<p>Given the <code>root</code> of a binary tree, the level of its root is <code>1</code>, the level of its children is <code>2</code>, and so on.</p>

<p>Return the <strong>smallest</strong> level <code>x</code> such that the sum of all the values of nodes at level <code>x</code> is <strong>maximal</strong>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2019/05/03/capture.JPG" style="width: 200px; height: 175px;" />
<pre>
<strong>Input:</strong> root = [1,7,0,7,-8,null,null]
<strong>Output:</strong> 2
<strong>Explanation: </strong>
Level 1 sum = 1.
Level 2 sum = 7 + 0 = 7.
Level 3 sum = 7 + -8 = -1.
So we return the level with the maximum sum which is level 2.
</pre>

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

<pre>
<strong>Input:</strong> root = [989,null,10250,98693,-89388,null,null,null,-32127]
<strong>Output:</strong> 2
</pre>

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

<ul>
	<li>The number of nodes in the tree is in the range <code>[1, 10<sup>4</sup>]</code>.</li>
	<li><code>-10<sup>5</sup> &lt;= Node.val &lt;= 10<sup>5</sup></code></li>
</ul>

# Definition for a binary tree node.
# class TreeNode:
#     def __init__(self, val=0, left=None, right=None):
#         self.val = val
#         self.left = left
#         self.right = right
class Solution:
    def maxLevelSum(self, root: Optional[TreeNode]) -> int:
        stack, sums = [(root, 0)], defaultdict(int)
        
        while stack:
            curr, lvl = stack.pop()
            sums[lvl] += curr.val

            if curr.left:
                stack.append([curr.left, lvl+1])
            if curr.right:
                stack.append([curr.right, lvl+1])
        
        m = max(sums.values())
        for i, v in sums.items():
            if v == m:
                return i+1

        # # BFS
        # def findLevelSum(root, depth, count):
        #     if not root:
        #         return count
        #     if depth == 1:
        #         count += root.val
        #         return count
        #     count += findLevelSum(root.left, depth - 1, count)
        #     count += findLevelSum(root.right, depth - 1, count)
        #     return count
        
        # def maxHeight(root, height):
        #     if not root:
        #         return height
        #     return max(maxHeight(root.left, height+1), maxHeight(root.right, height+1))
        
        # maxH = maxHeight(root, 0)
        # sums = {}
        # for i in range(1, maxH):
        #     sums[i] = findLevelSum(root, i , 0)
        
        # maxLevel = 0
        # maxSum = sums[1]
        # for i in sums.keys():
        #     if sums[i] > maxSum:
        #         maxSum = sums[i]
        #         maxLevel = i
        # return maxLevel
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