<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>

const int mod=1e9+7;
class Solution {
public:
    void getFactor(int e, unordered_map<int,vector<pair<int,int>>>& upp){
        for(int i=1;i<=sqrt(e);i++){
            if(i==e) continue;
            if(e%i==0){
                upp[e].push_back({i,e/i});
            }
        }
    }
    int numFactoredBinaryTrees(vector<int>& arr) {
        sort(arr.begin(),arr.end());
        unordered_map<int,vector<pair<int,int>>> upp;
        unordered_map<int,int> mpp;
        for(int i=0;i<arr.size();i++){
            getFactor(arr[i],upp);
            mpp[arr[i]]=1;
        }
        //for(int i=0;i<arr.size();i++){
        //    cout<<arr[i]<<"->";
        //    for(auto it:upp[arr[i]]){
        //        cout<<it.first<<" "<<it.second<<endl;
        //    }
        //}
        unordered_map<long long,long long> f;
        long long cnt=0;
        for(int i=0;i<arr.size();i++){
            int e=arr[i];
            long long s=1;
            for(auto it:upp[e]){
                int u=it.first, v=it.second;
                if(mpp.find(u)==mpp.end() || mpp.find(v)==mpp.end()) continue;
                if(u!=v){s=(s+(2*f[u]*f[v])%mod)%mod;}
                else s=(s+(f[u]*f[v])%mod)%mod;
            }
            cnt+=(s)%mod;
            f[arr[i]]=s%mod;
        }
        return cnt%mod;
    }
};
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