In a Track-and-Field training session, you record the running speeds of n players in the order they take off, stored in an array rating.

You want to form 3-player teams that meet the following conditions:

Choose three players with indices (i, j, k) such that 0 <= i < j < k < n.

The team is valid if their speeds follow one of these patterns:
- Increasing: rating[i] < rating[j] < rating[k]
- Decreasing: rating[i] > rating[j] > rating[k]

A player can be part of multiple teams.

Return the total number of valid 3-player teams.

Example 1:

Input: rating = [3,6,4,5,2]
Output: 3
Explanation: The valid teams are (3,4,5), (6,4,2), and (6,5,2).

Example 2:

Input: rating = [3,2,4]
Output: 0 
Explanation: No valid teams can be formed.

Example 3:

Input: rating = [2,3,4,5]
Output: 4 
Explanation: has C(4, 3) = 4 increasing triplets.
(2,3,4), (2,3,5), (2,4,5), (3,4,5)
Because the entire array is strictly increasing, every choice of three players 
in index order forms a valid increasing team.

Constraints

n == rating.length

3 <= n <= 1000

1 <= rating[i] <= 10⁵

All the integers in rating are unique.

94. Number of Valid Teams