<p>You have <code>n</code> boxes labeled from <code>0</code> to <code>n - 1</code>. You are given four arrays: <code>status</code>, <code>candies</code>, <code>keys</code>, and <code>containedBoxes</code> where:</p>

<ul>
	<li><code>status[i]</code> is <code>1</code> if the <code>i<sup>th</sup></code> box is open and <code>0</code> if the <code>i<sup>th</sup></code> box is closed,</li>
	<li><code>candies[i]</code> is the number of candies in the <code>i<sup>th</sup></code> box,</li>
	<li><code>keys[i]</code> is a list of the labels of the boxes you can open after opening the <code>i<sup>th</sup></code> box.</li>
	<li><code>containedBoxes[i]</code> is a list of the boxes you found inside the <code>i<sup>th</sup></code> box.</li>
</ul>

<p>You are given an integer array <code>initialBoxes</code> that contains the labels of the boxes you initially have. You can take all the candies in <strong>any open box</strong> and you can use the keys in it to open new boxes and you also can use the boxes you find in it.</p>

<p>Return <em>the maximum number of candies you can get following the rules above</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> status = [1,0,1,0], candies = [7,5,4,100], keys = [[],[],[1],[]], containedBoxes = [[1,2],[3],[],[]], initialBoxes = [0]
<strong>Output:</strong> 16
<strong>Explanation:</strong> 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 do not 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.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> 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]
<strong>Output:</strong> 6
<strong>Explanation:</strong> 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.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>n == status.length == candies.length == keys.length == containedBoxes.length</code></li>
	<li><code>1 &lt;= n &lt;= 1000</code></li>
	<li><code>status[i]</code> is either <code>0</code> or <code>1</code>.</li>
	<li><code>1 &lt;= candies[i] &lt;= 1000</code></li>
	<li><code>0 &lt;= keys[i].length &lt;= n</code></li>
	<li><code>0 &lt;= keys[i][j] &lt; n</code></li>
	<li>All values of <code>keys[i]</code> are <strong>unique</strong>.</li>
	<li><code>0 &lt;= containedBoxes[i].length &lt;= n</code></li>
	<li><code>0 &lt;= containedBoxes[i][j] &lt; n</code></li>
	<li>All values of <code>containedBoxes[i]</code> are unique.</li>
	<li>Each box is contained in one box at most.</li>
	<li><code>0 &lt;= initialBoxes.length &lt;= n</code></li>
	<li><code>0 &lt;= initialBoxes[i] &lt; n</code></li>
</ul>

class Solution:
    def maxCandies(self, status: List[int], candies: List[int], keys: List[List[int]], containedBoxes: List[List[int]], initialBoxes: List[int]) -> int:
        candiesCount = 0
        newBoxes = []
        update = False
        for box in initialBoxes:
            # if the box is openable
            if status[box]:
                update = True
                # grab the candies
                candiesCount += candies[box]
                # see if theres any new keys that can open boxes
                for key in keys[box]:
                    status[key] = 1
                # check to see if there are any boxes in your current box
                for containedBox in containedBoxes[box]:
                    newBoxes.append(containedBox)

            # if the box is not openable
            else:
                newBoxes.append(box)

        if update:
            # since there is a change in boxes we will recurse
            return candiesCount + self.maxCandies(status, candies, keys, containedBoxes, newBoxes) 
        else:
            # no changes has been made so recursing will get stuck in a loop
            return candiesCount




        
595