<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) 
    {
        int m = 1000000000 + 7; 
        sort(arr.begin(), arr.end());

        vector<int> result(arr.size(), 1);
        for(int i = 0; i < arr.size(); i++)
        {
            int x = 0;
            int y = i - 1;
            while(x <= y)
            {
                if((long long)arr[x] * (long long)arr[y] == (long long)arr[i])
                {
                    if(arr[x] != arr[y])
                    {
                        result[i] += ((long long)result[x] * (long long)result[y] * 2 ) % m;
                    }
                    else result[i] += ((long long)result[x] * (long long)result[y] ) % m;
                    result[i] %= m;
                    
                    x ++;
                    y --;
                }
                else if((long long)arr[x] * (long long)arr[y] < (long long)arr[i])
                {
                    x ++;
                }
                else y --;
            }
        } 
        int lastResult = 0;
        for(int i = 0; i < result.size(); i++)   
        {
            lastResult += (result[i] % m);
            lastResult %= m;
        }
        return lastResult;
    }
};
11000