloss_cmd[0]*slanting_mv_num
y -= min_sloss_cmd[1]*slanting_mv_num

ploss_cmd = []
ploss_val = []
for pmv, cmd in parallel_mv.items():
    ploss_cmd.append(pmv)
    ploss_val.append(abs(x - pmv[0]*parallel_mv_num) + abs(y - pmv[1]*parallel_mv_num))
min_ploss_val = min(ploss_val)
min_ploss_cmd = ploss_cmd[ploss_val.index(min_ploss_val)]
cmd_list += [parallel_mv[min_ploss_cmd] for i in range(parallel_mv_num)]

print(slanting_mv_num + parallel_mv_num)
print('\n'.join(cmd_list))


# class Board:
#     def __init__(self):
#         self.cols = ['a', 'b', 'c', 'd', 'e', 'f', 'g', 'h']
#         self.rows = ['1', '2', '3', '4', '5', '6', '7', '8']
#
#     def move(self, now_pos, mv):
#         now_num_pos = self.get_num_pos(now_pos)
#         mv_dist = [now_num_pos[i] + mv[i] for i in range(2)]
#         if mv_dist[0] in range(len(self.cols)) and mv_dist[1] in range(len(self.rows)):
#             return self.get_chara_pos(mv_dist)
#         else:
#             return 'out'
#
#     def get_num_pos(self, pos):
#         col, row = pos[0], pos[1]
#         return (self.cols.index(col), self.rows.index(row))
#
#     def get_chara_pos(self, num_pos):
#         return self.cols[num_pos[0]] + self.rows[num_pos[1]]
#
# class King:
#     def __init__(self, start_position):
#         self.position = start_position
#         self.mvdict = {'R': (1, 0), 'U': (0, 1), 'L': (-1, 0), 'D': (0, -1),
#                        'RU': (1, 1), 'LU': (-1, 1), 'RD': (1, -1), 'LD': (-1, -1)}
#         self.board = Board()
#
#     def get_pos():
#         return self.pos
#
#     def get_cmd_list():
#         return self.mvdict.keys()
#
#     def move(cmd):
#         if cmd not in self.mvdict:
#             print('Command not found')
#             return
#         if self.board.move(self.position, self.mvdict[cmd]) == 'out':
#             print('Can\'t move anymore')
#             return
#         self.position = self.board.move(self.position, self.mvdict[cmd])


# width = int(input())
# height = int(input())
# print('width =', width, ', height =', height)
#
# for i in range(width + height - 1):
#     print('--------- i =', i)
#     if i < min(width, height)-1:
#         a, b = i, i+1
#     elif i < max(width, height):
#         a, b = i, min(width, height)
#     else:
#         a, b = max(width, height)-1, (width+height)-i
#     for j in range(b):
#         x, y = (a, i-a) if width < height else (i-a, a)
#         a -= 1
#         print(x, y)