Given a positive integer n and you can do operations as follow:




If n is even, replace n with n/2.
If n is odd, you can replace n with either n + 1 or n - 1.




What is the minimum number of replacements needed for n to become 1?




Example 1:

Input:
8

Output:
3

Explanation:
8 -> 4 -> 2 -> 1



Example 2:

Input:
7

Output:
4

Explanation:
7 -> 8 -> 4 -> 2 -> 1
or
7 -> 6 -> 3 -> 2 -> 1

```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 = 'class Solution:\n     def integerReplacement(self, n):\n         """\n         :type n: int\n         :rtype: int\n         """\n         return self.integerReplacementDP(n)\n         # return self.integerReplacementBitwise(n)\n         if n == 1:\n             return 0\n \n         if n % 2 == 0:\n             return 1 + self.integerReplacement(n / 2)\n         else:\n             return 1 + min(self.integerReplacement(n + 1), self.integerReplacement(n - 1))\n         \n     def integerReplacementDP(self, n, dp=None):\n         if dp is None:\n             dp = {}\n             \n         if n == 1:\n             return 0\n         \n         if n not in dp:\n             if n % 2 == 0:\n                 dp[n] = 1 + self.integerReplacementDP(n / 2, dp=dp)\n             else:\n                 dp[n] = 1 + min(self.integerReplacementDP(n + 1, dp=dp), self.integerReplacementDP(n - 1, dp=dp))\n         return dp[n]\n \n     def integerReplacementBitwise(self, n):\n         """\n         \n         5 -> 4 -> 2 -> 1\n         5 -> 6 -> 3 -> 2 -> 1\n         \n         101 100\n         101 110   \n         \n         11 10\n         """\n         \n         count = 0\n         while n != 1:\n             if (n & 1) == 0:\n                 n >>= 1\n             elif n == 3 or bin(n + 1).count(\'1\') > bin(n - 1).count(\'1\'):\n                 n -= 1\n             else:\n                 n += 1\n             count += 1\n \n         return count\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'integerReplacement'
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: 5954