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 largestComponentSize(self, A: List[int]) -> int:\n        # https://leetcode.com/problems/largest-component-size-by-common-factor/discuss/819919/Python-Union-find-solution-explained\n        # This question feels like union find but u cannot link together\n        # First, find the primes factor of each number\n        # And then group together same prime factore\n        # The largest group is the largest component\n        # But the way to find primes set is a little confusing \n        # It loop from small to large and find the first factor and the primes set for the larger factor\n        # If two numbers share the same prime factor, they belong to the same group\n        # Then use union find to grouo together\n        n = len(A)\n        record = [-1]*n\n        primes = collections.defaultdict(list)\n        def get_primes(i):\n            for j in range(2,int(math.sqrt(i))+1):\n                if i%j == 0:\n                    # And find the primes set for the larger factor\n                    return get_primes(i//j) | set([j])\n            return set([i])\n                \n            return res\n        def find(a):\n            if record[a] < 0:return a\n            record[a] = find(record[a])\n            return record[a]\n        \n        \n        # U have been wrong on this several times\n        # When merge, it is the record[i] == root index, not root val\n        def union(i,j):\n            a,b = find(i),find(j)\n            if a!=b:\n                if a<b:\n                    record[a] = b\n                else:\n                    record[b] = a\n                \n            \n        for i, v in enumerate(A):\n            primes_set = get_primes(v)\n            for j in primes_set:\n                primes[j].append(i)\n            \n        for _,indexes in list(primes.items()):\n            for i in range(len(indexes)):\n                union(indexes[0],indexes[i])\n        \n        res = 0\n        mapping = collections.defaultdict(set)\n        for i in range(n):\n            root = find(i)\n            mapping[root].add(i)\n            if len(mapping[root]) > res:res = len(mapping[root])\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: 8790