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.