Bulk Buying

You may remember from Round 2 that Thomas really loves ducks. (Don't worry if you haven't done Round 2, though)

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You may have wondered how Thomas got all those ducks. The answer is that he buys them all in bulk from his favorite e-commerce website, AliDirect™. Specifically, he can buy ducks in lots of 2 for $A$ dollars, and lots of 3 for $B$ dollars.

Thomas wants to buy exactly $N$ ducks for the upcoming January training camp. Help him find the minimum amount he has to pay.

Input

The first line contains a single integer, $N$, the number of ducks Thomas would like to buy.

The second line contains a single integer, $A$, the cost of buying one lot of 2 ducks.

The third line contains a single integer, $B$, the cost of buying one lot of 3 ducks.

Output

You should print a single integer – the minimum cost of buying exactly $N$ ducks.

It is guaranteed that it will always be possible to buy exactly $N$ ducks.

Constraints

• $2 \le N \le 100\,000$ (Thomas buys a lot of ducks)
• $1 \le A,B \le 100$

Subtasks

• Subtask 1 (+20%): $A = 2, B = 3$
• Subtask 2 (+30%): $A = 3, B = 5$
• Subtask 3 (+50%): No further restrictions apply

Sample Explanations

Sample Input 1

The only way to buy 4 ducks is to buy 2 lots of 2 ducks, for a total of $2 \times 2 = 4$ dollars.

Sample Input 2

There are two different ways to buy 11 ducks:

• The first way is to buy 4 lots of 2 ducks and 1 lot of 3 ducks for a total of $4 \times 3 + 1 \times 5 = 17$ dollars.
• The second way is to buy 1 lot of 2 ducks and 3 lots of 3 ducks for a total of $1 \times 3 + 3 \times 5 = 18$ dollars.

The first way is cheaper, so the answer is 17.