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 Solution:\n    def largestComponentSize(self, A: List[int]) -> int:\n        def prime_factors(num):\n            '''\n            For a number returns it's prime factors in\n            ascending order\n            Input 12, output = [2,2,3]\n            '''\n            pfactors = []\n            factor = 2\n            while num >= factor * factor:\n                if num % factor == 0:\n                    pfactors.append(factor)\n                    num = num // factor\n                else:\n                    factor += 1\n            pfactors.append(num)\n            return pfactors\n        \n        class DisjointSetUnion(object):\n            '''\n            Union Find for 0 to n (inclusive)\n            '''\n            def __init__(self, n):\n                self.parent = {i:i for i in range(n+1)}\n                self.size = [1]*(1+n)\n            def find(self, x):\n                if self.parent[x] != x:\n                    #path compression during find\n                    self.parent[x] = self.find(self.parent[x])\n                return self.parent[x]\n                # while x != self.parent[x]:\n                #     x = self.parent[x]\n                # return self.parent[x]\n            def union(self, a, b):\n                x = self.find(a)\n                y = self.find(b)\n                # self.parent[y] = x\n                if x == y:\n                    return x\n                \n                if self.size[x] > self.size[y]:\n                    self.parent[y] = x\n                    self.size[x] += self.size[y]\n                    return x\n                \n                self.parent[x] = y\n                self.size[y] += self.size[x]\n                return y\n        \n        DS = DisjointSetUnion(max(A))\n        \n        #num_factor = defaultdict(list)\n        num_id = defaultdict(int)\n        for num in A:\n            pf = list(set(prime_factors(num)))\n            #num_factor[num] = pf\n            num_id[num] = pf[0]\n            for i in range(len(pf)-1):\n                #for num pf[i] and pf[i+1] can be unioned\n                DS.union(pf[i], pf[i+1]) \n        \n        max_size = 0        \n        #nums belong to groups which are root's of num_id[num]\n        group_count = defaultdict(int)\n        for num in A:\n            group_id = DS.find(num_id[num])\n            group_count[group_id] += 1\n            max_size = max(max_size, group_count[group_id])\n        \n        return max_size"
_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: 12364