<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:
        bfs_q = []
        bfs_q.append((root, 1))

        curr_level = 1
        curr_level_sum = 0
        max_level_sum = -math.inf
        max_level = 1
        while bfs_q:
            elem, level = bfs_q.pop(0)
            if (level == curr_level):
                if (elem):
                    curr_level_sum += elem.val
            else:
                # change level and update max
                if (curr_level_sum > max_level_sum):
                    max_level_sum = curr_level_sum
                    max_level = curr_level
                curr_level += 1
                curr_level_sum = elem.val
            
            # push new things on
            if (elem.right):
                bfs_q.append((elem.right, curr_level + 1))
            if (elem.left):
                bfs_q.append((elem.left, curr_level + 1))
        
        if (curr_level_sum > max_level_sum):
            max_level_sum = curr_level_sum
            max_level = curr_level
        return max_level


        
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