Problem: Snuke is introducing a robot arm with the following properties to his factory:

* The robot arm consists of m sections and m+1 joints. The sections are numbered 1, 2, ..., m, and the joints are numbered 0, 1, ..., m. Section i connects Joint i-1 and Joint i. The length of Section i is d_i.
* For each section, its mode can be specified individually. There are four modes: `L`, `R`, `D` and `U`. The mode of a section decides the direction of that section. If we consider the factory as a coordinate plane, the position of Joint i will be determined as follows (we denote its coordinates as (x_i, y_i)):
* (x_0, y_0) = (0, 0).
* If the mode of Section i is `L`, (x_{i}, y_{i}) = (x_{i-1} - d_{i}, y_{i-1}).
* If the mode of Section i is `R`, (x_{i}, y_{i}) = (x_{i-1} + d_{i}, y_{i-1}).
* If the mode of Section i is `D`, (x_{i}, y_{i}) = (x_{i-1}, y_{i-1} - d_{i}).
* If the mode of Section i is `U`, (x_{i}, y_{i}) = (x_{i-1}, y_{i-1} + d_{i}).



Snuke would like to introduce a robot arm so that the position of Joint m can be matched with all of the N points (X_1, Y_1), (X_2, Y_2), ..., (X_N, Y_N) by properly specifying the modes of the sections. Is this possible? If so, find such a robot arm and how to bring Joint m to each point (X_j, Y_j).

Constraints

* All values in input are integers.
* 1 \leq N \leq 1000
* -10^9 \leq X_i \leq 10^9
* -10^9 \leq Y_i \leq 10^9

Input

Input is given from Standard Input in the following format:


N
X_1 Y_1
X_2 Y_2
:
X_N Y_N


Output

If the condition can be satisfied, follow the following format. If the condition cannot be satisfied, print `-1`.


m
d_1 d_2 ... d_m
w_1
w_2
:
w_N


m and d_i are the configurations of the robot arm. Refer to the problem statement for what each of them means. Here, 1 \leq m \leq 40 and 1 \leq d_i \leq 10^{12} must hold. Also, m and d_i must all be integers.

w_j is a string of length m that represents the way to bring Joint m of the robot arm to point (X_j, Y_j). The i-th character of w_j should be one of the letters `L`, `R`, `D` and `U`, representing the mode of Section i.

Examples

Input

3
-1 0
0 3
2 -1


Output

2
1 2
RL
UU
DR


Input

5
0 0
1 0
2 0
3 0
4 0


Output

-1


Input

2
1 1
1 1


Output

2
1 1
RU
UR


Input

3
-7 -3
7 3
-3 -7


Output

5
3 1 4 1 5
LRDUL
RDULR
DULRD

Solution (in PYTHON3):

Solution:
N=int(input())
p=[[int(i) for i in input().split()] for i in range(N)]
p_copy=list(p)
p_copy.sort(key=lambda x:x[0]+x[1])
length=abs(p_copy[N-1][0])+abs(p_copy[N-1][1])
if length%2==0:
  edge=[1]
  a=1
  while a<length:
    edge.append(a)
    a=2*a
  edge.reverse()
else:
  edge=[]
  a=1
  while a<length:
    edge.append(a)
    a=2*a
  edge.reverse()
if len(edge)>40 or edge[len(edge)-1]>10**12:
  print(-1)
  exit()
w=[""]*N
for n in range(N):
  x,y=p[n][0],p[n][1]
  if (x+y)%2!=length%2:
    print(-1)
    exit()
  else:
    a,b=0,0
    for e in edge:
      R=abs(x-(a+e))+abs(y-(b))
      L=abs(x-(a-e))+abs(y-(b))
      U=abs(x-(a))+abs(y-(b+e))
      D=abs(x-(a))+abs(y-(b-e))
      if min([R,L,U,D])==R:
        a+=e
        w[n]+="R"
      elif min([R,L,U,D])==L:
        a+=-e
        w[n]+="L"
      elif min([R,L,U,D])==U:
        b+=e
        w[n]+="U"
      else:
        b+=-e
        w[n]+="D"
  
print(len(edge))
map_edge=map(str,edge)
print(" ".join(map_edge))
for n in range(N):
  print(w[n])