F. Max Correct Set
time limit per test
4 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

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