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 = 'import collections\n\n\nclass UnionFind:\n    def __init__(self, n):\n        self.n = n\n        self.parents = list(range(n))\n        self.ranks = [0 for _ in range(n)]\n\n    def get_root(self, x):\n        if self.parents[x] == x:\n            return x\n        self.parents[x] = self.get_root(self.parents[x])\n        return self.parents[x]\n\n    def merge(self, x, y):\n        x = self.get_root(x)\n        y = self.get_root(y)\n        if x != y:\n            if self.ranks[x] < self.ranks[y]:\n                self.parents[x] = y\n            else:\n                self.parents[y] = x\n                if self.ranks[x] == self.ranks[y]:\n                    self.ranks[x] += 1\n\n\ndef factorize_all(n):\n    factorizations = [None] * (n + 1)\n    factorizations[0] = {}\n    factorizations[1] = {}\n    for p in range(2, n + 1):\n        if factorizations[p] is None:\n            for k in range(1, n // p + 1):\n                if factorizations[k] is None:\n                    continue\n                fs = factorizations[k].copy()\n                if p in fs:\n                    fs[p] += 1\n                else:\n                    fs[p] = 1\n                factorizations[k * p] = fs\n    return factorizations\n\n\nclass Solution:\n    def largestComponentSize(self, A: List[int]) -> int:\n        uf = UnionFind(max(A) + 1)\n        factorization = factorize_all(max(A))\n        ids = dict()\n        for a in A:\n            if a < 2:\n                continue\n            factors = list(factorization[a].keys())\n            ids[a] = factors[0]\n            for p0, p1 in zip(factors, factors[1:]):\n                uf.merge(p0, p1)\n                \n        counter = collections.defaultdict(int)\n        maxval = 0\n        for a in A:\n            if a < 2:\n                continue\n            id_ = uf.get_root(ids[a])\n            counter[id_] += 1\n            maxval = max(maxval, counter[id_])\n            \n        return maxval'
_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: 16814