Very Easy Task

Source: Codeforces

Version: Phuoc Hung OJ Extended

Problem Statement

There is initially one original sheet and $n$ additional copies are required. Copier 1 needs $x$ seconds per copy and copier 2 needs $y$ seconds. A copier needs an existing sheet as source; after the first copy exists, both copiers may work simultaneously. Find the minimum time to produce $n$ copies.

Input

The only line contains $n,x,y$.

Output

Print the minimum number of seconds.

Subtasks

• Subtask 1 — 20%: $n\le10^4$.
• Subtask 2 — 30%: $n\le10^7$.
• Subtask 3 — 50%: $n\le2\cdot10^8$, $1\le x,y\le10$.

Example

Input

4 1 1

Output

3

Explanation

The first copy takes one second, after which both copiers can work in parallel.