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 node:\n    def __init__(self,val):\n        self.val=val\n        self.next=[]\nclass Solution:\n    def largestComponentSize(self, A: List[int]) -> int:\n        # l=[node(i) for i in A]\n        # for i in range(len(l)):\n        #     for j in range(len(l)):\n        #         if math.gcd(l[i].val,l[j].val)>1 and i!=j:\n        #             l[j].next.append(i)\n        # # for i in range(len(l)):\n        # #     print(l[i].next)\n        # # print(l)\n        # # def bfs(n,m):\n        # #     nonlocal l,vis\n        # #     # print(n,m,vis)\n        # #     vis[n]=True\n        # #     m+=1\n        # #     # k=m\n        # #     for i in l[n].next:\n        # #         if not vis[i]:\n        # #             m=dfs(i,m)\n        # #     return m\n        # def bfs(n):\n        #     nonlocal l,vis\n        #     q=[n]\n        #     # vis[n]=True\n        #     m=0\n        #     while q:\n        #         # print(q,vis)\n        #         k=[]\n        #         for i in q:\n        #             if not vis[i]:\n        #                 vis[i]=True\n        #                 k.extend(l[i].next)\n        #                 m+=1\n        #         q=k\n        #     return m\n        # mi=0\n        # vis=[False for i in range(len(l))]\n        # for i in range(len(l)):\n        #     if not vis[i]:\n        #         mi=max(mi,bfs(i))\n        # return mi\n        p=[2]\n        for i in range(3,int(max(A)**0.5)+1,2):\n            for y in p:\n                if i%y==0:\n                    break\n            else:\n                p.append(i)\n        f=collections.defaultdict(list)\n        for a in A:\n            x=a\n            for pp in p:\n                if pp**2>x:\n                    break\n                if x%pp==0:\n                    f[a].append(pp)\n                    while x%pp==0:\n                        x=x//pp\n            if x>1:\n                f[a].append(x)\n                p.append(x)\n        # print(p,f)\n        p=list(set(p))\n        n=len(p)\n        p2i={pp:i for i,pp in enumerate(p)}\n        par=[i for i in range(n)]\n        def find(i):\n            if i!=par[i]:\n                par[i]=find(par[i])\n            return par[i]\n        def union(i,j):\n            pi,pj=find(i),find(j)\n            if pi!=pj:\n                par[pi]=pj\n        for a in A:\n            if f[a]:\n                p0=f[a][0]\n                for pp in f[a][1:]:\n                    union(p2i[p0],p2i[pp])\n        # l=[find(p2i[f[a][0]]) for a in A]\n        c=collections.Counter(find(p2i[f[a][0]]) for a in A if f[a])\n        return max(c.values())\n        \n        \n        \n        \n        \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: 13326