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:\n  def __init__(self, nodes):\n    self.parents = [-1]* len(nodes)\n    self.map = {node: idx for idx, node in enumerate(nodes)}\n    \n  def find(self, node):\n    \n    idx = self.map[node]\n    \n    orig = idx\n    while(self.parents[idx] >= 0):\n      idx = self.parents[idx]\n      \n    parent, rank = idx, abs(self.parents[idx])\n    while(self.parents[orig] >= 0):\n      temp_parent = self.parents[orig]\n      self.parents[orig] = parent\n      orig = temp_parent\n    return parent, rank\n      \n  \n  def union(self, n1, n2):\n    idx1, idx2 = self.map[n1], self.map[n2]\n    parent1, rank1 = self.find(n1)\n    parent2, rank2 = self.find(n2)\n    \n    if parent1 == parent2:\n      return\n    \n    if rank1 >= rank2:\n      self.parents[parent1] -= rank2\n      self.parents[parent2] = parent1\n    else:\n      self.parents[parent2] -= rank1\n      self.parents[parent1] = parent2\n      \n  def get_max_rank(self):\n    return abs(min(self.parents))\n      \n\nclass Solution:\n    def largestComponentSize(self, A: List[int]) -> int:\n        \n        max_num = max(A)\n        primes_nodes = collections.defaultdict(set)\n        \n        def prime_factors(n):\n          original = n\n          result = set()\n          while n % 2 == 0: \n                 \n            n = n // 2\n            result.add(2)\n\n          # n must be odd at this point \n          # so a skip of 2 ( i = i + 2) can be used \n          for i in range(3,int(math.sqrt(n))+1,2): \n\n              # while i divides n , print i ad divide n \n              while n % i== 0: \n                  result.add(i)\n                  n = n // i \n\n          # Condition if n is a prime \n          # number greater than 2 \n          if n > 2: \n               result.add(n) \n              \n          return result\n          \n        uf_obj = UnionFind(A)\n        factor_first_multiple_map = {}\n        for node in A:\n          p_factors = prime_factors(node)\n          \n          for pf in p_factors:\n            #if pf already a prime factor of prev encountered num, union with that num the curr num\n            if pf in factor_first_multiple_map:\n              uf_obj.union(node, factor_first_multiple_map[pf])\n            else:\n              factor_first_multiple_map[pf] = node\n\n          \n        return uf_obj.get_max_rank()\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: 8130