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 = 'class UF:        \n    def __init__(self) -> None:\n        self.parent = {}\n        self.sz = {}\n        self.count = 0\n        \n    def add(self, p):    \n        if p not in self.parent:\n            self.parent[p] = p\n            self.sz[p] = 1\n            self.count += 1\n                          \n    def find(self, p: int) -> int:\n        while p != self.parent[p]:\n            self.parent[p] = self.parent[self.parent[p]]\n            p = self.parent[p]\n        return p  \n              \n    def union(self, p: int, q: int) -> None:\n        i = self.find(p)\n        j = self.find(q)             \n        if i == j:    \n            return \n        if self.sz[i] > self.sz[j]:                 \n            self.parent[j] = i\n            self.sz[i] += self.sz[j]\n        else:             \n            self.parent[i] = j\n            self.sz[j] += self.sz[i]                                           \n        self.count -= 1 \n        \nclass Solution:\n    def largestComponentSize(self, A: List[int]) -> int:\n        def fac(n): \n            for i in range(2, int(n**0.5)+1):\n                if n % i == 0:\n                    n //= i\n                    return set((i,)) | fac(n)\n            return set((n,))\n        @lru_cache(None) \n        def group_id(p):\n            return uf.find(p)\n        uf = UF()\n        c = Counter() \n        for n in A:\n            factors = fac(n)\n            key = tuple(sorted(factors))\n            c[key] += 1\n            if c[key] == 1:\n                p = factors.pop()\n                uf.add(p)\n                for q in factors:\n                    uf.add(q)\n                    uf.union(p, q)\n        if uf.count == 1:\n            return len(A)            \n        groups = Counter()\n        for factors, value in list(c.items()):\n            groups[group_id(factors[0])] += value\n        return groups.most_common()[0][1]    \n            \n            \n            \n            \n            \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: 12290