"Abstractions are fine, but I think people also have to breathe air and eat bread.'' is a quote from Das Glasperlenspiel, or The Glass Bead Game, a novel published in 1946 written by the German author Hermann Hesse.

You are playing with distinct glass beads in some order. In each step, you move exactly one bead to the front. The cost of moving the bead to the front is the number of beads before that bead. For example, if we move in the list the total cost is and the resulting sequence of beads is .

Suppose that at each step glass bead is moved with probability , where . What is the limit of the expected cost of the -th move, when tends to infinity?

The first line contains an integer  ().

The second line contains  real numbers  each with 6 digits of precision.

Output one real number, the answer.

Your answer will be considered correct if its absolute or relative error does not exceed . Formally let your answer be , jury answer be . Your answer will be considered correct if .

2
0.500000 0.500000

0.500000000000000

3
0.500000 0.250000 0.250000

0.916666666666667