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 = '# from functools import lru_cache\n\n# # 暴力bfs能过，但是是top-down的，比赛的时候我搞错了\n# class Solution:\n#     def minDays(self, n: int) -> int:\n        \n#         vis = set()\n#         q = collections.deque([n])\n#         cost = 1\n#         while True:\n#             for i in range(len(q)):\n#                 cur = q.popleft()\n#                 if cur <= 1:\n#                     return cost\n#                 if cur in vis:\n#                     continue\n#                 vis.add(cur)\n#                 q.append(cur-1)\n#                 if not cur % 2:\n#                     q.append(cur//2)\n#                 if not cur % 3:\n#                     q.append(cur//3)\n#             cost += 1\n                \n#         return dfs(n)\n    \n## 之后是剪枝\n\n## 剪枝一，\nclass Solution:\n    def minDays(self, n: int) -> int:\n        ans = 1\n        queue = [n]\n        seen = set()\n        while queue: #bfs \n            newq = []\n            for x in queue: \n                if x == 1: return ans \n                seen.add(x)\n                if x-1 not in seen: newq.append(x-1)\n                if x % 2 == 0 and x//2 not in seen: newq.append(x//2)\n                if x % 3 == 0 and x//3 not in seen: newq.append(x//3)\n            ans += 1\n            queue = newq \n            \n            \n## 剪枝2 https://leetcode.com/problems/minimum-number-of-days-to-eat-n-oranges/discuss/794088/Intuitive-solution-with-Proof\n\n# from functools import lru_cache\n# class Solution:\n#     def minDays(self, n: int) -> int:\n        \n#         @lru_cache(None)\n#         def helper(n, one=0):\n#             if one >= 3:\n#                 return math.inf\n#             if n < 1: return n\n            \n#             prev = helper(n - 1, one + 1)\n#             if not n % 2:\n#                 prev = min(prev, helper(n // 2))\n#             if not n % 3:                \n#                 prev = min(prev, helper(n // 3))\n#             return prev + 1                \n        \n#         return helper(n)\n\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: 6084