<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 {
public:

long long int mod = 1e9 + 7;  
int numFactoredBinaryTrees(vector<int>& arr)
{
    sort(arr.begin(), arr.end());
    unordered_map<int,long long int> mp;
    long long int ans = 0;
    
    int n = arr.size();
    for(int i=0;i<n;i++)
    {
        mp[arr[i]] = 1;  
    }
    
    for(int i=0; i<n; i++)
    {
        for(int j=0; j<i; j++)
        {
            if(arr[i] % arr[j] == 0)
            {
                mp[arr[i]] = (mp[arr[i]] % mod + mp[arr[j]] * mp[arr[i] / arr[j]] % mod) % mod;
            //     int Lnum = arr[j];
            //     int Rnum = arr[i] / arr[j];
            //     if(mp.find(Rnum) != mp.end())
            //     {
            //         long long int temp = (mp[Lnum] % mod * mp[Rnum] % mod) % mod;
            //         mp[arr[i]] += (temp % mod);
            //     }               
            }
        }
        ans += (mp[arr[i]] % mod);
    }
    return ans % mod;
}    

};
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