Problem D. Duel of battleships

Author:И. Блинов   Time limit:1 sec
Input file:Standard input   Memory limit:256 Mb
Output file:Standard output  


Two sailing battleships fight against each other. Each ship have a length of L meters. The guns on the ships are located every meter and are directed strictly perpendicular to the ship. The first gun is located at a distance of 1 meter from the start of the ship. The power of each gun on the first ship is p1, and on the second p2.

The duel of the battleships proceeds as follows: two ships sail towards each other along parallel trajectories, at some point the ship's captain gives the order to open fire and all the guns on board the ship shoot in their direction. Two ships can fire in any order, or simultaneously. Each ship shoots exactly once. If at the moment of firing k guns hit the enemy ship, enemy will take p ⋅ k damage, where p is the current firepower of shooting ship's guns, and the firepower of each enemy gun will decrease by (p ⋅ k)1000.

The captain of the first ship wants to understand what maximum damage his ship can inflict on an enemy ship, provided that the enemy is trying to minimize the damage done to his ship.

Input format

The first line of the input contains three numbers: L, p1, p2.

Output format

The output must contain a single number  — the maximum damage that the first ship can cause, with an accuracy of at least two decimal places.


1 ≤ L ≤ 109; 1 ≤ p1, p2 ≤ 107

Sample tests

No. Standard input Standard output
4 100 100000
10.0 1000.0 112

0.134s 0.029s 13