Equal balls#1316
In an opaque, closed box with a small hole, there are balls ( is an even number), half of which are black and the other half are white. You have a fair coin that you begin to flip.
If heads comes up, remove a white ball;
If tails comes up, remove a black ball;
This process continues until exactly two balls remain in the box. At this point, they will be of the same color, and continuing to flip the coin is unnecessary. Up to this moment, there is always at least one black and one white ball in the box.
What is the probability that the described situation will occur?
Each line represents a separate test case and contains an even integer , where 0 < n \le 10^5 — the number of balls in the box.
For each test case, print in a separate line the probability of the described situation occurring. The answer should be printed with eight decimal places.
Example 1