Given n boxes, each box is given in the format [status, candies, keys, containedBoxes] where:

status[i]: an integer which is 1 if box[i] is open and 0 if box[i] is closed.
candies[i]: an integer representing the number of candies in box[i].
keys[i]: an array contains the indices of the boxes you can open with the key in box[i].
containedBoxes[i]: an array contains the indices of the boxes found in box[i].

You will start with some boxes given in initialBoxes array. You can take all the candies in any open box and you can use the keys in it to open new boxes and you also can use the boxes you find in it.
Return the maximum number of candies you can get following the rules above.
 
Example 1:
Input: status = [1,0,1,0], candies = [7,5,4,100], keys = [[],[],[1],[]], containedBoxes = [[1,2],[3],[],[]], initialBoxes = [0]
Output: 16
Explanation: You will be initially given box 0. You will find 7 candies in it and boxes 1 and 2. Box 1 is closed and you don't have a key for it so you will open box 2. You will find 4 candies and a key to box 1 in box 2.
In box 1, you will find 5 candies and box 3 but you will not find a key to box 3 so box 3 will remain closed.
Total number of candies collected = 7 + 4 + 5 = 16 candy.

Example 2:
Input: status = [1,0,0,0,0,0], candies = [1,1,1,1,1,1], keys = [[1,2,3,4,5],[],[],[],[],[]], containedBoxes = [[1,2,3,4,5],[],[],[],[],[]], initialBoxes = [0]
Output: 6
Explanation: You have initially box 0. Opening it you can find boxes 1,2,3,4 and 5 and their keys. The total number of candies will be 6.

Example 3:
Input: status = [1,1,1], candies = [100,1,100], keys = [[],[0,2],[]], containedBoxes = [[],[],[]], initialBoxes = [1]
Output: 1

Example 4:
Input: status = [1], candies = [100], keys = [[]], containedBoxes = [[]], initialBoxes = []
Output: 0

Example 5:
Input: status = [1,1,1], candies = [2,3,2], keys = [[],[],[]], containedBoxes = [[],[],[]], initialBoxes = [2,1,0]
Output: 7

 
Constraints:

1 <= status.length <= 1000
status.length == candies.length == keys.length == containedBoxes.length == n
status[i] is 0 or 1.
1 <= candies[i] <= 1000
0 <= keys[i].length <= status.length
0 <= keys[i][j] < status.length
All values in keys[i] are unique.
0 <= containedBoxes[i].length <= status.length
0 <= containedBoxes[i][j] < status.length
All values in containedBoxes[i] are unique.
Each box is contained in one box at most.
0 <= initialBoxes.length <= status.length
0 <= initialBoxes[i] < status.length

```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 maxCandies(self, status: List[int], candies: List[int], keys: List[List[int]], containedBoxes: List[List[int]], initialBoxes: List[int]) -> int:\n        \n        \n        #Approach 1:  use set \n        #The queue only contains boxes which is accessible\n#         q=collections.deque()\n#         keys_set=set()   #Set for all available keys\n#         boxes_set=set()  #set for all un-opened boxes\n        \n#         #Initialize the queue to process box\n#         for box in initialBoxes:\n#             if(status[box]==1 or box in keys_set):  #Check if this box is open or there is key available\n#                 q.append(box)\n#                 for key in keys[box]:\n#                     keys_set.add(key)\n#                     if(key in boxes_set):           #Check if the new key can open a box in boxes_set\n#                         q.append(key)\n#                         boxes_set.remove(key)\n#             else:\n#                 boxes_set.add(box)\n                \n\n#         res=0\n#         visited=set()\n        \n#         #use DFS to populate the queue\n#         while q:\n            \n#             boxi=q.popleft()\n#             #Avoid duplicated couting of candies\n#             if(boxi in visited):\n#                 continue\n#             else:\n#                 visited.add(boxi)\n#                 res +=candies[boxi]\n                \n#             #Check all neighbors of current boxi\n#             for nei in containedBoxes[boxi]:\n#                 if(status[nei]==1 or nei in keys_set):   #Check if this box is open or there is a key for this box\n#                     q.append(nei)\n#                     for key in keys[nei]:\n#                         keys_set.add(key)\n#                         if(key in boxes_set):             #check if the new key can open a box in boxes_set\n#                             q.append(key)\n#                             boxes_set.remove(key)\n#                 else:\n#                     boxes_set.add(nei)\n        \n#         return res\n    \n    \n        #Approach 2: use list\n        \n        haskeys=status[:]\n        seen=[0]*len(status)\n        q=collections.deque()   #Only contains boxes that are accessible\n        \n        for box in initialBoxes:\n            seen[box]=1\n            if(haskeys[box]):\n                q.append(box)   #Include the one only accessible\n                \n        res=0\n        while q:\n            \n            boxi=q.popleft()\n            res+=candies[boxi]\n            \n            #Since eachbox is contained in one box at most\n            #it will not result in duplicated elements in q\n            for nei in containedBoxes[boxi]:\n                seen[nei]=1\n                if(haskeys[nei]): q.append(nei)\n            \n            #Iterate through all available keys, \n            #inlcude the box has been seen but doesn't have key to the queue\n            for key in keys[boxi]:\n                if(seen[key] and haskeys[key]==0):  #Meaning it has not been included in queue\n                    q.append(key)\n                haskeys[key]=1\n        \n        return res\n                    \n                \n            \n            \n            \n        \n        \n        \n        \n        \n        \n        \n        \n        \n        \n        \n        \n        \n        \n        \n        \n        \n        \n        \n        \n        \n        \n        \n            \n            \n            \n"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'maxCandies'
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: 6418