# 1395. Count Number of Teams

<https://leetcode.com/problems/count-number-of-teams>

## Description

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:** 3
**Explanation:** 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:** 0
**Explanation:** 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] <= 105`
* All the integers in `rating` are **unique**.

## ac

```java
```