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Problems

Fruit Feast

Fruit Feast

Time limit 1 second
Memory limit 128 MiB

Bessie has broken into Farmer John's house again! She has discovered a pile of lemons and a pile of oranges in the kitchen (effectively an unlimited number of each), and she is determined to eat as much as possible.

Bessie has a maximum fullness of t. Eating an orange increases her fullness by a, and eating a lemon increases her fullness by b. Additionally, if she wants, Bessi can drink water at most one time, which will instantly decrease his fullness by half (and will round down).

Help Bessie determine the maximum fullness she can achieve!

Input data

One line has three integers t\:(1 \le t \le 5 \cdot 10^6), a and b\:(1 \le a, b \le t).

Output data

Print a single integer, representing the maximum fullness Bessie can achieve.

Examples

Input example #1
8 5 6
Output example #1
8
Source 2015 USACO December, Gold