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 = 'from typing import List, Set, Tuple\n\ndef prime_factors(n: int) -> Set[int]:\n    f = set()\n    i = 1\n    while n % 2 == 0 and n:\n        f.add(2)\n        n //= 2\n    while n % 3 == 0 and n:\n        f.add(3)\n        n //= 3\n    root = int(n ** 0.5) + 1\n    while True and n:\n        a, b = 6 * i + 1, 6 * i - 1\n        while n % a == 0:\n            n //= a\n            f.add(a)\n        while n % b == 0:\n            n //= b\n            f.add(b)\n        if a > root:\n            break\n        i += 1\n    if n > 1:\n        f.add(n)\n    return f\n\nclass Solution:\n    def largestComponentSize(self, A: List[int]) -> int:\n        A.sort(reverse=True)\n        islands: List[Tuple[Set[int], int]] = []\n        primes: Set[int] = set()\n        for n in A:\n            factors = prime_factors(n)\n            first_merged = None\n            to_delete: Set[int] = set()\n            for i, (g, v) in enumerate(islands):\n                if factors.isdisjoint(g):\n                    continue\n                if first_merged is None:\n                    g.update(factors)\n                    islands[i] = (g, v + 1)\n                    first_merged = i\n                else:\n                    gf, vf = islands[first_merged]\n                    gf.update(g)\n                    islands[first_merged] = (gf, vf + v)\n                    to_delete.add(i)\n            primes_inside = factors & primes\n            if primes_inside:\n                if first_merged is None:\n                    new_v = len(primes_inside) + 1\n                    islands.append((factors, new_v))\n                else:\n                    gf, vf = islands[first_merged]\n                    islands[first_merged] = (gf, vf + len(primes_inside))\n                primes.difference_update(primes_inside)\n            elif first_merged is None:\n                if n in factors:\n                    primes.add(n)\n                else:\n                    islands.append((factors, 1))\n            islands = [g for i, g in enumerate(islands) if i not in to_delete]\n        return max(v for g, v in islands)\n            \n            \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: 8534