beecrowd | 1946

Pyramid of Fortune

By M.C. Pinto, UNILA BR Brazil

Timelimit: 1

A great TV show gives prizes to the audience through the Pyramid of Fortune. One guest throws at the top of the pyramid (which is actually a triangle) and it goes down to the left or to the right until it hits one of the slots at the pyramid base. The guest wins the prize that is mapped to that slot.

The grand prize is always at the middle of the pyramid base. So, its base always have an odd number of slots. The figure shows one pyramid with 15 slots.

Pyramid

The TV show producers wants to save as much as possible and have asked you to calculate what is the probability of winning the grand prize, given the number of slots at the pyramid base. Consider that, in each point of the pyramid, the ball has the same probability to go to the left or to the right.

Input

The input is given in a single line, which contains the number S of slots at the pyramid base (3 ≤ S ≤ 4999). S is always an odd number.

Output

The output must be given in a single line, which contains the probability of the ball hits the slot with the grand prize. The probability must be printed with 2 decimal places.

Input Samples Output Samples

3

50.00

5

37.50

15

20.95