There are n soldiers standing in a line. Each soldier is assigned a unique rating value, represented by an integer array rating.

A team is composed of $3$ soldiers located at indices i, j, and k with $0 \leq i < j < k < n$ such that one of the following conditions is satisfied:

• rating[i] $<$ rating[j] $<$ rating[k]

• rating[i] $>$ rating[j] $>$ rating[k]

Return the total number of teams that can be formed according to these rules.

Constraints:

• n == rating.length

• $3 \leq$ n $\leq 1000$

• $1 \leq$ rating[i] $\leq 10^5$

• All the integers in rating are unique.

Now, let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

Implement your solution in the following coding playground.