<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 numFactoredBinaryTrees(vector<int>& arr) {
        sort(arr.begin(), arr.end());
        unordered_map<int, unsigned long long> ars;
        int mod = 1e9 + 7;
        unsigned long long ans = 0;
        for(int i: arr) {
            ars[i] = 1;
        }
        for(int num: arr) {
            unsigned long long ansN = 1;
            for(int i = 2; i*i <= num; i++) {
                if(num%i == 0 ){
                    int mul = i*i == num? 1 : 2;
                    ansN+= (unsigned long long)ars[i] * (unsigned long long)ars[num/i] * (unsigned long long)mul;
                    // cout<<num<<' '<<i<<' '<<ars[i]<<' '<<ars[num/i]<<' '<<mul<<'\n';
                }
            }
            cout<<num<<' '<<ansN<<'\n';
            ars[num] = ansN%mod;
            ans+=ansN;
            ans %= mod;
        }
        // int ans2 = 0;
        // for(auto [k,v]: ars) {
        //     ans2+=v;
        // }

        return ans;
    }
};
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