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823\. Binary Trees With Factors
Medium
Given an array of unique integers, `arr`, where each integer `arr[i]` is strictly greater than `1`.
We make a binary tree using these integers, and each number may be used for any number of times. Each non-leaf node's value should be equal to the product of the values of its children.
Return _the number of binary trees we can make_. The answer may be too large so return the answer **modulo** 109 + 7.
**Example 1:**
**Input:** arr = [2,4]
**Output:** 3
**Explanation:** We can make these trees: `[2], [4], [4, 2, 2]`
**Example 2:**
**Input:** arr = [2,4,5,10]
**Output:** 7
**Explanation:** We can make these trees: `[2], [4], [5], [10], [4, 2, 2], [10, 2, 5], [10, 5, 2]`.
**Constraints:**
* `1 <= arr.length <= 1000`
* 2 <= arr[i] <= 109
* All the values of `arr` are **unique**.