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        queue = [(n,0)]\n        visited = set()\n        while queue:\n            remain, day = queue.pop(0)\n            if remain == 0: return day\n            if remain % 2 == 0 and remain//2 not in visited:\n                queue.append((remain//2, day+1))\n                visited.add(remain//2)\n            if remain % 3 == 0 and remain//3 not in visited:\n                queue.append((remain//3, day+1))\n                visited.add(remain//3)\n            if remain-1 not in visited:\n                queue.append((remain - 1, day+1))\n            \n            \n        # dp = {}\n        # dp[0] = 0\n        # dp[1] = 1\n        # for i in range(2, n+1):\n        #     if i % 2 == 0 and i % 3 == 0:\n        #         dp[i] = min(dp[i//2], dp[i//3], dp[i-1]) + 1\n        #     elif i % 2 == 0:\n        #         dp[i] = min(dp[i//2], dp[i-1]) + 1\n        #     elif i % 3 == 0:\n        #         dp[i] = min(dp[i//3], dp[i-1]) + 1\n        #     else:\n        #         dp[i] = dp[i-1] + 1\n        # return dp[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: 6176