There are n oranges in the kitchen and you decided to eat some of these oranges every day as follows:

Eat one orange.
If the number of remaining oranges (n) is divisible by 2 then you can eat  n/2 oranges.
If the number of remaining oranges (n) is divisible by 3 then you can eat  2*(n/3) oranges.

You can only choose one of the actions per day.
Return the minimum number of days to eat n oranges.
 
Example 1:
Input: n = 10
Output: 4
Explanation: You have 10 oranges.
Day 1: Eat 1 orange,  10 - 1 = 9.  
Day 2: Eat 6 oranges, 9 - 2*(9/3) = 9 - 6 = 3. (Since 9 is divisible by 3)
Day 3: Eat 2 oranges, 3 - 2*(3/3) = 3 - 2 = 1. 
Day 4: Eat the last orange  1 - 1  = 0.
You need at least 4 days to eat the 10 oranges.

Example 2:
Input: n = 6
Output: 3
Explanation: You have 6 oranges.
Day 1: Eat 3 oranges, 6 - 6/2 = 6 - 3 = 3. (Since 6 is divisible by 2).
Day 2: Eat 2 oranges, 3 - 2*(3/3) = 3 - 2 = 1. (Since 3 is divisible by 3)
Day 3: Eat the last orange  1 - 1  = 0.
You need at least 3 days to eat the 6 oranges.

Example 3:
Input: n = 1
Output: 1

Example 4:
Input: n = 56
Output: 6

 
Constraints:

1 <= n <= 2*10^9

```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 minDays(self, n: int) -> int:\n#         return self._find(n, {0: 0})\n    \n    \n#     def _find(self, n, cache):\n\n#         if n in cache:\n#             return cache[n]\n        \n#         ret = inf\n#         if n % 3 == 0:\n#             ret = 1 + self._find(n // 3, cache)\n#         if n % 2 == 0:\n#             ret = min(ret, 1 + self._find(n // 2, cache))\n#         if n < 50000:\n#             ret = min(ret, 1 + self._find(n - 1, cache, terminate - 1))\n        \n\n#         return ret\n\n\n# from collections import deque\n\n# class Solution:\n#     def minDays(self, n: int) -> int:\n#         q1 = deque([0, None])\n#         q2 = deque([n, None])\n#         visited = {n}\n        \n#         for i in range(n):\n#             tmp = set()\n#             while True:\n#                 n = q1.popleft()\n#                 if n is None:\n#                     q1.append(None)\n#                     break\n#                 for m in [n + 1, n * 2, n * 3]:\n#                     if m in visited:\n#                         return i * 2 + 1\n#                     if m not in tmp:\n#                         tmp.add(m)\n#                         q1.append(m)\n#             visited = tmp\n            \n#             tmp = set()\n#             while True:\n#                 n = q2.popleft()\n#                 if n is None:\n#                     q2.append(None)\n#                     break\n#                 l = [n - 1]\n#                 if n % 2 == 0:\n#                     l.append(n // 2)\n#                 if n % 3 == 0:\n#                     l.append(n // 3)\n#                 for m in l:\n#                     if m in visited:\n#                         return i * 2 + 2\n#                     if m not in tmp:\n#                         q2.append(m)\n#                         tmp.add(m)\n#             visited = tmp\n\n\nclass Solution:\n    def minDays(self, n: int) -> int:\n        q1 = deque([0, None])\n        q2 = deque([n, None])\n        visited1 = {0}\n        visited2 = {n}\n        \n        for i in range(n):\n            while True:\n                n = q1.popleft()\n                if n is None:\n                    q1.append(None)\n                    break\n                for m in [n + 1, n * 2, n * 3]:\n                    if m in visited2:\n                        return i * 2 + 1\n                    if m not in visited1:\n                        visited1.add(m)\n                        q1.append(m)\n            \n            while True:\n                n = q2.popleft()\n                if n is None:\n                    q2.append(None)\n                    break\n                l = [n - 1]\n                if n % 2 == 0:\n                    l.append(n // 2)\n                if n % 3 == 0:\n                    l.append(n // 3)\n                for m in l:\n                    if m in visited1:\n                        return i * 2 + 2\n                    if m not in visited2:\n                        q2.append(m)\n                        visited2.add(m)\n\n\n# class Solution:\n#     def minDays(self, n: int) -> int:\n#         # self.hit0 = 0\n#         # self.hit1 = 0\n#         # self.total = 0\n        \n#         # cache = {0: 0}\n#         # return self._find(n, cache, inf)\n        \n#         return self._find(n, {0: 0}, inf)\n        \n#         # self._find(n, cache, inf)\n#         # hit = self.hit0 + self.hit1\n#         # print(self.total, hit, self.hit0, self.hit1, hit / self.total, self.hit0 / hit)\n        \n#         # print(cache)\n#         # return cache[n]\n\n\n#     def _find(self, n, cache, terminate):\n        \n#         if n in cache:\n#             return cache[n]\n        \n#         # # self.total += 1\n#         # if n in cache:\n#         #     if cache[n] > terminate:\n#         #         # self.hit0 += 1\n#         #         return inf\n#         #     # self.hit1 += 1\n#         #     return cache[n]\n        \n#         if terminate <= 0:\n#             return inf\n        \n#         oldTerminate = terminate\n#         ret = inf\n#         if n % 3 == 0:\n#             ret = 1 + self._find(n // 3, cache, terminate - 1)\n#             terminate = min(terminate, ret - 1)\n#         if n % 2 == 0:\n#             ret = min(ret, 1 + self._find(n // 2, cache, terminate - 1))\n#             terminate = min(terminate, ret - 1)\n#         ret = min(ret, 1 + self._find(n - 1, cache, terminate - 1))\n        \n#         # if ret < inf:\n#         #     cache[n] = ret\n#         # return ret\n        \n#         if ret <= oldTerminate:\n#             cache[n] = ret\n#             return ret\n#         return inf\n\n\n# class Solution:\n#     def minDays(self, n: int) -> int:\n#         return self._find(n, {0: 0}, inf)\n    \n    \n#     def _find(self, n, cache, terminate):\n\n#         if n in cache:\n#             return cache[n]\n        \n#         if terminate <= -15:\n#             return inf\n        \n#         ret = inf\n#         if n % 3 == 0:\n#             ret = 1 + self._find(n // 3, cache, terminate - 1)\n#             terminate = min(terminate, ret - 1)\n#         if n % 2 == 0:\n#             ret = min(ret, 1 + self._find(n // 2, cache, terminate - 1))\n#             terminate = min(terminate, ret - 1)\n#         ret = min(ret, 1 + self._find(n - 1, cache, terminate - 1))\n        \n#         if ret < inf:\n#             cache[n] = ret\n#         return ret\n\n\n# class Solution:\n#     def minDays(self, n: int) -> int:\n#         arr = [0]\n#         for i in range(1, n + 1):\n#             n = arr[-1]\n#             if i % 2 == 0:\n#                 n = min(n, arr[i // 2])\n#             if i % 3 == 0:\n#                 n = min(n, arr[i // 3])\n#             arr.append(n + 1)\n        \n#         return arr[-1]\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'minDays'
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: 7894