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 DSU:\n  def __init__(self):\n    self.N = 0\n    self.map = {}\n    self.parent = []\n    self.count = []\n  \n  def __contains__(self, obj):\n    return obj in self.map\n  \n  def add(self, obj):\n    if obj in self:\n      return\n    i = self.N\n    self.N += 1\n    self.map[obj] = i\n    self.parent.append(i)\n    self.count.append(0)\n\n  def find(self, obj):\n    p = self.parent\n    \n    origI = self.map[obj]\n    \n    i = origI\n    while p[i] != i:\n      i = p[i]\n    root = i\n    \n    i = origI\n    while p[i] != i:\n        p[i], i = root, p[i]\n    \n    return root\n\n  def union(self, objA, objB):\n    rObjA = self.find(objA)\n    rObjB = self.find(objB)\n    if rObjA == rObjB:\n      return\n    self.count[rObjA] += self.count[rObjB]\n    self.parent[rObjB] = rObjA\n\n  def incCount(self, obj):\n    rObj = self.find(obj)\n    self.count[rObj] += 1\n    return self.count[rObj]\n\nclass Solution:\n  def largestComponentSize(self, nums) -> int:\n    UF = DSU()\n    max_ = 1\n    for num in nums:\n      if num == 1:\n        continue\n      pDs = self.primeDivisors(num)\n      pD0 = pDs.pop()\n      UF.add(pD0)\n      for pD in pDs:\n        UF.add(pD)\n        UF.union(pD0, pD)\n      count = UF.incCount(pD0)\n      max_ = max(max_, count)\n    return max_\n    \n  def primeDivisors(self, num: int):\n      x = num\n      \n      pDs = set()\n      \n      if x % 2 == 0:\n          pDs.add(2)\n          while x % 2 == 0:\n              x >>= 1\n          \n      if x % 3 == 0:\n          pDs.add(3)\n          while x % 3 == 0:\n              x //= 3\n      \n      div = 5\n      d2 = True\n      while x >= div*div:\n          if x % div == 0:\n              pDs.add(div)\n              while x % div == 0:\n                  x //= div\n          div += 2 if d2 else 4\n          d2 = not d2\n      \n      if x > 1:\n        pDs.add(x)\n      \n      return pDs\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: 7768