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:
import copy
N = int(input())
X = []
X.append(list(map(int, input().split())))
#Y = []
T = (X[0][0] + X[0][1]) % 2
max = abs(X[0][0]) + abs(X[0][1])
for i in range(1,N):
  X.append(list(map(int, input().split())))
  t = abs(X[i][0]) + abs(X[i][1])
  if t % 2 != T:
    print(-1)
    exit()
  if max < t:
    max = t
    
# 奇数: D =    1, 2, 4, 8...
# 偶数: D = 1, 1, 2, 4, 8...
# sum(D) > max
D = []
sum = 0
if T == 0:
  max -= 1
t = 1
while 1:
  D.append(t)
  sum += t
  if sum >= max:
    break
  t *= 2
if T == 0:
  D.append(1)
D.reverse()

# m
print(len(D))
# d1, d2, ... dm
s = ""
for i in range(len(D)):
  s += str(D[i]) + " "
print (s)

# w1, w2, ... wm
for i in range(N):
  U = X[i][0] + X[i][1]
  V = X[i][0] - X[i][1]
  s = ""
  for j in range(len(D)):
    if U >= 0:
      if V >= 0:
        s += "R"
        U -= D[j]
        V -= D[j]
      else:
        s += "U"
        U -= D[j]
        V += D[j]
    else:
      if V >= 0:
        s += "D"
        U += D[j]
        V -= D[j]
      else:
        s += "L"
        U += D[j]
        V += D[j]
  print(s)