Score : $100$ points

Problem Statement

A fruit store sells apples. You may perform the following operations as many times as you want in any order:

• Buy one apple for $X$ yen (the currency in Japan).
• Buy three apples for $Y$ yen.

How much yen do you need to pay to obtain exactly $N$ apples?

Constraints

• $1 \leq X \leq Y \leq 100$
• $1 \leq N \leq 100$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$X$ $Y$ $N$

Output

Print the answer as an integer.

10 25 10

85

Buy three apples for $25$ yen three times and one apple for $10$ yen, and you will obtain exactly $10$ apples for a total of $85$ yen. You cannot obtain exactly $10$ apples for a lower cost, so the answer is $85$ yen.

10 40 10

100

It is optimal to buy an apple for $10$ yen $10$ times.

100 100 2

200

The only way to obtain exactly $2$ apples is to buy an apple for $100$ yen twice.

100 100 100

3400