<p>Given the <code>root</code> of a binary tree, split the binary tree into two subtrees by removing one edge such that the product of the sums of the subtrees is maximized.</p>

<p>Return <em>the maximum product of the sums of the two subtrees</em>. Since the answer may be too large, return it <strong>modulo</strong> <code>10<sup>9</sup> + 7</code>.</p>

<p><strong>Note</strong> that you need to maximize the answer before taking the mod and not after taking it.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/01/21/sample_1_1699.png" style="width: 500px; height: 167px;" />
<pre>
<strong>Input:</strong> root = [1,2,3,4,5,6]
<strong>Output:</strong> 110
<strong>Explanation:</strong> Remove the red edge and get 2 binary trees with sum 11 and 10. Their product is 110 (11*10)
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/01/21/sample_2_1699.png" style="width: 500px; height: 211px;" />
<pre>
<strong>Input:</strong> root = [1,null,2,3,4,null,null,5,6]
<strong>Output:</strong> 90
<strong>Explanation:</strong> Remove the red edge and get 2 binary trees with sum 15 and 6.Their product is 90 (15*6)
</pre>

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

<ul>
	<li>The number of nodes in the tree is in the range <code>[2, 5 * 10<sup>4</sup>]</code>.</li>
	<li><code>1 &lt;= Node.val &lt;= 10<sup>4</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 maxProduct(self, root: Optional[TreeNode]) -> int:
        sums=[]
        def dfs(root):
            if root==None: return 0
            if root.left:
                dfs(root.left)
                root.val+= root.left.val
            if root.right:
                dfs(root.right)
                root.val +=root.right.val
            sums.append(root.val)
        print(sums)
        dfs(root)
        maxi= sums[-1]
        return max(v*(maxi-v) for v in sums) % 1000000007

        # x=dfs(root)
        # print(x)
        # maxi=[0]
        # def dfs1(root):
        #     a, b= 0, 0
        #     if root.left:               a= root.left.val 
        #     if root.right:              b= root.right.val            
        #     maxi[0]= max(maxi[0], max(a*(x-a),b*(x-b) ))
        #     if root.left: dfs1(root.left)
        #     if root.right: dfs1(root.right)

        # dfs1(root)
        # return int(maxi[0]% (1e9+7))

 
            
            

35100