Given an integer n, you must transform it into 0 using the following operations any number of times:

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

Return the minimum number of operations to transform n into 0.
 
Example 1:
Input: n = 0
Output: 0

Example 2:
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 3:
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.

Example 4:
Input: n = 9
Output: 14

Example 5:
Input: n = 333
Output: 393

 
Constraints:

0 <= n <= 109

```python

USER_FILENAME = "<user_code>"
import sys, json, builtins
import math, heapq, bisect, itertools, functools, collections, statistics, fractions, decimal, operator, array, random, re, string, os, pathlib
try:
    import resource as _res
except Exception:
    _res = None
from collections import Counter, defaultdict, deque, OrderedDict
from functools import lru_cache, reduce
from itertools import accumulate, permutations, combinations, product
from math import gcd, ceil, floor, sqrt
from decimal import Decimal
try:
    from typing import *
except Exception:
    pass
try:
    sys.setrecursionlimit(1_000_000)
except Exception:
    pass
try:
    import site as _site
    try:
        _sys_sites = _site.getsitepackages() if hasattr(_site, "getsitepackages") else []
        for _p in _sys_sites:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
    try:
        _usp = _site.getusersitepackages()
        if isinstance(_usp, str):
            _usp = [_usp]
        for _p in _usp:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
except Exception:
    pass

def _disabled_input(*args, **kwargs):
    raise RuntimeError("input() is disabled in callable mode")
builtins.input = _disabled_input

ns = {"__name__": "__judge__"}  # prevent if __name__ == "__main__" blocks
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = 'from functools import lru_cache\n\n# removehigh = [(1 << l) - 1 for l in range(31)]\n@lru_cache()\ndef removehigh(l: int) -> int:\n    if l <= 1:\n        return l + 1\n    return (1 << l)\n    \n@lru_cache()\ndef sethigh(l: int, n: int) -> int:\n    if n == 0:\n        return removehigh(l) - 1\n    \n    t2 = 1 << l - 2\n    \n    if n >= t2:\n        return removehigh(l - 1) + remove(n - t2)\n    \n    if n & (n - 1) == 0:\n        return removehigh(l) - removehigh(n.bit_length())\n    \n    return removehigh(l - 1) + sethigh(l - 1, n) \n\n    \n@lru_cache()\ndef remove(n: int) -> int:\n    if n <= 1:\n        return n\n    elif n <= 3:\n        return 5 - n\n    \n    l = n.bit_length()\n    if n & (n - 1) == 0:\n        return removehigh(l) - 1\n    \n    t3 = 3 << l - 2\n    if n >= t3:\n        return removehigh(l - 1) + remove(n - t3)\n    \n    t1 = 1 << l - 1\n    return removehigh(l - 1) + sethigh(l - 1, n - t1) \n\n\n\nclass Solution:\n    def minimumOneBitOperations(self, n: int) -> int:\n        return remove(n)\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'minimumOneBitOperations'
if _fn_name:
    if "Solution" in ns:
        try:
            _obj = ns["Solution"]()
            if hasattr(_obj, _fn_name):
                _target = getattr(_obj, _fn_name)
        except Exception:
            _target = None
    if _target is None and _fn_name in ns and callable(ns[_fn_name]):
        _target = ns[_fn_name]
# Fallback: if there's exactly one user-defined function, use it
if _target is None:
    _cands = [v for k, v in ns.items() if callable(v) and getattr(v, "__module__", "") in ("__judge__", "__main__")]
    _user_funcs = [c for c in _cands if getattr(c, "__name__", "").startswith("_") is False]
    if len(_user_funcs) == 1:
        _target = _user_funcs[0]
if _target is None:
    raise RuntimeError(f"Could not resolve callable '{_fn_name}'")

_raw = sys.stdin.read().strip()
if _raw:
    _parsed = json.loads(_raw)
    if isinstance(_parsed, dict):
        _kwargs = _parsed.get("kwargs", {})
        _args = _parsed.get("args", [])
    else:
        _args, _kwargs = _parsed, {}
else:
    _args, _kwargs = [], {}
if not isinstance(_args, (list, tuple)):
    _args = [_args]
_res = _target(*_args, **_kwargs)
try:
    sys.stdout.write(repr(_res) + "\n")
except Exception:
    pass

```

Measured memory_bytes: 5848