<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>

const int MOD = 1000000007;
typedef long long ll;

unordered_set<int> nums_set;
unordered_map<int, ll> memory;	// we can save in int, but will need casting

// Return how many trees that has x as a root
ll cnt_trees(int x) {	// O(N^2) where N is input array size
	if (memory.count(x))
		return memory[x];

	ll cnt = 1;	// use as a leaf

	// Find all my divisors x = a * b, then F(a) * F(b) are possible solutions
	for (auto i : nums_set)
		if (x % i == 0 && nums_set.count(x / i)) {	// x = a * b
			// Carefully handle overflows
			auto sub_trees = (cnt_trees(i) * cnt_trees(x / i)) % MOD;
			cnt += sub_trees;
			cnt %= MOD;
		}
	return memory[x] = cnt;
}

class Solution {
public:
	int numFactoredBinaryTrees(const vector<int> &A) {
		// leetcode share global variables between cases. you must clean
		nums_set.clear();
		memory.clear();
		nums_set.insert(A.begin(), A.end());

		ll sum = 0;
		for (auto x : nums_set) {
			sum += cnt_trees(x);
			sum %= MOD;
		}
		return sum;
	}
};

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