Takahashi has a red jewel of level $N$. (He has no other jewels.)  
Takahashi can do the following operations any number of times.

-   Convert a red jewel of level $n$ ($n$ is at least $2$) into "a red jewel of level $(n-1)$ and $X$ blue jewels of level $n$".
-   Convert a blue jewel of level $n$ ($n$ is at least $2$) into "a red jewel of level $(n-1)$ and $Y$ blue jewels of level $(n-1)$".

Takahashi wants as many blue jewels of level $1$ as possible. At most, how many blue jewels of level $1$ can he obtain by the operations?

Input is given from Standard Input in the following format:

```
$N$ $X$ $Y$
```

Print the answer.

-   $1 \leq N \leq 10$
-   $1 \leq X \leq 5$
-   $1 \leq Y \leq 5$
-   All values in input are integers.

12

Takahashi can obtain 12 blue jewels of level 1 by the following conversions.

• First, he converts a red jewel of level 2 into a red jewel of level 1 and 3 blue jewels of level 2.
  • After this operation, Takahashi has 1 red jewel of level 1 and 3 blue jewels of level 2.
• Next, he repeats the following conversion 3 times: converting a blue jewel of level 2 into a red jewel of level 1 and 4 blue jewels of level 1.
  • After these operations, Takahashi has 4 red jewels of level 11 and 12 blue jewels of level 1.
• He cannot perform a conversion anymore.

He cannot obtain more than 12 blue jewels of level 1, so the answer is 12.

0

Takahashi may not be able to obtain a blue jewel of level 1.