Consider an infinite two-dimensional coordinate plane. Takahashi, who is initially standing at $(0,0)$, will do $N$ jumps in one of the four directions he chooses every time: up, down, left, or right. The length of each jump is fixed. Specifically, the $i$-th jump should cover the distance of $D_i$. Determine whether it is possible to be exactly at $(A, B)$ after $N$ jumps. If it is possible, show one way to do so.

Here, for each direction, a jump of length $D$ from $(X, Y)$ takes him to the following point:

-   up: $(X,Y) \to (X,Y+D)$
-   down: $(X,Y) \to (X,Y-D)$
-   left: $(X,Y) \to (X-D,Y)$
-   right: $(X,Y) \to (X+D,Y)$.

Input is given from Standard Input in the following format:

```
$N$ $A$ $B$
$D_1$ $D_2$ $\ldots$ $D_N$
```

In the first line, print `Yes` if there is a desired sequence of jumps, and `No` otherwise.  
In the case of `Yes`, print in the second line a desired sequence of jumps as a string $S$ of length $N$ consisting of `U` , `D` , `L` , `R`, as follows:

-   if the $i$-th jump is upward, the $i$-th character should be `U`;
-   if the $i$-th jump is downward, the $i$-th character should be `D`;
-   if the $i$-th jump is to the left, the $i$-th character should be `L`;
-   if the $i$-th jump is to the right, the $i$-th character should be `R`.

-   $1 \leq N \leq 2000$
-   $\lvert A\rvert, \lvert B\rvert \leq 3.6\times 10^6$
-   $1 \leq D_i \leq 1800$
-   All values in input are integers.

Yes
LDR

If he jumps left, down, right in this order, Takahashi moves (0,0)→(−1,0)→(−1,−2)→(2,−2) and ends up at (2,−2), which is desired.

No

It is impossible to be exactly at (1,0) after the two jumps.