Chocolate lover

Aziz is very fond of eating chocolate. But since chocolate is very bad for teeth, his father won't let him eat a lot of chocolate. This time he managed to convince his father and get permission to eat one chocolate every day. Aziz loves two types of chocolate. One weighs $a$ grams, the other $b$ grams. Aziz's father allowed him to eat one chocolate every day for $n$ days, but with condition that he should not eat the same chocolate for two days in a row. Now Aziz is worried about only one question. How to make sure that within $n$ days he could eat the maximum amount (in grams) of chocolate.

Help him with this.

Input

One line contains three integers $n,a$ and $b(1\le n,a,b\le 10^9)$.

Output

Print the maximum amount of chocolate (in grams) that Aziz can consume during $n$ days.

Examples