<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 int mod = 1e9 + 7;
     int numFactoredBinaryTrees(vector< int>& arr) {
        set<long long int> s;
        long long int n = arr.size();
        for (long long int i = 0; i < n; i++) {
            s.insert(arr[i]);
        }
        map<long long int, long long int> mp;
        sort(arr.begin(),arr.end());
        long long int ans = 0;
        for (long long int i = 0; i < n; i++) {
            long long int x = arr[i];
            mp[x]++;
            for (long long int i = 2; i * i <= x; i++) {
                if (x % i == 0) {
                    if (i * i == x) {
                        mp[x] += mp[i] * mp[i];
                        mp[x] %= mod;
                    } 
                    else {
                        mp[x] += ((mp[i] * mp[x / i]) )%mod* 2;
                        mp[x] %= mod;
                    }
                }
            }
                ans += mp[x];
                ans %= mod;
                cout << mp[x] << endl;
            }

            return (int)ans;
        }
    };
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