THE BRIGHTNESS DIAL

Difficulty: Easy Tags: Activation Functions

Story

Adobe's auto-brightness tool squashes an unbounded adjustment score into (0, 1) before applying it as a blend factor: sigmoid, forward and backward, exactly as every deep learning framework implements it.

The Math

sigma(x)  = 1 / (1 + e^-x)
sigma'(x) = sigma(x) * (1 - sigma(x))

Input Format

n
x_1 ... x_n

Output Format

Two lines: sigma(x) and sigma'(x), 6 decimals each.

Constraints

• 1 <= n <= 10^5, |x_i| <= 50
• Time limit: 1.0 second.

Example

Input

1
0.5

Output

0.622459
0.235004