Given an array of integers arr, and three integers a, b and c. You need to find the number of good triplets.
A triplet (arr[i], arr[j], arr[k]) is good if the following conditions are true:

0 <= i < j < k < arr.length
|arr[i] - arr[j]| <= a
|arr[j] - arr[k]| <= b
|arr[i] - arr[k]| <= c

Where |x| denotes the absolute value of x.
Return the number of good triplets.
 
Example 1:
Input: arr = [3,0,1,1,9,7], a = 7, b = 2, c = 3
Output: 4
Explanation: There are 4 good triplets: [(3,0,1), (3,0,1), (3,1,1), (0,1,1)].

Example 2:
Input: arr = [1,1,2,2,3], a = 0, b = 0, c = 1
Output: 0
Explanation: No triplet satisfies all conditions.

 
Constraints:

3 <= arr.length <= 100
0 <= arr[i] <= 1000
0 <= a, b, c <= 1000

```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 Solution: \n  def countGoodTripletsCase1(self, arr: List[int], a: int, b: int) -> int:\n    count = 0\n    for j in range(1, len(arr) - 1):\n      l = sum(abs(arr[i] - arr[j]) <= a for i in range(0, j))\n      r = sum(abs(arr[j] - arr[k]) <= b for k in range(j + 1, len(arr)))\n      count += l * r\n    return count\n\n  def countGoodTripletsCase2(self, arr: List[int], a: int, b: int, c: int) -> int:\n    index = sorted(range(len(arr)), key=lambda k: arr[k])\n    count = 0\n    for j in range(len(arr) - 1, 0, -1):\n      for i in range(j - 1, -1, -1):\n        if index[j] == j: break\n        index[j], index[i] = index[i], index[j]\n      for k in range(j + 2, len(arr)):\n        if arr[index[k - 1]] > arr[index[k]]:\n          index[k - 1], index[k] = index[k], index[k - 1]\n\n      i_min = next((i for i in range(0, j) if arr[index[i]] >= arr[j] - a), j)\n      i_max = next((i for i in range(i_min, j) if arr[index[i]] > arr[j] + a), j)\n\n      ic_min, ic_max = i_min, i_min\n      k = next((i for i in range(j + 1, len(arr)) if arr[index[i]] >= arr[j] - b), len(arr))\n      while k < len(arr) and arr[index[k]] <= arr[j] + b:\n        while ic_min < i_max and arr[index[ic_min]] < arr[index[k]] - c: ic_min += 1\n        while ic_max < i_max and arr[index[ic_max]] <= arr[index[k]] + c: ic_max += 1\n        count += ic_max - ic_min\n        k += 1\n\n    return count\n\n  def countGoodTriplets(self, arr: List[int], a: int, b: int, c: int) -> int:\n    if c >= a + b:\n      return self.countGoodTripletsCase1(arr, a, b)\n    else:\n      return self.countGoodTripletsCase2(arr, a, b, c)'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'countGoodTriplets'
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: 8108