There are `n`

soldiers standing in a line. Each soldier is assigned a **unique** `rating`

value.

You have to form a team of 3 soldiers amongst them under the following rules:

- Choose 3 soldiers with index (
`i`

,`j`

,`k`

) with rating (`rating[i]`

,`rating[j]`

,`rating[k]`

). - A team is valid if: (
`rating[i] < rating[j] < rating[k]`

) or (`rating[i] > rating[j] > rating[k]`

) where (`0 <= i < j < k < n`

).

Return the number of teams you can form given the conditions. (soldiers can be part of multiple teams).

**Example 1:**

Input:rating = [2,5,3,4,1]Output:3Explanation:We can form three teams given the conditions. (2,3,4), (5,4,1), (5,3,1).

**Example 2:**

Input:rating = [2,1,3]Output:0Explanation:We can't form any team given the conditions.

**Example 3:**

Input:rating = [1,2,3,4]Output:4

**Constraints:**

`n == rating.length`

`3 <= n <= 1000`

`1 <= rating[i] <= 10`

^{5}- All the integers in
`rating`

are**unique**.

class Solution {
public int numTeams(int[] rating) {
}
}