Lights [II]

Lights [II]

The blurb for this problem is the same as Lights [I], save for the statement of the problem.

You stand before an infinitely long corridor containing lights and their respective switches. You'd like to turn a subset of the lights on using little robots that will flick certain switches infinitely along the corridor.

In this second problem, you'll be sending an infinite number of robots. The $i^\text{th}$ robot will flick switches according the the following rule:

Robot $i$ flicks light switch $j$ if $2^{i-1}$ divides $j$. In other words, the $i^\text{th}$ robot flicks every $2^{i-1 \text{th}}$ switch.

A light switch stays on if after all robots are done, it has been flicked an odd number of times. For example, Light Switch $\#4$ is on because it was flicked by Robots 1, 2 and 3. While Light Switch $\#2$ is off because it was flicked by Robots 1 and 2.

Input

Input will contain a single integer $n$, representing how many lights we'll be considering

Output

Output will contain a single integer, representing the total number of lights at position at or before the $n^\text{th}$ light that are on at the end of execution

Constraints

• $1 \leq n \leq 10^{18}$

Examples

3

2

Explanation

2 is the only light switch that is turned off.

4

3

Explanation

2 is the only light switch that is turned off.

10

6

Explanation

2, 6, 8, 10 are the only light switches that are turned off.