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 = '# all primes less than sqrt(100000)\nprimes = [\n    2,\n    3,\n    5,\n    7,\n    11,\n    13,\n    17,\n    19,\n    23,\n    29,\n    31,\n    37,\n    41,\n    43,\n    47,\n    53,\n    59,\n    61,\n    67,\n    71,\n    73,\n    79,\n    83,\n    89,\n    97,\n    101,\n    103,\n    107,\n    109,\n    113,\n    127,\n    131,\n    137,\n    139,\n    149,\n    151,\n    157,\n    163,\n    167,\n    173,\n    179,\n    181,\n    191,\n    193,\n    197,\n    199,\n    211,\n    223,\n    227,\n    229,\n    233,\n    239,\n    241,\n    251,\n    257,\n    263,\n    269,\n    271,\n    277,\n    281,\n    283,\n    293,\n    307,\n    311,\n    313,\n]\n\n\ndef prime_factors(n: int) -> List[int]:\n    if n == 1:\n        return []\n    for p in primes:\n        if n % p == 0:\n            return [p] + prime_factors(n // p)\n    return [n]\n\n\ndef group_by_factors(A):\n    groups = defaultdict(set)\n    for a in A:\n        for p in prime_factors(a):\n            groups[p].add(a)\n    return list(groups.values())\n\n\n# TODO: this uses up about 2/3 of the runtime by itself\ndef adjacencies_by_intersection(gs):\n    adj = [[] for _ in range(len(gs))]\n    for x in range(len(gs)):\n        for y in range(x):\n            if gs[x] & gs[y]:\n                adj[x].append(y)\n                adj[y].append(x)\n    return adj\n\n\ndef bfs(gs, adj, target):\n    unvisited = set(range(len(gs)))\n    largest = 0\n    while unvisited:\n        v = unvisited.pop()\n        q = [v]\n\n        group = set()\n        while q:\n            n = q.pop()\n            group.add(n)\n            for x in adj[n]:\n                if x in unvisited:\n                    unvisited.remove(x)\n                    q.append(x)\n        largest = max(largest, len(set(n for i in group for n in gs[i])))\n        # try to short circuit\n        if largest >= target:\n            return largest\n    return largest\n\n\nclass Solution:\n    def largestComponentSize(self, A: List[int]) -> int:\n        # group by prime factors and filter out singletons\n        gs = [g for g in group_by_factors(A) if len(g) > 1]\n\n        # build adjacency relations\n        adj = adjacencies_by_intersection(gs)\n\n        # bfs\n        target = len(A) // 2\n        return bfs(gs, adj, target)\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: 8888