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 math\nfrom collections import deque\n\nclass UnionFind:\n    def __init__(self, n):\n        self.parent = [-1]*n\n        \n    def find(self, a):\n        if self.parent[a] < 0:\n            return a\n        self.parent[a] = self.find(self.parent[a])\n        return self.parent[a]\n    \n    def union(self, a, b):\n        root_a = self.find(a)\n        root_b = self.find(b)\n        if root_a != root_b:\n            if self.parent[root_a] <= self.parent[root_b]:\n                self.parent[root_a] += self.parent[root_b]\n                self.parent[root_b] = root_a\n            else:\n                self.parent[root_b] += self.parent[root_a]\n                self.parent[root_a] = root_b\n                \n########################## Solution inspired by discussion O(n sqrt(max(A))) ################\n# The main idea of this is to use prime factorization for each number in A which takes O(n sqrt(max(A))) and build a dictionary with the key of prime number and value of list of indices of A that have that prime factor. Then connect the indices in each list with union find.\n\nimport math\nfrom collections import defaultdict\nclass Solution:\n    def largestComponentSize(self, A: List[int]) -> int:\n        \n        def prime_factors(num):\n            for i in range(2, int(math.sqrt(num))+1):\n                if num%i == 0:\n                    return set([i]) | prime_factors(num//i)\n            return set([num])\n        \n        uf = UnionFind(len(A))\n        d = defaultdict(list)\n        for i, a in enumerate(A):\n            for p in prime_factors(a):\n                d[p].append(i)\n        \n        for p, idx_list in list(d.items()):\n            for i in range(len(idx_list)-1):\n                uf.union(idx_list[i], idx_list[i+1])\n        return -min(uf.parent)\n        \n    \n                \n                \n                \n\n                \n                \n########################### My O(n^2) solution which is TLE #############################         \n# class Solution:\n    # def largestComponentSize(self, A: List[int]) -> int:\n    #     uf = UnionFind(len(A))\n    #     for i in range(len(A)-1):\n    #         for j in range(i+1, len(A)):\n    #             p1 = uf.find(i)\n    #             p2 = uf.find(j)\n    #             if p1 != p2 and math.gcd(A[i], A[j]) > 1:\n    #                 uf.union(i, j)\n    #     return -min(uf.parent)\n    \n    \n            \n########################### My simple bfs solution which is O(n^2) ##############################\n# class Solution:\n#     def largestComponentSize(self, A: List[int]) -> int:\n#         max_so_far = 0\n#         seen = [0]*len(A)\n#         first_unseen = 0\n#         while first_unseen is not None:\n#             tmp = 0\n#             seen[first_unseen] = 1\n#             q = deque([(first_unseen, A[first_unseen])])\n#             first_unseen = None\n#             while q:\n#                 idx, num1 = q.popleft()\n#                 tmp += 1\n#                 for i, a in enumerate(A):\n#                     if not seen[i]:\n#                         if math.gcd(a, num1) > 1:\n#                             seen[i] = 1\n#                             q.append((i, a))\n#                         else:\n#                             first_unseen = i\n#             max_so_far = max(max_so_far, tmp)\n#         return max_so_far\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: 8178