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 DisjointSet:\n    def __init__(self, n):\n        self.parent = [i for i in range(n)]\n        self.rank = [0 for i in range(n)]\n        \n    def GetParent(self, i):\n        if self.parent[i] != i:\n            self.parent[i] = self.GetParent(self.parent[i])\n            \n        return self.parent[i]\n    \n    def Union(self, i, j):\n        i_idx = self.GetParent(i)\n        j_idx = self.GetParent(j)\n        \n        if j_idx == i_idx:\n            return\n        \n        if self.rank[i_idx] > self.rank[j_idx]:\n            self.parent[j_idx] = i_idx\n        else:\n            if self.rank[i_idx] == self.rank[j_idx]:\n                self.rank[j_idx] += 1\n            \n            self.parent[i_idx] = j_idx\n        \n\nclass Solution:\n    def largestComponentSize(self, A: List[int]) -> int:\n        def prime_set(n):\n            for i in range(2, math.floor(math.sqrt(n)) + 1):\n                if n % i == 0:\n                    return prime_set(n // i) | set([i])\n                    \n            return set([n])\n        \n        ds = DisjointSet(len(A))\n        \n        primes = {}    \n        \n        for i in range(len(A)):\n            curr_prime_set = prime_set(A[i])\n            \n            for prime in curr_prime_set:\n                primes.setdefault(prime, [])\n                primes[prime].append(i)\n                \n        for key in primes:\n            for i in range(len(primes[key]) - 1):\n                ds.Union(primes[key][i], primes[key][i + 1])\n                \n        set_counter = {}\n        \n        for i in range(len(A)):\n            set_counter.setdefault(ds.GetParent(i), 0)\n            set_counter[ds.GetParent(i)] += 1\n            \n        # print(set_counter)\n        return max(set_counter.values())\n        \n        \n#     def largestComponentSize(self, A: List[int]) -> int:\n#         def gcd(a, b):\n#             nonlocal gcd_hash\n#             if (a, b) in gcd_hash:\n#                 return gcd_hash[(a, b)]\n            \n#             if b == 0:\n#                 return a\n            \n#             if a >= b:\n#                 return gcd(b, a % b)\n#             else:\n#                 return gcd(a, b % a)\n            \n            \n#         def Explore(u, adj_list, visited):\n#             visited[u] = 1\n            \n#             for v in adj_list[u]:\n#                 if not visited[v]:\n#                     nonlocal cc_length\n#                     cc_length += 1\n#                     Explore(v, adj_list, visited)\n                 \n                \n#         gcd_hash = {}\n#         V = len(A)\n#         adj_list = [[] for _ in range(V)]\n        \n#         for i in range(len(A)):\n#             for j in range(i + 1, V):\n#                 curr_gcd = gcd(A[i], A[j])\n#                 gcd_hash[(A[i], A[j])] = curr_gcd\n#                 gcd_hash[(A[j], A[i])] = curr_gcd\n                \n#                 if curr_gcd > 1:\n#                     adj_list[i].append(j)\n#                     adj_list[j].append(i)\n        \n#         # print(adj_list)\n        \n#         visited = [0 for _ in range(V)]\n#         max_cc_length = 0\n#         cc_num = 0\n#         cc_length = 1\n        \n#         for i in range(V):\n#             if not visited[i]:\n#                 Explore(i, adj_list, visited)\n#                 cc_num += 1\n                \n#                 if cc_length > max_cc_length:\n#                     max_cc_length = cc_length\n                \n#                 cc_length = 1\n                \n#         # print(cc_num)\n#         # print(max_cc_length)\n        \n#         return max_cc_length\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: 8574