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 Solution:\n    def find(self, g,i):\n        # find the group id of element i\n        if i in g:   gid=g[i]\n        else: gid=g[i]=i\n            \n        if gid!=i:\n            new_gid=self.find(g,gid)\n            g[i]=new_gid\n        return g[i]\n            \n    def merge(self,g,i,j):\n        # merge two groups\n        gid=self.find(g,i)\n        gjd=self.find(g,j)\n        if gid!=gjd:\n            g[gid]=gjd\n\n    def prime_factors(self, x):\n        if x==1: return [1]\n        \n        primes=[2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, \n               67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, \n               139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, \n               223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, \n               293, 307, 311, 313, 317 ]\n        \n        ans={x}\n        idx,p=0,primes[0]\n        while p*p<=x:\n            if x % p == 0:  \n                ans.add(p)\n                x//=p\n            else:\n                idx+=1\n                p=primes[idx]\n        if x>1: ans.add(x)\n        return ans\n        \n    def largestComponentSize(self, A: List[int]) -> int:\n        \n        n=len(A)\n        print(n)\n        g=dict()\n        \n        for x in A:\n            pfs=list(self.prime_factors(x))\n            \n            for p in pfs[1:]:\n                self.merge(g, pfs[0], p)\n            \n        groups=[self.find(g,x) for x in A]\n        ans=collections.Counter(groups).most_common(1)\n        return ans[0][1]\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: 12510