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    def get_prime_numbers(self, num_to_idx_dict, max_num: int) -> List[int]:\n        is_prime_list = [True] * (max_num + 1)        \n        prime_to_nums_dict = defaultdict(list)\n        \n        for i in range(2, max_num // 2 + 1):            \n            if is_prime_list[i] == False: continue\n            \n            num = i\n            while num <= max_num:\n                if num in num_to_idx_dict:\n                    prime_to_nums_dict[i].append(num_to_idx_dict[num])\n                is_prime_list[num] = False\n                num += i         \n        \n        return prime_to_nums_dict\n    \n    def find(self, union_list, index: int) -> int:\n        if index == union_list[index]: return index\n        #return self.find(union_list, union_list[index])    \n        parent = self.find(union_list, union_list[index])\n        union_list[index] = parent\n        return parent\n        \n    def union(self, union_list, index1: int, index2: int) -> None:\n        union1, union2 = self.find(union_list, index1), self.find(union_list, index2)                \n        #union_list[union1], union_list[index2] = union2, union2\n        union_list[union1] = union2\n        \n    def largestComponentSize(self, A: List[int]) -> int:\n        if len(A) == 0: return 0        \n        max_num = max(A)\n        union_list = [i for i in range(len(A))]\n        count_list = [0] * (len(A))\n        num_to_idx_dict = dict(list(zip(A, list(range(len(A))))))\n        \n        # get prime numbers\n        prime_to_nums_dict = self.get_prime_numbers(num_to_idx_dict, max_num) # prime numbers of A's numbers\n        \n        # linking numbers having the same prime \n        for prime, nums in list(prime_to_nums_dict.items()):\n            for i in range(len(nums) - 1):\n                self.union(union_list, nums[i], nums[i + 1])\n        \n        # counting numbers in a component        \n        for i, num in enumerate(A):\n            count_list[self.find(union_list, i)] += 1        \n            \n        return max(count_list)\n# Time complexity: O(n * p) where n is the maximum number of A and p is the number of prime numbers less than n\n# Space complexity: O(n + p) we can ignore p\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: 8512