Solve the programming task below in a Python markdown code block.
Let's call the set of positive integers $S$ correct if the following two conditions are met:

$S \subseteq \{1, 2, \dots, n\}$;

if $a \in S$ and $b \in S$, then $|a-b| \neq x$ and $|a-b| \neq y$.

For the given values $n$, $x$, and $y$, you have to find the maximum size of the correct set.


-----Input-----

A single line contains three integers $n$, $x$ and $y$ ($1 \le n \le 10^9$; $1 \le x, y \le 22$).


-----Output-----

Print one integer — the maximum size of the correct set.


-----Examples-----

Input
10 2 5
Output
5
Input
21 4 6
Output
9
Input
1337 7 7
Output
672
Input
455678451 22 17
Output
221997195


-----Note-----

None