<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:
    map<long long,vector<pair<int,int>>> mp1;
    vector<int> dp;
    int mod = 1e9 + 7;
    int recsoln(int root,auto &arr){

        if(dp[root] != -1)return dp[root];

        long long ans = 1;

        for(auto i : mp1[root]){
            if(i.first == i.second)
                ans += (1LL*(recsoln(i.first,arr)%mod) * (recsoln(i.second,arr)%mod))%mod;
            else
                ans += (2LL*(recsoln(i.first,arr)%mod) *1LL* (recsoln(i.second,arr)%mod))% mod;
            ans %= mod;
        }
        return dp[root] = ans % mod;
    }
    int numFactoredBinaryTrees(vector<int>& arr) {
        map<long long,int> mp;
        int n = arr.size();
        sort(arr.begin(),arr.end());

        for(int i = 0;i < n;i++)mp[arr[i]] = i;;

        for(int i = 0;i < n;i++){
            for(int j  = i;j < n;j++){
                long long mult = 1LL*arr[i]*arr[j];
                if(mp.find(mult) != mp.end()){
                    mp1[mp[mult]].push_back({i,j});
                }
            }
        }

        // for(auto i:mp1){
        //     cout<<arr[i.first]<<" -> ";
        //     for(auto j:i.second){
        //         cout<<arr[j.first]<<" "<<arr[j.second]<<endl;
        //     }
        //     cout<<endl;
        // }

        dp.assign(n+1,-1);
        long long ans = 0;
        for(int i = 0;i < n;i++){
            if(dp[i] == -1){
                ans += recsoln(i,arr);
                ans %= mod;
            }
        }
        return ans;
    }
};
15100