<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 mod=1e9+7;
    long long solve(long long ind,vector<int>&arr,unordered_map<long long,long long>&mpp,vector<long long>&dp){
        if(ind==arr.size()||ind<0){
            return 0;
        }
        if(dp[ind]!=-1){
            return dp[ind];
        }
        long long num=arr[ind];
        long long ans=1;
        for(long long j=0;j<ind;j++){
            if(num%arr[j]==0&&mpp.find(num/arr[j])!=mpp.end()){
                long long left=solve(j,arr,mpp,dp)%mod;
                long long right=solve(mpp[num/arr[j]],arr,mpp,dp)%mod;
                ans=(ans+(left*right)%mod)%mod;
            }
        }

        return dp[ind]=ans;
    }
    int numFactoredBinaryTrees(vector<int>& arr) {
        long long n=arr.size();

        sort(arr.begin(),arr.end());
        unordered_map<long long,long long> mpp;
        for(long long i=0;i<n;i++){
            mpp[arr[i]]=i;
        }
        long long cnt=0;
        vector<long long> dp(n+1,-1);
        
        for(long long i=0;i<n;i++){
            cnt=(cnt+solve(i,arr,mpp,dp))%mod;
        }
        return cnt%mod;
    }
};
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