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