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 DSU:\n    def __init__(self, N):\n        self.p = list(range(N))\n\n    def find(self, x):\n        if self.p[x] != x:\n            self.p[x] = self.find(self.p[x])\n        return self.p[x]\n\n    def union(self, x, y):\n        xr, yr = self.find(x), self.find(y)\n        self.p[xr] = yr\n\nclass Solution:\n    def primes_set(self,n):\n        for i in range(2, int(math.sqrt(n))+1):\n            if n % i == 0:\n                return self.primes_set(n//i) | set([i])\n        return set([n])\n\n    def largestComponentSize2(self, A):\n        n = len(A)\n        UF = DSU(n)\n        primes = defaultdict(list)\n        for i, num in enumerate(A):\n            pr_set = self.primes_set(num)\n            for q in pr_set: primes[q].append(i)\n        #print(primes,UF.__dict__)\n        for _, indexes in list(primes.items()):\n            for i in range(len(indexes)-1):\n                UF.union(indexes[i], indexes[i+1])\n\n        return max(Counter([UF.find(i) for i in range(n)]).values())\n    \n    \n    def largestComponentSize1(self, A: List[int]) -> int:\n        g = set(range(len(A)))\n        r = 0\n        while g:\n            gc = A[g.pop()]\n            #print(gc,g)\n            ri = 1\n            while True:\n                gm = set()\n                gc2 = 1\n                for i in g:\n                    #print(gc,i,A[i])\n                    if gcd(A[i],gc) > 1:\n                        ri+=1\n                        gm.add(i)\n                        gc2 *= A[i]\n                if not gm: break\n                g -= gm\n                gc = gc2\n            r = max(r,ri)\n                \n        return r\n        \n        \n    def find(self, x):\n        if self.p[x] != x:\n            self.p[x] = self.find(self.p[x])\n        return self.p[x]\n        \n        \n    def largestComponentSize(self, A: List[int]) -> int:\n        #@lru_cache(maxsize=None)\n        \n        self.p = list(range(len(A)))\n        \n        def factors(n:int)->set:\n            return set(factor for i in range(2, int(n**0.5) + 1) if n % i == 0\n                       for factor in (i, n//i))\n        d = {}\n        g = set(range(len(A)))\n        fx = []\n        for i,v in enumerate(A):\n            f = factors(v)\n            f.add(v)\n            #print(i,v,f)\n            fx += [f]\n            for fi in f:\n                l = d.setdefault(fi,[])\n                l += [i]\n        \n        for di in list(d.values()):\n            for a,b in zip(di[1:],di):\n                self.p[self.find(a)] = self.find(b)\n                      \n        return max(Counter(self.find(i) for i in self.p).values())\n                      \n        r = 0                     \n        #print(fx,d)\n        while g:\n            gi = [g.pop()]\n            #print(gi,g)\n            g1 = [gi]\n            \n            while gi:\n                gii = gi.pop()\n                for f in fx[gii]:\n                    for di in d[f]:\n                        if di in g:\n                            g.remove(di)\n                            g1 += [di]\n                            gi+=[di]\n            r = max(r,len(g1))\n    \n        return r\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: 14318