THE FRAUD LABEL SURPRISE

Difficulty: Easy Tags: Information Theory

Story

Stripe's risk team runs a daily check on how "surprising" the label mix looks: entropy near zero means the day was almost entirely one class, worth a glance before trusting any model metric computed on it.

The Math

H(p) = -sum_i p_i * log2(p_i)

Input Format

k
p_1 ... p_k

A valid probability distribution, given directly.

Output Format

H(p), 6 decimals.

Constraints

• 2 <= k <= 100, sum(p_i) = 1 guaranteed within 1e-6
• Time limit: 1.0 second.

Example

Input

2
0.995 0.005

Output

0.045415