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    \n    def get_factors(self, n: int):\n        factors = set()\n        for factor in self.total_factors:\n            if factor > n:\n                break\n            if n % factor == 0:\n                factors.add(factor)\n        for factor in factors:\n            self.total_factors.remove(factor)\n        return factors\n    \n    def get_prime_numbers(self, n_max: int):\n        self.total_factors = [2,3]\n        for val in range(3, n_max//2 + 2, 2):\n            for i in range(3, int(val**0.5) + 2, 2):\n                if val % i == 0:\n                    break\n                else:\n                    if i >= int(val**0.5):\n                        self.total_factors.append(val)\n    \n    def largestComponentSize(self, A: List[int]) -> int:\n        #A.sort()\n        #self.get_prime_numbers(A[-1])\n        #print(self.total_factors)\n        N = max(A) + 1\n        nods = {d:d for d in range(N)}\n        \n        def find(x):\n            root = x\n            while nods[root] != root:\n                root = nods[root]\n            while nods[x] != root:\n                parent = nods[x]\n                nods[x] = root\n                x = parent\n            return root\n        \n        def union(x,y):\n            rx,ry = find(x), find(y)\n            if rx != ry:\n                nods[ry] = rx\n        \n        for a in A:\n            for factor in range(2, int(sqrt(a))+1):\n                if a % factor == 0:\n                    union(a, factor)\n                    union(a, a//factor)\n                    \n        counts = collections.defaultdict(int)\n        for a in A:\n            counts[find(a)] += 1\n        print(counts)\n        return max(counts.values())\n            \n                \n    \n    def largestComponentSize_slow(self, A: List[int]) -> int:\n        A.sort()\n        self.get_prime_numbers(A[-1])\n        #print(self.total_factors)\n        max_len = 0\n        while len(A) > max_len:\n            factors = self.get_factors(A[0])\n            new_len = 1\n            A.remove(A[0])\n            while factors:\n                factor = factors.pop()\n                to_remove = []\n                for i in range(len(A)):\n                    if A[i] % factor == 0:\n                        new_len += 1\n                        rest = A[i] / factor\n                        while rest % factor == 0:\n                            rest /= factor\n                        factors = factors | self.get_factors(rest)\n                        to_remove.append(i)\n                A = [A[i] for i in range(len(A)) if i not in to_remove]\n            max_len = max(new_len, max_len)\n        return max_len\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: 8063