Return the Shannon entropy of a discrete distribution, in bits.

$$H = -\sum_i p_i \log_2 p_i$$

Treat $p_i = 0$ as contributing nothing, since $0\log 0$ is taken as 0 by the limit rather than being undefined. Entropy is maximal for a uniform distribution and zero when one outcome is certain.

Input

[0.5, 0.5]

Output

1.0