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())
XY=[]
for i in range(N):
  XY.append(list(map(int,input().split())))
mr=abs(XY[0][0])+abs(XY[0][1])  
for i in range(1,N):
  if abs(XY[i][0])+abs(XY[i][1])>mr:
    mr=abs(XY[i][0])+abs(XY[i][1])
import math
m=int(math.log(mr,2)//1+1)
g=(XY[0][0]+XY[0][1])%2
cnt=0
for i in range(N):
  if (XY[i][0]+XY[i][1])%2==g:
    cnt+=1
if cnt!=N:
  print(-1)
else:
  if g==1:
    W=['']*N
    for i in range(N):
      for j in range(m):
        if abs(XY[i][0])>=abs(XY[i][1]) and XY[i][0]>=0:
          W[i]+='R'
          XY[i][0]-=2**(m-j-1)
        elif abs(XY[i][0])>=abs(XY[i][1]) and XY[i][0]<0:
          W[i]+='L'
          XY[i][0]+=2**(m-j-1)
        elif abs(XY[i][0])<abs(XY[i][1]) and XY[i][1]>=0:
          W[i]+='U'
          XY[i][1]-=2**(m-j-1)
        elif abs(XY[i][0])<abs(XY[i][1]) and XY[i][1]<0:
          W[i]+='D'
          XY[i][1]+=2**(m-j-1)
    print(m)
    for i in range(m):
       print(2**i,end=' ')
    print()
    for j in range(N):
      print(W[j][::-1])
  else:
    for i in range(N):
      XY[i][0]+=1
    W=['']*N
    for i in range(N):
      for j in range(m):
        if abs(XY[i][0])>=abs(XY[i][1]) and XY[i][0]>=0:
          W[i]+='R'
          XY[i][0]-=2**(m-j-1)
        elif abs(XY[i][0])>=abs(XY[i][1]) and XY[i][0]<0:
          W[i]+='L'
          XY[i][0]+=2**(m-j-1)
        elif abs(XY[i][0])<abs(XY[i][1]) and XY[i][1]>=0:
          W[i]+='U'
          XY[i][1]-=2**(m-j-1)
        elif abs(XY[i][0])<abs(XY[i][1]) and XY[i][1]<0:
          W[i]+='D'
          XY[i][1]+=2**(m-j-1)
    print(m+1)
    print(1,end=' ')
    for i in range(m):
      print(2**i,end=' ')
    print()
    for j in range(N):
      W[j]+='L'
      print(W[j][::-1])