Problem Statement

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.
• $1 \leq N \leq 1000$
• $-10^9 \leq X_i \leq 10^9$
• $-10^9 \leq Y_i \leq 10^9$

Partial Score

• In the test cases worth $300$ points, $-10 \leq X_i \leq 10$ and $-10 \leq Y_i \leq 10$ hold.

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 $i$.