<p>Given an array of unique integers, <code>arr</code>, where each integer <code>arr[i]</code> is strictly greater than <code>1</code>.</p>

<p>We make a binary tree using these integers, and each number may be used for any number of times. Each non-leaf node&#39;s value should be equal to the product of the values of its children.</p>

<p>Return <em>the number of binary trees we can make</em>. The answer may be too large so return the answer <strong>modulo</strong> <code>10<sup>9</sup> + 7</code>.</p>

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

<pre>
<strong>Input:</strong> arr = [2,4]
<strong>Output:</strong> 3
<strong>Explanation:</strong> We can make these trees: <code>[2], [4], [4, 2, 2]</code></pre>

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

<pre>
<strong>Input:</strong> arr = [2,4,5,10]
<strong>Output:</strong> 7
<strong>Explanation:</strong> We can make these trees: <code>[2], [4], [5], [10], [4, 2, 2], [10, 2, 5], [10, 5, 2]</code>.</pre>

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

<ul>
	<li><code>1 &lt;= arr.length &lt;= 1000</code></li>
	<li><code>2 &lt;= arr[i] &lt;= 10<sup>9</sup></code></li>
	<li>All the values of <code>arr</code> are <strong>unique</strong>.</li>
</ul>

class Solution {
    private:
    int MOD = 1e9+7;
    int countTrees(int val, unordered_map<int, long long>& dp, unordered_map<int, vector<int>>& adj){
        if(adj.find(val) == adj.end()) return 1;
        unordered_map<int, int> considered;
        long long res = 0;
        for(int a : adj[val]){
            // cout<<val<<" : "<<a<<endl;
            if( considered.find(a) == considered.end() && considered.find(val/a) == considered.end()){
                considered[a] = 1;
                considered[val/a] = 1;
                if(a == val/a){
                    res += (dp[a]*dp[val/a])%MOD; 
                }
                else res += (2*( ( (dp[a]%MOD )* (dp[val/a]%MOD) ) %MOD))%MOD;
            }
        }
        return dp[val] = (res+1)%MOD;
    }
public:
    int numFactoredBinaryTrees(vector<int>& arr) {
        sort(arr.begin(), arr.end());
        unordered_map<int, vector<int>> adj;
        unordered_map<int, long long> dp;
        for(int a : arr) dp[a] = 1;
        for(int i = arr.size()-1; i>=0; i--){
            for(int j = i-1; j>= 0; j--){
                if(arr[i] > arr[j] && arr[i] % arr[j] == 0 && dp.find(arr[i]/arr[j]) != dp.end()){
                    adj[arr[i]].push_back(arr[j]);
                }
            }
        }
        int result = 0;
        for(int a : arr){
            // cout<<"Counting trees for : "<<a<<endl;
            int b = countTrees(a, dp, adj);
            // cout<<"Trees for "<<a<<" : "<<dp[a]<<", "<<b<<endl;
            result += b % MOD;
            result %= MOD;
        }
        return result;
    }
};
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