# 0823. Binary Trees With Factors

https://leetcode.com/problems/binary-trees-with-factors

## Description

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**.

## ac

```java
```
