# Game

Alice and Bob play the next game. First, they collect N small stones and put them in one pile. Then they take turns, beginning with Alice, throw a coin. If a player rolls an eagle, it takes a heap of stone, if tails, then do not take it. The winner is the one who takes the last stone. Known ability of players to throw the correct side of a coin. More precisely, if Alice wants to throw his way toward a coin, then it throws it aside with a probability P. Same probability for Bob is Q. Required to find the probability with which Alice will win the game, provided that both players will play optimally.

## Input

The first line contains one integer N (1 <= N <= 99 999 999). Second line set P, in the third Q (0.5 <= P, Q <= 0.999 999 99). The probabilities are given no more than eight characters after the comma.

## Output

Bring one real number - the probability with which Alice will win the game. A display with an accuracy of 8 decimal places.