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 UnionFind(object):\n    def uf(self, n):  \n        self.uf = [i for i in range(n)]\n        self.size = [1] * n\n        \n    def find(self, x):  \n        while x != self.uf[x]:\n            self.uf[x] = self.uf[self.uf[x]]\n            x = self.uf[x]\n        return self.uf[x]\n\n    def union(self, x, y):  \n        x_root = self.find(x)\n        y_root = self.find(y)\n        if x_root == y_root:\n            return\n        self.uf[x_root] = y_root\n        self.size[y_root] += self.size[x_root]\n        self.size[x_root] = 0\nclass Solution:\n    def largestComponentSize(self, A: List[int]) -> int:\n        def primeFactors(n):  # Prime factor decomposition\n            out = set()\n            while n % 2 == 0: \n                out.add(2)\n                n //= 2\n            for i in range(3, int(math.sqrt(n))+1, 2): \n                while n % i== 0: \n                    out.add(i) \n                    n //= i \n            if n > 2: \n                out.add(n)\n            return out\n        \n        idx_lookup = {A[i]: i for i in range(len(A))} # in order to find idx in uf\n        uf = UnionFind()\n        uf.uf(len(A))\n        primeAndItsMultiples = collections.defaultdict(list) # {2: [4, 6], 3: [6, 15], 5: [15, 35], 7: [35]})\n        \n        for i in A:\n            factors = primeFactors(i)\n            for f in factors:\n                primeAndItsMultiples[f].append(i)\n\n        # we don't need to connect all the multiples of a prime, \n        # just use the first multiple as their root\n        for idx, multiples in primeAndItsMultiples.items():\n            if multiples:\n                root = multiples[0] # use the first multiple as their root\n                for node in multiples[1:]:\n                    uf.union(idx_lookup[node], idx_lookup[root]) # connect node with root\n                    \n        return max(uf.size)"
_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: 8506