<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:
    int dp[1001];
    int mod=1e9+7;
    map<int,int>mp;
    int rec(int i, int n, vector<int>& arr){
        if(i==0)return 1;
        if(dp[i]!=-1)return dp[i];
        long long ans=1;
        //ans+=rec(i-1,n,arr);
        for(int j=i-1;j>=0;j--){
            if(arr[i]%arr[j]==0 && mp.find(arr[i]/arr[j])!=mp.end()){
                //cout<<"hehe";
                int idx=mp[arr[i]/arr[j]];
                
                ans=(ans%mod + (1ll*(rec(j,n,arr)%mod)*(rec(idx,n,arr)%mod))%mod)%mod;
            }
        }
        return dp[i]=ans;       
    }
    int numFactoredBinaryTrees(vector<int>& arr) {
        int n = arr.size();
        sort(arr.begin(),arr.end());
        //reverse(arr.begin(),arr.end());
        for(int i=0;i<n;i++)mp[arr[i]]=i;
        memset(dp,-1,sizeof(dp));
        int ans=0;
        for(int i=n-1;i>=0;i--){
            //cout<<arr[i]<<" ";
            ans=(ans%mod + rec(i,n,arr)%mod)%mod;
            cout<<ans<<" ";
        }
        return ans;
    }
};
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