"""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"""

class Solution:
    def numTeams(self, rating: List[int]) -> int:
        n = len(rating)
        count = 0
        
        for i in range(1, n-1):
            less, greater = [0]*2, [0]*2
            for j in range(n):
                if rating[i] > rating[j]:
                    less[i < j] += 1
                if rating[i] < rating[j]:
                    greater[i < j] += 1
            count += less[0]*greater[1] + greater[0]*less[1]
                        
        return count

"""Runtime: 2015 ms, faster than 17.02% of Python3 online submissions for Count Number of Teams.
Memory Usage: 14.1 MB, less than 99.49% of Python3 online submissions for Count Number of Teams."""