<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:
const int mod=1e9+7;
    long long solve(vector<int>&arr, int i, unordered_set<int>&st, unordered_map<int,long long>&mp){
        long long cnt=1;
        if(mp.find(i)!=mp.end())return mp[i];
        for(auto it:arr){
            if(it>i)break;
            if(i%it==0 && st.find(i/it)!=st.end()){
                cnt= cnt%mod + (solve(arr,it,st,mp) * solve(arr,i/it,st,mp))%mod;
            }
        }
        return mp[i]=cnt%mod;
    }
    long long  numFactoredBinaryTrees(vector<int>& arr) {
       sort(arr.begin(),arr.end());
       unordered_set<int>st;
       unordered_map<int,long long>mp;
       for(auto it: arr){
            st.insert(it);
       }
       long long ans=0;
       for(auto it:arr){
            ans= ans + solve(arr,it,st,mp)%mod;
       }
       return ans%mod;
    }
};
13800