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 = '\nfrom collections import defaultdict\nclass Solution:\n    def largestComponentSize(self, A: List[int]) -> int:\n        \n        def getFactors(n):\n            if n==1:\n                return [1]\n            factor_set=[]\n            if n%2==0:\n                factor_set.append(2)\n                while n%2==0:\n                    n=n//2\n            if n>1:\n                for i in range(3,math.floor(math.sqrt(n))+1,2):\n                    if n%i==0:\n                        factor_set.append(i)\n                        while n%i==0:\n                            n=n//i\n                    if n==1:\n                        break\n            if n>2:\n                factor_set.append(n)\n            return factor_set\n                    \n        \n        def find(parent,n):\n            result=parent[n]\n            if result!=n:\n                parent[n]=find(parent,result)\n            return parent[n]\n        \n        def union(parent,n1,n2):\n            r1=rank[n1]\n            r2=rank[n2]\n            x1=find(parent,n1)\n            x2=find(parent,n2)\n            if x1!=x2:\n                if r1>=r2:\n                    parent[x2]=parent[x1]\n                    rank[x1]+=1\n                else:\n                    parent[x1]=parent[x2]\n                    rank[x2]+=1\n            \n        # print(\\"--------------\\")\n \n        max_elem=max(A)\n        parent=[i for i in range(max_elem+1)]\n        rank=[0]*(max_elem+1)\n        \n        for item in A:\n            factor_set=getFactors(item)\n            # print(item,factor_set)\n            v1=find(parent,item)\n            if v1==item:\n                union(parent,factor_set[0],v1)\n                for factor in factor_set[1:]:\n                    union(parent,factor_set[0],factor)\n        count=defaultdict(int)\n        for item in A:\n            count[find(parent,item)]+=1\n        # print(count)\n        # print(parent)\n        return max(count.values())\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: 8204