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 = 'from typing import List\nfrom collections import defaultdict\nimport time\n\nDEBUG = False\n# DEBUG = True\n\ndef debug(*args):\n    if not DEBUG:\n        return\n    print((*args))\n\nclass Sieve:\n    def __init__(self, max_n):\n        self.prime_factors = defaultdict(list)\n        for i in range(2, max_n + 1):\n            if len(self.prime_factors[i]) > 0:\n                continue\n            for j in range(i, max_n + 1, i):\n                self.prime_factors[j].append(i)\n\n\n    def factors(self, n):\n        return self.prime_factors[n]\n\nsieve = Sieve(100000)\n\n# s = Sieve(10000)\n# print(s.factors(6))\n# print(s.factors(512))\n# print(s.factors(1007))\n# print(s.factors(5040))\n\nclass Solution:\n    def largestComponentSize(self, a: List[int]) -> int:\n        # start = time.time()\n        #\n        by_factors = defaultdict(list)\n        for x in a:\n            for f in sieve.factors(x):\n                by_factors[f].append(x)\n\n        seen = set()\n        seenf = set()\n        ans = 0\n\n        for x in a:\n            if x in seen:\n                continue\n            seen.add(x)\n            streak = 1\n            todo = [f for f in sieve.factors(x) if f not in seenf]\n            while len(todo) > 0:\n                f = todo.pop()\n                seenf.add(f)\n                for cousin in by_factors[f]:\n                    if cousin not in seen:\n                        seen.add(cousin)\n                        streak += 1\n                        for ff in sieve.factors(cousin):\n                            if ff not in seenf:\n                                todo.append(ff)\n                                seenf.add(ff)\n            ans = max(ans, streak)\n\n        # end = time.time()\n        # print(end - start)\n        return ans\n\n'
_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: