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\n\nclass UnionFind:\n    \n    def __init__(self, n):\n        self.data = list(range(n))\n        self.size = [1] * n\n        \n    def find(self, x):\n        if self.data[x] != x:\n            self.data[x] = self.find(self.data[x])\n        return self.data[x]\n    \n    def union(self, x, y):\n        ix, iy = self.find(x), self.find(y)\n        if ix != iy:\n            self.data[ix] = iy\n            self.size[iy] += self.size[ix]\n            self.size[ix] = 0\n\n\nclass Solution:\n    def largestComponentSize(self, A: List[int]) -> int:\n        \n        def prime_set(num):\n            res = set()\n            while num % 2 == 0:\n                res.add(2)\n                num //= 2\n            for i in range(3, int(math.sqrt(num)) + 1, 2):\n                while num % i == 0:\n                    res.add(i)\n                    num //= i\n            if num > 2:\n                res.add(num)\n            return res\n        \n        n = len(A)\n        uf = UnionFind(n)\n        primes_dict = collections.defaultdict(list)\n        for i, num in enumerate(A):\n            pr_set = prime_set(num)\n            for p in pr_set:\n                primes_dict[p].append(i)\n        for indices in primes_dict.values():\n            for j in range(1, len(indices)):\n                uf.union(indices[j - 1], indices[j])\n                \n        return max(collections.Counter(uf.find(i) for i in range(n)).values())\n        \n        \n    def gcd_with_bfs(self, A: List[int]) -> int:\n        graph = collections.defaultdict(set)\n        \n        for i in range(len(A)):\n            for j in range(i, len(A)):\n                if math.gcd(A[i], A[j]) > 1:\n                    graph[A[i]].add(A[j])\n                    graph[A[j]].add(A[i])\n        \n        res = 0\n        seen = set()\n        for a in A:\n            if a not in seen:\n                node_count = 0\n                q = collections.deque([a])\n                seen.add(a)\n                while q:\n                    node = q.popleft()\n                    node_count += 1\n                    seen.add(node)\n                    for child in graph[node]:\n                        if child not in seen:\n                            seen.add(child)\n                            q.append(child)\n                res = max(res, node_count)\n        return res'
_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: 13330