A player wins each point independently with probability p. From 30-30, which is deuce, they must go two points clear to win. Return their probability of winning the game.

Let $W$ be the answer. From deuce they either take both points, lose both, or split and return to deuce:

$$W = p^2 + 2p(1-p)W \quad\Rightarrow\quad W = \frac{p^2}{1 - 2p(1-p)}$$

Input

0.5

Output

0.5