Given an array of integers A, find the number of triples of indices (i, j, k) such that:

0 <= i < A.length
0 <= j < A.length
0 <= k < A.length
A[i] & A[j] & A[k] == 0, where & represents the bitwise-AND operator.

 
Example 1:
Input: [2,1,3]
Output: 12
Explanation: We could choose the following i, j, k triples:
(i=0, j=0, k=1) : 2 & 2 & 1
(i=0, j=1, k=0) : 2 & 1 & 2
(i=0, j=1, k=1) : 2 & 1 & 1
(i=0, j=1, k=2) : 2 & 1 & 3
(i=0, j=2, k=1) : 2 & 3 & 1
(i=1, j=0, k=0) : 1 & 2 & 2
(i=1, j=0, k=1) : 1 & 2 & 1
(i=1, j=0, k=2) : 1 & 2 & 3
(i=1, j=1, k=0) : 1 & 1 & 2
(i=1, j=2, k=0) : 1 & 3 & 2
(i=2, j=0, k=1) : 3 & 2 & 1
(i=2, j=1, k=0) : 3 & 1 & 2

 
Note:

1 <= A.length <= 1000
0 <= A[i] < 2^16

```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 countTriplets(self, A: List[int]) -> int:\n        c = Counter(x & y for x in A for y in A)\n        return sum(c[xy] for xy in c for z in A if xy & z == 0)\n#         bitsOneDict = {\\"@\\": 20}\n#         ans = 0\n#         ALen = len(A)\n#         for j, num in enumerate(A):\n#             i = 0\n#             pointer = bitsOneDict\n#             while num > 0:\n#                 if num & 1:\n#                     if i not in pointer:\n#                         pointer[i] = {}\n#                     if \\"@\\" not in pointer:\n#                         pointer[\\"@\\"] = i\n#                     else:\n#                         pointer[\\"@\\"] = max(i, pointer[\\"@\\"])\n#                     pointer = pointer[i]\n#                 num >>= 1\n#                 i += 1\n#             if \\"$\\" in pointer:\n#                 pointer[\\"$\\"].add(j)\n#             else:\n#                 pointer[\\"$\\"] = set([j])\n#             if \\"@\\" not in pointer:\n#                 pointer[\\"@\\"] = i+1\n#             else:\n#                 pointer[\\"@\\"] = max(i+1, pointer[\\"@\\"])\n                \n#         for j1, num1 in enumerate(A):\n#             for j2 in range(j1, ALen):\n#                 num2 = A[j2]\n#                 num12 = num1 & num2\n#                 if num12 == 0:\n#                     if j1 == j2:\n#                         ans += ALen\n#                     else:\n#                         ans += ALen*2\n#                 else:\n#                     pointers = [bitsOneDict]\n#                     i = 0          \n#                     subAns = set()\n#                     while i < 16:\n#                         if num12 & 1 == 0:\n#                             newPointers = []\n#                             for k in range(len(pointers)-1, -1, -1):\n#                                 pointer = pointers[k]\n#                                 if i in pointer:\n#                                     newPointers.append(pointer[i])\n#                                 else:\n#                                     if i > pointer[\\"@\\"]:\n#                                         if \\"$\\" in pointer:\n#                                             subAns |= pointer[\\"$\\"]\n#                                         pointers.pop(k)   \n#                             pointers += newPointers\n#                         num12 >>= 1\n#                         i += 1\n#                     for pointer in pointers:\n#                         if \\"$\\" in pointer:\n#                             subAns |= pointer[\\"$\\"]\n#                     if j1 == j2:\n#                         ans += len(subAns)\n#                     else:\n#                         ans += len(subAns)*2\n#         return ans\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'countTriplets'
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: 10660