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 \(T\) (\(1 \le T \le 5,000,000\)). Eating an orange
increases her fullness by \(A\), and eating a lemon increases her fullness by \(B\)
(\(1 \le A, B \le T\)). Additionally, if she wants, Bessie can drink water at most
one time, which will instantly decrease her fullness by half (and will round
down).

Help Bessie determine the maximum fullness she can achieve!

Problem credits: Nathan Pinsker

Problem credits: Nathan Pinsker

The first (and only) line has three integers \(T\), \(A\), and \(B\).

A single integer, representing the maximum fullness Bessie can achieve.

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