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 = 'from collections import defaultdict, Counter\n\nclass DSU:\n    def __init__(self, N):\n        self.par = list(range(N))\n        self.rnk = [0] * N\n        self.siz = [1] * N\n\n    def find(self, x):\n        if self.par[x] != x:\n            self.par[x] = self.find(self.par[x])\n        return self.par[x]\n\n    def union(self, x, y):\n        xr, yr = list(map(self.find, (x, y)))\n        if xr == yr: return\n        if self.rnk[xr] < self.rnk[yr]:\n            xr, yr = yr, xr\n        if self.rnk[xr] == self.rnk[yr]:\n            self.rnk[xr] += 1\n\n        self.par[yr] = xr \n        self.siz[xr] += self.siz[yr]\n\nclass Solution:\n    def largestComponentSize(self, A: List[int]) -> int:\n        # Union-Find on Prime Factors\n        # Time  complexity: O(N x (logM x logM + sqrt(M)))\n        # Space complexity: O(M + N)\n        # def primeDecompose(num):\n        #     factor = 2\n        #     prime_factors = []\n        #     while num >= factor * factor:\n        #         if num % factor == 0:\n        #             prime_factors.append(factor)\n        #             num //= factor\n        #         else:\n        #             factor += 1\n        #     prime_factors.append(num)\n        #     return prime_factors\n\n        # dsu = DSU(max(A) + 1)\n        # num_factor_map = {}\n\n        # for num in A:\n        #     prime_factors = list(set(primeDecompose(num)))\n        #     # map a number to its first prime factor\n        #     num_factor_map[num] = prime_factors[0]\n        #     # merge all groups that contain the prime factors.\n        #     for i in range(0, len(prime_factors) - 1):\n        #         dsu.union(prime_factors[i], prime_factors[i + 1])\n\n        # max_size = 0\n        # group_count = defaultdict(int)\n        # for num in A:\n        #     group_id = dsu.find(num_factor_map[num])\n        #     group_count[group_id] += 1\n        #     max_size = max(max_size, group_count[group_id])\n\n        # return max_size\n\n\n        B = []\n        for x in A:\n            facs = []\n            d = 2\n            while d * d <= x:\n                if x % d == 0:\n                    while x % d == 0:\n                        x //= d\n                    facs.append(d)\n                d += 1\n            if x > 1 or not facs:\n                facs.append(x)\n            B.append(facs)\n\n        primes = list({p for facs in B for p in facs})\n        prime_to_index = {p: i for i, p in enumerate(primes)}\n\n        dsu = DSU(len(primes))\n        for facs in B:\n            for x in facs:\n                dsu.union(prime_to_index[facs[0]], prime_to_index[x])\n\n        count = Counter(dsu.find(prime_to_index[facs[0]]) for facs in B)\n        return max(count.values())\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: 13196