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.
One line contains three integers n,a and b (1≤n,a,b≤109).
Print the maximum amount of chocolate (in grams) that Aziz can consume during n days.