<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.
 * struct TreeNode {
 *     int val;
 *     TreeNode *left;
 *     TreeNode *right;
 *     TreeNode() : val(0), left(nullptr), right(nullptr) {}
 *     TreeNode(int x) : val(x), left(nullptr), right(nullptr) {}
 *     TreeNode(int x, TreeNode *left, TreeNode *right) : val(x), left(left), right(right) {}
 * };
 */
class Solution {
public:
    void computeS(TreeNode* &root, map<TreeNode*, long long>& s){
        if(root->left == NULL && root->right == NULL){
            s[root] = root->val;
            return;
        }
        if(root->left != NULL && s.find(root->left) == s.end())
            computeS(root->left, s);
        
        if(root->right != NULL && s.find(root->right) == s.end())
            computeS(root->right, s);

        if(root->left != NULL){
            if(root->right != NULL){
                s[root] = s[root->left] + s[root->right] + root->val;
            }
            else
                s[root] = s[root->left] + root->val;
        }
        else
            s[root] = s[root->right] + root->val;
        return;
    }

    int maxProduct(TreeNode* root) {
        int mod = 1000000007;
        map<TreeNode*, long long> s;

        computeS(root, s);
        //for(auto & k : s)
        //   cout << k.first <<" " << k.second << "\n";

        int sumall = s[root];

        long long max = -1;
        queue<TreeNode*> q;
        q.push(root);

        while(q.size() != 0){
            TreeNode* top= q.front();
            q.pop();

            if (top->right != NULL)
                if(top->left != NULL){
                    q.push(top->right);
                    q.push(top->left);
                    long long prod = s[top->right] * (sumall - s[top->right]);
                    if (prod > max)
                        max = prod;
                    prod = s[top->left] * (sumall - s[top->left]);
                    if (prod > max)
                        max = prod;
                }
            else{
                q.push(top->right);
                long long prod = s[top->right] * (sumall - s[top->right]);
                if (prod > max)
                    max = prod;
                
            }
            else{
                if(top->left != NULL){
                    q.push(top->left);
                    long long prod = s[top->left] * (sumall - s[top->left]);
                    if (prod > max)
                        max = prod;
                }
            }
        }

        return max % mod;
    }
};
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