M. Museum Tickets
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

A group of $$$n$$$ friends wants to visit the Acropolis Museum in Athens.

The museum offers two types of tickets. An individual ticket costs $$$a$$$ euros and admits one person. A group ticket costs $$$b$$$ euros and admits all $$$n$$$ friends.

What is the minimum total cost of tickets that allow all the friends to enter the museum?

Input

The first line contains an integer $$$n$$$ ($$$1\le n\le1000$$$): the number of friends.

The second line contains an integer $$$a$$$ ($$$1\le a\le1000$$$): the price of an individual ticket, in euros.

The third line contains an integer $$$b$$$ ($$$1\le b\le1000$$$): the price of a group ticket, in euros.

Output

Print one integer: the minimum total cost, in euros.

Examples
Input
4
8
25
Output
25
Input
3
7
30
Output
21
Input
5
6
30
Output
30
Note

In the first example, four individual tickets cost $$$32$$$ euros, while a group ticket costs $$$25$$$ euros. Buy a group ticket.

In the second example, three individual tickets cost $$$21$$$ euros, which is cheaper than a group ticket.

In the third example, both options cost $$$30$$$ euros.