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,n):\n        self.p=[i for i in range(n)]  # parent array\n        self.s=[1]*n  # size array\n        \n    def find(self,x): # find the representative/root of x\n        if self.p[x]!=x:\n            self.p[x]=self.find(self.p[x])\n        return self.p[x]\n\nclass Solution:\n    M=100000\n    sieve=[0]*(M+1) # stores the minimum prime divisor of integers up to M\n    for i in range(2,M+1):\n        if sieve[i]!=0:\n            continue\n        for j in range(1,M//i+1):\n            sieve[j*i]=i\n        \n    def largestComponentSize(self, A: List[int]) -> int:   \n        g=UF(len(A))\n        primes=defaultdict(list) # {q:[nums]} list of integers that's divisible by prime q\n        for i,num in enumerate(A):\n            tmp=-1\n            while num>1:\n                q=self.sieve[num]\n                num//=q\n                if q!=tmp:\n                    primes[q].append(i) # add the element to be divisible by q\n                    tmp=q\n                    \n        for l in primes.values():\n            root=g.find(l[0]) # representative/root of the 1st integer divisible by q\n            for i in l[1:]: # joins all components with root\n                node=g.find(i)\n                if node!=root:\n                    if g.s[root]<g.s[node]: # connect the smaller set to the larger one\n                        root,node=node,root\n                    g.p[node]=root\n                    g.s[root]+=g.s[node]\n        \n        return max(g.s)"
_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: 7174