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

见题面

见题面