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 UF:\n    def __init__(self, n):\n        self.f = list(range(n))\n        self.cc = [1] * n\n        \n    def find(self, x):\n        while x != self.f[x]: # while, not if\n            x = self.f[x]\n        return x\n\n    def union(self, x, y):\n        fx, fy = self.find(x), self.find(y)\n        if fx != fy: #\n            if self.cc[fx] <= self.cc[fy]: # path compression?\n                self.f[fx] = fy\n                self.cc[fx], self.cc[fy] = 0, self.cc[fx] + self.cc[fy]\n            else:\n                self.f[fy] = fx\n                self.cc[fy], self.cc[fx] = 0, self.cc[fx] + self.cc[fy]\n    \nclass Solution:\n    def largestComponentSize(self, A: List[int]) -> int:\n        if not A:\n            return 0\n        n = len(A)\n        uf = UF(n)\n        \n        '''\n        def gcd(a, b):\n            while b != 0:\n                a, b = b, a % b\n            return a\n        \n        for i in range(n):\n            for j in range(n):\n                if i == j:\n                    continue\n                if gcd(A[i], A[j]) > 1:\n                    uf.union(i, j)\n        '''\n        def getPrimeSets(num, num2primes):\n            if num2primes[num]:\n                return num2primes[num]\n            \n            for i in range(2, int(math.sqrt(num)) + 1):\n                if num % i == 0:\n                    num2primes[num] = getPrimeSets(i, num2primes) | getPrimeSets(num // i, num2primes)\n                    return num2primes[num]\n                \n            num2primes[num] = set([num]) # num is prime\n            return num2primes[num]\n            \n        num2primes = collections.defaultdict(set)\n        for num in sorted(A):\n            getPrimeSets(num, num2primes)\n        \n        prime2numIdxs = collections.defaultdict(list)\n        for idx, num in enumerate(A):\n            ps = num2primes[num]\n            for p in ps:\n                prime2numIdxs[p].append(idx)\n                \n        for _, idxs in list(prime2numIdxs.items()):\n            for i in range(len(idxs) - 1):\n                uf.union(idxs[i], idxs[i+1])\n            \n        # print(uf.f)\n        # print(uf.cc)\n        res = 1\n        for i in range(n):\n            res = max(uf.cc[i], res)\n        return res\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: 10628