<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:
    const int mod = 1e9 + 7;
    int n;
    vector<int> dp, nodes;
    int countTreesWithRoot(int idx) {
        if (dp[idx] != -1)
            return dp[idx];
        int ret = 1, curr = nodes[idx];
        for (int i = 0; i < idx; ++i) {
            if (curr % nodes[i])
                continue;
            int child1 = nodes[i];
            auto child2 = lower_bound(nodes.begin(), nodes.begin() + idx + 1, curr / child1);
            if (*child2 != curr / child1)
                continue;
            ret = (ret % mod + ((countTreesWithRoot(i) % mod) * (long long)(countTreesWithRoot(child2 - nodes.begin()) % mod)) % mod) % mod;
        }
        return dp[idx] = ret % mod;
    }
    int numFactoredBinaryTrees(vector<int>& arr) {
        sort(arr.begin(), arr.end());
        n = arr.size();
        nodes = arr;
        dp.assign(n, -1);
        int ans = 0;
        for (int i = 0; i < n; ++i)
            ans = (ans + countTreesWithRoot(i)) % mod;
        return ans;
    }
};
12000