Given two arrays of integers nums1 and nums2, return the number of triplets formed (type 1 and type 2) under the following rules:

Type 1: Triplet (i, j, k) if nums1[i]2 == nums2[j] * nums2[k] where 0 <= i < nums1.length and 0 <= j < k < nums2.length.
Type 2: Triplet (i, j, k) if nums2[i]2 == nums1[j] * nums1[k] where 0 <= i < nums2.length and 0 <= j < k < nums1.length.

 
Example 1:
Input: nums1 = [7,4], nums2 = [5,2,8,9]
Output: 1
Explanation: Type 1: (1,1,2), nums1[1]^2 = nums2[1] * nums2[2]. (4^2 = 2 * 8). 

Example 2:
Input: nums1 = [1,1], nums2 = [1,1,1]
Output: 9
Explanation: All Triplets are valid, because 1^2 = 1 * 1.
Type 1: (0,0,1), (0,0,2), (0,1,2), (1,0,1), (1,0,2), (1,1,2).  nums1[i]^2 = nums2[j] * nums2[k].
Type 2: (0,0,1), (1,0,1), (2,0,1). nums2[i]^2 = nums1[j] * nums1[k].

Example 3:
Input: nums1 = [7,7,8,3], nums2 = [1,2,9,7]
Output: 2
Explanation: There are 2 valid triplets.
Type 1: (3,0,2).  nums1[3]^2 = nums2[0] * nums2[2].
Type 2: (3,0,1).  nums2[3]^2 = nums1[0] * nums1[1].

Example 4:
Input: nums1 = [4,7,9,11,23], nums2 = [3,5,1024,12,18]
Output: 0
Explanation: There are no valid triplets.

 
Constraints:

1 <= nums1.length, nums2.length <= 1000
1 <= nums1[i], nums2[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 Solution:\n    def numTriplets(self, nums1: List[int], nums2: List[int]) -> int:\n        \n        def count(nums1, nums2):\n            # triplets = set()\n            triplets = 0\n\n            cnt2 = {}\n            for i2, num2 in enumerate(nums2):\n                if num2 not in cnt2:\n                    cnt2[num2] = []\n                cnt2[num2].append(i2)        \n\n            for i1, num1 in enumerate(nums1):\n                # print('stage1', i1, num1)\n                square = num1 ** 2\n\n                for num2j, idxs2j in cnt2.items():\n                    if square % num2j != 0:\n                        continue\n\n                    num2k = int(square // num2j)\n\n                    if num2k not in cnt2:\n                        continue\n\n                    idxs2k = cnt2[num2k]\n                    \n                    combined = []\n                    for idx2j in idxs2j:\n                        combined.append((idx2j, 0))  # j\n                    for idx2k in idxs2k:\n                        combined.append((idx2k, 1))\n                    combined.sort()\n                    temp_cnt = 0\n                    for comb in combined:\n                        idx, ty = comb\n                        if ty == 0:\n                            triplets += temp_cnt\n                        else:\n                            temp_cnt += 1\n                    \n                    \n#                     print(num1, square, idxs2j, idxs2k, j, k)\n#                     while j >= 0:\n#                         print(j, k, larger)\n#                         if idxs2j[j] < idxs2k[k]:\n#                             if k > 0:\n#                                 larger += 1\n#                                 k -= 1\n#                             else:\n#                                 if larger == 0:\n#                                     larger = 1\n#                                 triplets += larger\n#                                 j -= 1\n#                             # if k < 0:\n#                             #     triplets += larger\n#                             #     break\n#                         else:\n#                             triplets += larger\n#                             j -= 1\n#                     # triplets += larger\n                    \n#                     print('triplets=', triplets)\n                    \n                    \n                    # print('stage2', idxs2k)\n                    \n                    # for idx2j in idxs2j:\n                    #     for idx2k in idxs2k:\n                    #         if idx2k <= idx2j:\n                    #             continue\n                    #         triplets += 1\n                            # triplets.add((i1, idx2j, idx2k))\n                            # print(num1, nums2[idx2j], nums2[idx2k])\n\n            return triplets\n            \n        \n        triplets1 = count(nums1, nums2)\n        triplets2 = count(nums2, nums1)\n                \n        # return len(triplets1) + len(triplets2)\n        return triplets1 + triplets2"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'numTriplets'
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: 7054