 # Largest Divisible Subset

You are given a set of numbers `nums` consisting of distinct numbers. Find the size of the largest subset that satisfies the following condition: for each two number pairings in the set, one number is divisible by the other.

### Input

• `nums`: a list integers representing the set.

### Output

An integer representing the size of the largest subset that satisfy the condition.

### Examples

#### Example 1:

Input:

``1nums = [1, 2, 3]``

Output: `2`

Explanation:

Either `[1, 2]` or `[1, 3]` satisfy the condition, because both `2` and `3` are both divisible by `1`. Either way, the largest set has a size of `2`.

#### Example 2:

Input:

``1nums = [1, 2, 4, 8]``

Output: `4`

Explanation:

In this set, for each pair of numbers, at least one is divisible by the other because they are all powers of `2`. As such, the max subset has a size of `4`, the size of the original set.

### Constraints

• `1 <= len(nums) <= 1000`
• `1 <= nums[i] <= 10^9`
• Each number in `nums` is unique