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** `10`

.^{9} + 7

**Example 1:**

Input:arr = [2,4]Output:3Explanation:We can make these trees:`[2], [4], [4, 2, 2]`

**Example 2:**

Input:arr = [2,4,5,10]Output:7Explanation: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] <= 10`

^{9}- All the values of
`arr`

are**unique**.

class Solution:
def numFactoredBinaryTrees(self, arr: List[int]) -> int: