You want to build some obstacle courses. You are given a 0-indexed integer array `obstacles` of length `n`, where `obstacles[i]` describes the height of the `ith` obstacle.

For every index `i` between `0` and `n - 1` (inclusive), find the length of the longest obstacle course in `obstacles` such that:

- You choose any number of obstacles between `0` and `i` inclusive.
- You must include the `ith` obstacle in the course.
- You must put the chosen obstacles in the same order as they appear in `obstacles`.
- Every obstacle (except the first) is taller than or the same height as the obstacle immediately before it.

Return an array `ans` of length `n`, where `ans[i]` is the length of the longest obstacle course for index `i` as described above.

Example 1:

    Input: obstacles = [1,2,3,2]
    Output: [1,2,3,3]
    Explanation: The longest valid obstacle course at each position is:
    - i = 0: [1], [1] has length 1.
    - i = 1: [1,2], [1,2] has length 2.
    - i = 2: [1,2,3], [1,2,3] has length 3.
    - i = 3: [1,2,3,2], [1,2,2] has length 3.

Example 2:

    Input: obstacles = [2,2,1]
    Output: [1,2,1]
    Explanation: The longest valid obstacle course at each position is:
    - i = 0: [2], [2] has length 1.
    - i = 1: [2,2], [2,2] has length 2.
    - i = 2: [2,2,1], [1] has length 1.

Example 3:

    Input: obstacles = [3,1,5,6,4,2]
    Output: [1,1,2,3,2,2]
    Explanation: The longest valid obstacle course at each position is:
    - i = 0: [3], [3] has length 1.
    - i = 1: [3,1], [1] has length 1.
    - i = 2: [3,1,5], [3,5] has length 2. [1,5] is also valid.
    - i = 3: [3,1,5,6], [3,5,6] has length 3. [1,5,6] is also valid.
    - i = 4: [3,1,5,6,4], [3,4] has length 2. [1,4] is also valid.
    - i = 5: [3,1,5,6,4,2], [1,2] has length 2.

Constraints:

- `n == obstacles.length`
- `1 <= n <= 105`
- `1 <= obstacles[i] <= 107`