Minimum One Bit Operations to Make Integers Zero

Hard

You receive an integer n, you must transform it into 0 using the following operations any count of times:

Change the rightmost ( 0^th ) bit in the binary representation of n.
Change the i^th bit in the binary representation of n if the (i-1)^th bit is set to 1 and the (i-2)^th through 0^th bits are set to 0.

Find and provide the fewest count of operations to transform n into 0.

Example 1

Input: n = 3

Output: 2

Explanation: The binary representation of 3 is "11".

"11" -> "01" with the 2nd operation since the 0th bit is 1.

"01" -> "00" with the 1st operation.

Example 2

Input: n = 6

Output: 4

Explanation: The binary representation of 6 is "110".

"110" -> "010" with the 2nd operation since the 1st bit is 1 and 0th through 0th bits are 0.

"010" -> "011" with the 1st operation.

"011" -> "001" with the 2nd operation since the 0th bit is 1.

"001" -> "000" with the 1st operation.

Constraints

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