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 wrapper(self, toSquare, toProd):\n        \n        #create a hash table of count of unique squared ints in arr 1\n        table = {}\n        for integer in toSquare:\n            squared = integer**2\n            if squared not in table:\n                table[squared] = 1\n            else:\n                table[squared] += 1\n        \n        counter = 0\n        #get all pairs products, check in hash table, if so, inc counter by count in table\n        i = 0\n        while i < len(toProd): #minus one ok too?\n            j = i + 1\n            while j < len(toProd):\n                product = toProd[i] * toProd[j]\n                if product in table:\n                    counter += table[product]\n                j += 1\n            i += 1\n        \n        return counter\n                    \n    def numTriplets1(self, nums1: List[int], nums2: List[int]) -> int:\n        \n        counter = 0\n        counter += self.wrapper(nums1, nums2)\n        counter += self.wrapper(nums2, nums1)\n        return counter\n    \n    def get_tables(self, nums):\n        squares = {}\n        products = {}\n        i = 0\n        while i != len(nums):\n            j = i\n            while j != len(nums):   # O(N^2)\n                product_or_square = nums[i] * nums[j]\n                if i == j:\n                    if product_or_square not in squares:    # O(1)\n                        squares[product_or_square] = 1     # O(1) \n                    else:\n                        squares[product_or_square] += 1     # O(1)\n                else:\n                    if product_or_square not in products:\n                        products[product_or_square] = 1\n                    else:\n                        products[product_or_square] += 1\n                j += 1\n            i += 1\n        \n        return products, squares\n    \n    def get_counts(self, products, squares):\n        # iterate over the smaller set\n        counter = 0\n        if len(products) > len(squares):\n            for square in squares:          # O(N)\n                if square in products:\n                    counter += squares[square] * products[square]\n        else:\n            for product in products:        #O(M)\n                if product in squares:\n                    counter += products[product] * squares[product]\n        \n        return counter\n    \n    def numTriplets2(self, nums1: List[int], nums2: List[int]) -> int:\n        products1, squares1 = self.get_tables(nums1)\n        products2, squares2 = self.get_tables(nums2)\n        counter = 0\n        counter += self.get_counts(products1, squares2)\n        counter += self.get_counts(products2, squares1)\n\n        return counter\n    \n    def get_products(self, nums):\n        table = {}\n        i = 0\n        while i < len(nums) - 1:\n            j = i + 1\n            while j < len(nums):\n                prod = nums[i] * nums[j]\n                if prod not in table:\n                    table[prod] = 1\n                else:\n                    table[prod] += 1\n                j += 1\n            i += 1\n        \n        return table\n    \n    def check_squares_in_prods(self, nums, prods):\n        counter = 0\n        for i in nums:\n            sq = i**2\n            if sq in prods:\n                counter += prods[sq]\n        return counter\n    \n    def numTriplets(self, nums1: List[int], nums2: List[int]) -> int:\n        \n        prods1 = self.get_products(nums1)\n        prods2 = self.get_products(nums2)\n\n        counter = 0\n        counter += self.check_squares_in_prods(nums1, prods2)\n        counter += self.check_squares_in_prods(nums2, prods1)\n        \n        return counter\n'
_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: 6092