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    # O(n x sqrt(max)) time, O(n x sqrt(max)) space\n    def largestComponentSize(self, A: List[int]) -> int:\n        \n        # Somehow using this version will mysteriously have TLE\n        def find_prime_factors(num):\n            result = []\n            candidate = 2\n            cur_num = num\n            upper_limit = int(math.sqrt(num))\n            while candidate <= upper_limit:\n                if cur_num % candidate == 0:\n                    result.append(candidate)\n                    while cur_num % candidate == 0:\n                        cur_num //= candidate\n                candidate += 1\n\n            if cur_num != 1:\n                result.append(cur_num)\n            return result\n        \n        # Using the recursive version to avoid TLE, although it should have the same\n        # time complexity as the iterative version\n        # def find_prime_factors(num):\n        #     for i in range(2, int(math.sqrt(num)) + 1):\n        #         if num % i == 0:\n        #             return find_prime_factors(num // i) | set([i])\n        #     return set([num])\n        \n        def find_root(x):\n            if root[x] != x:\n                root[x] = find_root(root[x])\n            return root[x]\n        \n        def union(x, y):\n            root[find_root(x)] = root[find_root(y)]\n        \n        root = [i for i in range(len(A))]\n        prime_factor_to_index = defaultdict(list)\n        # O(n x sqrt(max))\n        for i, num in enumerate(A):\n            prime_factors = find_prime_factors(num)\n            for factor in prime_factors:\n                prime_factor_to_index[factor].append(i)\n        \n        # O(n x sqrt(max))\n        for indices in list(prime_factor_to_index.values()):\n            for i in range(1, len(indices)):\n                union(indices[i - 1], indices[i])\n        \n        # O(n)\n        root_count = Counter(find_root(i) for i in range(len(A)))\n        return max(root_count.values())\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: 13514