A game has outcomes with the given probabilities and matching payouts. Return (expected_value, variance).

$$E = \sum_i p_i x_i, \qquad \mathrm{Var} = \sum_i p_i x_i^2 - E^2$$

Input

probabilities = [0.5, 0.5]
payouts = [1.0, -1.0]

Output

(0.0, 1.0)