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
1 <= n <= 200
1 <= rating[i] <= 10^5

```python

USER_FILENAME = "<user_code>"
import sys, json, builtins
import math, heapq, bisect, itertools, functools, collections, statistics, fractions, decimal, operator, array, random, re, string, os, pathlib
try:
    import resource as _res
except Exception:
    _res = None
from collections import Counter, defaultdict, deque, OrderedDict
from functools import lru_cache, reduce
from itertools import accumulate, permutations, combinations, product
from math import gcd, ceil, floor, sqrt
from decimal import Decimal
try:
    from typing import *
except Exception:
    pass
try:
    sys.setrecursionlimit(1_000_000)
except Exception:
    pass
try:
    import site as _site
    try:
        _sys_sites = _site.getsitepackages() if hasattr(_site, "getsitepackages") else []
        for _p in _sys_sites:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
    try:
        _usp = _site.getusersitepackages()
        if isinstance(_usp, str):
            _usp = [_usp]
        for _p in _usp:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
except Exception:
    pass

def _disabled_input(*args, **kwargs):
    raise RuntimeError("input() is disabled in callable mode")
builtins.input = _disabled_input

ns = {"__name__": "__judge__"}  # prevent if __name__ == "__main__" blocks
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = 'class node:\n    \n    def __init__(self,val):\n        \n        self.val = val\n        \n        self.right = None\n        \n        self.left = None\n\nclass Solution:\n    \n    def update(self,i,j,ind,root):\n    \n        if i == j:\n            root.val += 1\n        else:\n            \n            mid = (i+j) // 2\n            \n            if ind <=mid:\n                self.update(i,mid,ind,root.left)\n            elif ind > mid:\n                self.update(mid+1,j,ind,root.right)\n                \n            root.val = 0\n            \n            if root.left:\n                root.val +=root.left.val\n            if root.right:\n                root.val += root.right.val\n                \n                \n      \n    def findSum(self,i,j,left,right,root):\n        \n        if left<=i and right>=j:\n            return root.val\n        \n        elif right<i or left > j:\n            return 0\n        \n        mid = (i+j) // 2\n        \n        if right<=mid:\n            return self.findSum(i,mid,left,right,root.left)\n        elif left>mid:\n            return self.findSum(mid+1,j,left,right,root.right)\n        \n        else:\n            \n            x = self.findSum(i,mid,left,mid,root.left)\n            \n            y = self.findSum(mid+1,j,mid+1,right,root.right)\n            \n            return x+y\n        \n    \n    def build(self,i,j):\n        \n        if i == j:\n            root = node(0)\n            \n        else:\n            \n            mid = (i+j) // 2\n            root = node(0)\n            root.left = self.build(i,mid)\n            root.right = self.build(mid+1,j)\n            \n            \n            \n            if root.left:\n                root.val+=root.left.val\n                \n            if root.right:\n                root.val+=root.right.val\n                \n                \n        return root\n            \n   \n    def solve(self,rating):\n        n = max(rating) + 1\n        \n        self.arr = [0]*n\n        \n        length = len(rating)\n        \n        left = [0]*length\n        right = [0]*length\n        rootLeft = self.build(0,n)\n        rootRight = self.build(0,n)\n        \n        \n        for i in range(length):\n            \n            left[i] = self.findSum(0,n,0,rating[i]-1,rootLeft)\n            self.update(0,n,rating[i],rootLeft)\n                \n        for i in range(length-1,-1,-1):\n            \n            right[i] = self.findSum(0,n,rating[i]+1,n,rootRight)\n            self.update(0,n,rating[i],rootRight)\n            \n        \n        ans = 0\n        for i in range(1,length-1):\n            \n            ans = ans + left[i]*right[i]\n        \n        # print(left)\n        # print(right)\n        # print(\\"************\\")\n        return ans\n        \n    def numTeams(self, rating: List[int]) -> int:\n        \n        if len(rating)<3:\n            return 0\n        \n        temp = rating[:]\n        temp.sort()\n        \n        value = 1\n        \n        self.mp = {}\n        \n        for x in temp:\n            \n            if x not in self.mp:\n                \n                self.mp[x] = value\n                \n                value +=1\n                \n            \n        for i in range(len(rating)):\n            \n            rating[i] = self.mp[rating[i]]\n            \n            \n        \n        ans = self.solve(rating)+self.solve(rating[::-1])\n        \n        return ans\n        \n        \n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'numTeams'
if _fn_name:
    if "Solution" in ns:
        try:
            _obj = ns["Solution"]()
            if hasattr(_obj, _fn_name):
                _target = getattr(_obj, _fn_name)
        except Exception:
            _target = None
    if _target is None and _fn_name in ns and callable(ns[_fn_name]):
        _target = ns[_fn_name]
# Fallback: if there's exactly one user-defined function, use it
if _target is None:
    _cands = [v for k, v in ns.items() if callable(v) and getattr(v, "__module__", "") in ("__judge__", "__main__")]
    _user_funcs = [c for c in _cands if getattr(c, "__name__", "").startswith("_") is False]
    if len(_user_funcs) == 1:
        _target = _user_funcs[0]
if _target is None:
    raise RuntimeError(f"Could not resolve callable '{_fn_name}'")

_raw = sys.stdin.read().strip()
if _raw:
    _parsed = json.loads(_raw)
    if isinstance(_parsed, dict):
        _kwargs = _parsed.get("kwargs", {})
        _args = _parsed.get("args", [])
    else:
        _args, _kwargs = _parsed, {}
else:
    _args, _kwargs = [], {}
if not isinstance(_args, (list, tuple)):
    _args = [_args]
_res = _target(*_args, **_kwargs)
try:
    sys.stdout.write(repr(_res) + "\n")
except Exception:
    pass

```

Measured memory_bytes: 14424