Given true labels y (0 or 1) and predicted probabilities, return the mean binary cross-entropy.

$$L = -\frac{1}{n}\sum_i \bigl[y_i \log p_i + (1-y_i)\log(1-p_i)\bigr]$$

This is the negative log-likelihood of the Bernoulli model: minimising the loss and maximising the likelihood are the same operation.

Input

y = [1, 0, 1]
probabilities = [0.9, 0.1, 0.8]

Output

0.14462152754328741