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 (ijk) 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
• 1 <= n <= 200
• 1 <= rating[i] <= 10^5

## Solution 1: Brute Force

Time complexity: O(n^3)
Space complexity: O(1)

## Solution 2: Math

For each soldier j, count how many soldiers on his left has smaller ratings as left[j], count how many soldiers his right side has larger ratings as right[j]

ans = sum(left[j] * right[j] + (j – left[j]) * (n – j – 1 * right[j])

Time complexity: O(n^2)
Space complexity: O(1)

## C++

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