Binary Trees With Factors

Medium

Arrays Hash Tables Dynamic Programming Sorting Dynamic Programming

Problem

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.

Constraints

1 <= arr.length <= 1000
2 <= arr[i] <= 10^9
All the values of arr are unique

Examples

Input: arr = [2, 4]

Output: 3

We can make these trees: [2], [4], [4, 2, 2]. Each single node counts as a tree, and 4 can be the root with two children of value 2 since 2 * 2 = 4.

Input: arr = [2, 4, 5, 10]

Output: 7

We can make these trees: [2], [4], [5], [10], [4, 2, 2], [10, 2, 5], [10, 5, 2]. Note that [10, 2, 5] and [10, 5, 2] are different trees because the left and right children are swapped.

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