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 = '# Largest Component Size by Common Factor\n# https://www.youtube.com/watch?v=6Ud_4A9qTp4\n\nfrom math import sqrt\nfrom collections import Counter\nclass Solution:\n    def largestComponentSize(self, A: List[int]) -> int:\n        parent = {}\n        \n        def ufind(a):\n            if a not in parent:\n                parent[a] = a\n            if a != parent[a]:\n                parent[a] = ufind(parent[a])\n            return parent[a]\n        \n        def uunion(a,b):\n            ua = ufind(a)\n            ub = ufind(b)\n\n            parent[ua] = ub\n        \n        count = Counter()\n        for x in A:\n            y = 2\n            factors = []\n            # # 1\n            # find common & primes of X\n            while x >= y * y:\n                if x % y == 0:\n                    factors.append(y)\n                    # delete y common\n                    while x % y == 0:\n                        x //= y\n                y += 1\n            if x > 1: # find new primes\n                factors.append(x)\n\n            # # 2\n            # zip(factors, factors[1:]) -> [a,b,c] => ab , bc ~~\n            # Linking parent (if link => small -> large)\n            for a, b in zip(factors, factors[1:]):\n                uunion(a, b)\n\n            # # 3\n            # prime > 0 \n            # minimum factors += 1\n            if len(factors)>0:\n                count[factors[0]] += 1\n        \n        final_count = Counter()\n\n        for key in count.keys():\n            final_count[ufind(key)] += count[key]\n\n        best = 0\n        for key in final_count.keys():\n            best = max(best, final_count[key])\n\n        return best'
_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: 8418