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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.

class Solution: def numTeams(self, rating: List[int]) -> int: