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 $(X_j, Y_j)$.

Input is given from Standard Input in the following format:

```
$N$
$X_1$ $Y_1$
$X_2$ $Y_2$
$:$
$X_N$ $Y_N$
```

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 $i$.

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

2
1 2
RL
UU
DR

In the given way to bring Joint m of the robot arm to each $(X_j,Y_j)$, the positions of the joints will be as follows:

• To $(X_1,Y_1)=(−1,0)$: First, the position of Joint 0 is $(x_0,y_0)=(0,0)$. As the mode of Section 1 is R, the position of Joint 1 is $(x_1,y_1)=(1,0)$. Then, as the mode of Section 2 is L, the position of Joint 2 is $(x_2,y_2)=(−1,0)$.
• To $(X_2,Y_2)=(0,3):\ (x_0,y_0)=(0,0),\ (x_1,y_1)=(0,1),\ (x_2,y_2)=(0,3)$.
• To $(X3,Y3)=(2,−1):\ (x_0,y_0)=(0,0),\ (x_1,y_1)=(0,−1),\ (x_2,y_2)=(2,−1)$.

2
1 1
RU
UR

There may be duplicated points among $(X_j,Y_j)$.