Buns

Huseyn likes buns very much, which are sold at ADA University in building C. It is known that

• you can buy one bun for $a$ qəpiks;

• you can buy three buns for $b$ qəpiks;

Huseyn wants to buy exactly $n$ buns. What is the least number of qəpiks he should spend?

Input

Three positive integers $a,b$ and $n$, each is not greater than $10^9$.

Output

Print the least amount of qəpiks that Huseyn should spend to buy exactly $n$ buns.

Examples