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 = "'''\nStart a dfs from every node not reached yet\nKeep max of dfs length\nKeep nodes visited and nodes to visit in dfs\n'''\nclass Solution:\n    def largestComponentSize(self, A: List[int]) -> int:\n        primes = []\n        for x in range(2, int(max(A)**0.5)+1):\n            for y in primes:\n                if x % y == 0:\n                    break\n            else:\n                primes.append(x)\n    \n        factors = collections.defaultdict(list)         # compute factors of each 'a'\n        for a in A:\n            x = a\n            for p in primes:\n                if p*p > x:\n                    break\n                if x % p == 0:\n                    factors[a].append(p)\n                    while x % p == 0:\n                        x //= p\n            if x > 1:                                   # a new prime found\n                factors[a].append(x)\n                primes.append(x)\n                \n        primes = list(set(primes))\n        n = len(primes)\n        p2i = {p: i for i,p in enumerate(primes)}       # prime to index\n        \n        parent = [i for i in range(n)]                  # union-find on primes\n        \n        def find(i):\n            if i != parent[i]:\n                parent[i] = find(parent[i])\n            return parent[i]\n        \n        def union(i,j):\n            pi, pj = find(i), find(j)\n            if pi != pj:\n                parent[pi] = pj\n\n        for a in A:\n            if factors[a]:\n                p0 = factors[a][0]\n                for p in factors[a][1:]:                # link two primes if they are factors of 'a'\n                    union(p2i[p0], p2i[p])\n        \n        count = collections.Counter(find(p2i[factors[a][0]]) for a in A if factors[a])      # each 'a' corresponds to a prime index\n        return max(count.values())        \n#         self.ret = float(-1)\n#         self.visited = set()        \n#         self.not_visited = set(A)\n#         self.factors = {}\n        \n#         for i in A:\n#             self.factors[i] = get_factors(i)\n            \n#         print(self.factors)\n            \n#         def dfs(cur, length):\n#             try:\n#                 self.not_visited.remove(cur)    \n#             except:\n#                 return\n\n#             if length > self.ret:\n#                 self.ret = length\n            \n#             for num in self.not_visited.copy():\n#                 if num == cur:\n#                     continue\n                    \n#                 for i in self.factors[num]:\n#                     if i in self.factors[cur]:\n#                         self.visited.add(num)\n#                         dfs(num, length + 1)\n#                         break\n                        \n#         for i in A:\n#             dfs(i, 1)\n#         return self.ret\n                    \n# def get_factors(x):\n#     res = set()\n#     for i in range(2, x + 1):\n#         if x % i == 0:\n#             res.add(i)\n#     return res\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: 13314