Problem Statement

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

Input is given from Standard Input in the following format:
N X Y

Output

Print the answer.

Constraints

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

Sample Input 1

2 3 4

Sample Output 1

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 1 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.

Sample Input 2

1 5 5

Sample Output 2

0

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

Sample Input 3

10 5 5

Sample Output 3

3942349900

Note that the answer may not fit into a 32-bit integer type.

见题面 Input 部分

见题面 Output 部分