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Contest: Task: Related: TaskB

Score : $100$ points

Problem Statement

You are parking at a parking lot. You can choose from the following two fee plans:

  • Plan $1$: The fee will be $A×T$ yen (the currency of Japan) when you park for $T$ hours.
  • Plan $2$: The fee will be $B$ yen, regardless of the duration.

Find the minimum fee when you park for $N$ hours.

Constraints

  • $1≤N≤20$
  • $1≤A≤100$
  • $1≤B≤2000$
  • All input values are integers.

Input

Input is given from Standard Input in the following format:

$N$ $A$ $B$

Output

When the minimum fee is $x$ yen, print the value of $x$.

Sample Input 1

7 17 120

Sample Output 1

119
  • If you choose Plan $1$, the fee will be $7×17=119$ yen.
  • If you choose Plan $2$, the fee will be $120$ yen.

Thus, the minimum fee is $119$ yen.

Sample Input 2

5 20 100

Sample Output 2

100

The fee might be the same in the two plans.

Sample Input 3

6 18 100

Sample Output 3

100