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 = 'isp = [True for i in range(100000)]\npr = []\nfor i in range(2,100000):\n    c = i\n    if isp[i]:\n        pr.append(i)\n        while c<100000-i:\n            c+=i\n            isp[c] = False\n\nclass Solution:\n    def largestComponentSize(self, A: List[int]) -> int:\n        def pcr(n):\n            r = n**0.5\n            ans = {n}\n            for p in pr:\n                if p>r:\n                    if n>1:\n                        ans.add(n)\n                    break\n                if n%p==0:\n                    ans.add(p)\n                    while n%p==0:\n                        n=n//p\n                    r = n**0.5\n            return ans\n        def iscf(n1,n2):\n            nn1,nn2 = max(n1,n2),min(n1,n2)\n            while nn1%nn2!=0:\n                n1=nn1-nn2\n                n2 = nn2\n                nn1,nn2 = max(n1,n2),min(n1,n2)\n            n = min(nn1,nn2)\n            return True if n>1 else False\n        prn = {a:pcr(a) for a in A}\n        print(prn)\n        #return\n        while True:\n            rms = set()\n            ks = list(prn.keys())\n            kn = len(ks)\n            for i,k in enumerate(ks):\n                if len(prn[k])==1:\n                    rms.add(k)\n                    continue\n                for j in range(i+1,kn):\n                    if len(prn[ks[j]])==1:\n                        rms.add(ks[j])\n                        continue\n                    if prn[k].intersection(prn[ks[j]]):\n                        #print(k,ks[j],prn[k])\n                        prn[k].update(prn[ks[j]])\n                        #print(k,ks[j],prn[k])\n                        rms.add(ks[j])\n                if rms:\n                    break\n            for k in rms:\n                del prn[k]\n            if not rms:\n                break\n        aa = set(A)\n        #print([(k,len(v)) for k,v in prn.items()])\n        #print(prn)\n        cdd = [len(v&aa) for v in prn.values()]\n        return max(cdd)'
_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: 9198