Given a non-empty array of unique positive integers A, consider the following graph:

There are A.length nodes, labelled A[0] to A[A.length - 1];
There is an edge between A[i] and A[j] if and only if A[i] and A[j] share a common factor greater than 1.

Return the size of the largest connected component in the graph.
 



Example 1:
Input: [4,6,15,35]
Output: 4



Example 2:
Input: [20,50,9,63]
Output: 2



Example 3:
Input: [2,3,6,7,4,12,21,39]
Output: 8


Note:

1 <= A.length <= 20000
1 <= A[i] <= 100000

```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 = 'def get_primes(max_num):\n    return []\n#     primes = []\n#     possible_primes = [True for _ in range(max_num + 1)]\n#     value = 2\n#     while value <= max_num:\n#         if possible_primes[value]:\n#             primes.append(value)\n#             for multiplier in range(2, max_num // value + 1):\n#                 possible_primes[multiplier * value] = False\n                \n#         value += 1\n        \n#     return primes\n\n\ndef get_prime_factors(num, primes):\n    for i in range(2, int(math.sqrt(num)) + 1):\n        if num % i == 0:\n            return list(set(get_prime_factors(num // i, primes) + [i]))\n                \n            \n    return [num]\n#     if num == 1:\n#         return [1]\n    \n#     prime_factors = set()\n    \n#     for prime in primes:\n#         if num < prime:\n#             break\n#         while num % prime == 0:\n#             num = num // prime\n#             prime_factors.add(prime)\n            \n#     return list(prime_factors)\n\n\nclass DisjointSet:\n    def __init__(self, primes):\n        self.primes = primes\n        self.prime_parents = {}\n        self.parent_to_count = {}\n        \n    def get_parent(self, prime):\n        if prime not in self.prime_parents:\n            self.prime_parents[prime] = -1\n            return prime\n        \n        current = prime\n        while self.prime_parents[current] > 0:\n            current = self.prime_parents[current]\n            \n        return current\n    \n    def join(self, left, right):\n        left_parent = self.get_parent(left)\n        right_parent = self.get_parent(right)\n\n        if left_parent == right_parent:\n            return\n        \n        if self.prime_parents[left_parent] < self.prime_parents[right_parent]:\n            larger = left_parent\n            smaller = right_parent\n        else:\n            larger = right_parent\n            smaller = left_parent\n            \n        self.prime_parents[larger] += self.prime_parents[smaller]\n        self.parent_to_count[larger] = self.parent_to_count.get(larger, 0) + self.parent_to_count.get(smaller, 0)\n        self.prime_parents[smaller] = larger\n            \n    \n    def add(self, val):\n        prime_factors = get_prime_factors(val, self.primes)\n        for l, r in zip(prime_factors, prime_factors[1:]):\n            self.join(l, r)\n            \n        parent = self.get_parent(prime_factors[0])\n        self.parent_to_count[parent] = self.parent_to_count.get(parent, 0) + 1\n           \n\n    \n    def get_largest_set_size(self):\n        return max(self.parent_to_count.values())\n    \n\nclass Solution:\n    def largestComponentSize(self, A: List[int]) -> int:\n        max_val = max(A)\n        primes = get_primes(max_val)\n        \n        dj_set = DisjointSet(primes)\n        for val in A:\n            dj_set.add(val)\n            \n        return dj_set.get_largest_set_size()'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'largestComponentSize'
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: 8178