The Sigmoid Function

Kestrel Freight's late-delivery model does not hand back a probability. It hands back a score on an unbounded scale: strongly negative when the job looks safe, strongly positive when it looks doomed, and zero when the evidence is evenly balanced. The dispatch screen cannot show that to a customer. What it needs is the standard sigmoid, the S-shaped logistic curve built on the natural exponential, which squashes any score onto the open range between 0 and 1 — never quite reaching either end, sitting at exactly one half when the score is zero, and treating a score and its negative as mirror images.

Task: Print the probability the sigmoid gives for this score.

Input

One line holding a single number, the model's score. It may be negative and it may have a decimal point.

Output

One line holding the probability rounded to 4 decimal places, with no label.

Example:

Input:
0

Output:
0.5000