<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 {
    int mod=1e9+7;
    int solve(int i, auto &mp, auto &dp){
        if(dp[i]!=-1)return dp[i];
        long long ans=1;
        for(auto it:mp[i]){
            int tmp1=solve(it.first,mp,dp);
            int tmp2=solve(it.second,mp,dp);
            if(it.first!=it.second)ans+=2ll*tmp1*tmp2;
            else ans+=1ll*tmp1*tmp2;
            ans%=mod;
        }
        return dp[i]=ans;
    }
public:
    int numFactoredBinaryTrees(vector<int>& arr) {
        int n=arr.size();
        sort(arr.begin(),arr.end(),greater<int>());
        map<int,vector<pair<int,int>>> mp;
        for(int i=0; i<n; i++){
            int j=i+1, k=n-1;
            while(j<=k){
                long long tmp=1ll*arr[j]*arr[k];
                if(tmp==arr[i]){
                    mp[i].push_back({j,k});
                    j++; k--;
                }else if(tmp>arr[i])j++;
                else k--;
            }
        }
        vector<int> dp(n,-1);
        for(int i=0; i<n; i++){
            if(dp[i]==-1)solve(i,mp,dp);
        }
        int ans=0;
        for(int i=0; i<n; i++){
            ans+=dp[i];
            ans%=mod;
            // cout<<arr[i]<<"->"<<dp[i]<<" ";
        }
        return ans;
    }
};
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