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:
s=input()
t=input()
d={}
j=1
for i in range(97,105):
    d[chr(i)]=j
    j+=1
#print(d)
x0,y0=d[s[0]],int(s[1])
x,y=d[t[0]],int(t[1])
n=max(abs(x-x0),abs(y-y0))#1 8 8 1
print(n)
while x0<x and y0<y:#Right upper diagonal
    if x0==x and y0==y:
        break
    print("RU")
    x0+=1
    y0+=1
while x0<x and y0>y:#right down diagonal
    if x0==x and y0==y:
        break
    print("RD")
    x0+=1
    y0-=1
while x0>x and y0<y:# Left upper diagonal
    if x0==x and y0==y:
        break
    print("LU")
    x0-=1
    y0+=1
while x0>x and y0>y: #right lower diagonal
    if x0==x and y0==y:
        break
    print("LD")
    x0-=1
    y0-=1
while x0<x: #along the right
    if x0==x:
        break
    print("R")
    x0+=1
while x0>x:  #along the left
    if x0==x:
        break
    print("L")
    x0-=1
while y0<y: #along the upper
    if y0==y:
        break
    print("U")
    y0+=1
while y0>y: #along the down
    if y0==y:
        break
    print("D")
    y0-=1