- At the beginning of the game, you are given N as input.
- Set V=N, and set X=1
- Flip a fair coin.

3a. If the coin lands on heads: Increase V by X, and then set X=1

3b. If the coin lands on tails: Decrease V by X, and then set X=2X - If V less than or equal to 0 or V greater than or equal to 2N

4a. End the game. - Proceed to step 3.

Given the initial value N, what is the expected number of turns (coin flips) you will play before ending the game?

constraints-Input:

Input consists of a single integer, N (with 1≤N≤1,000,000), the initial input to the game.

Output:

A single decimal number, containing the expected number of turns you will play this game before it ends. Your output will be accepted if it is within 10−6 absolute or relative error.

Sample Input 1:

1

Sample Output 1:

1.000000000000

Sample Input 2:

3

Sample Output 2:

3.9609375