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\nfrom math import sqrt\nclass DSU(object):\n    def __init__(self, n):\n        self.ds = list(range(n))\n    \n    \n    def find(self, v):\n        if self.ds[v] != v:\n            self.ds[v] = self.find(self.ds[v])\n        return self.ds[v]\n\n    def union(self, p1, p2):\n        pp1, pp2 = self.find(p1), self.find(p2)\n        self.ds[pp1] = pp2\n    \nclass Solution(object):    \n    def uniqPrime(self, n):\n        l = []\n        while n % 2 == 0:\n            l.append(2)\n            n = n//2\n        \n        for i in range(3, int(sqrt(n)) + 1, 2):\n            while n % i == 0:\n                l.append(i)\n                n = n//i\n        if n > 2:\n            l.append(n)\n        \n        return list(set(l))\n        \n    def largestComponentSize(self, A):\n        primes = defaultdict(list)\n        n = len(A)\n        for i in range(n):\n            p = self.uniqPrime(A[i])\n            for x in p:\n                primes[x].append(i)\n        \n        #now we need to merge the disjoint sets and see which is the longest\n        uf = DSU(n)\n        for i in list(primes.items()):\n            vals = i[1]\n            for j in range(len(vals) - 1):\n                uf.union(vals[j], vals[j+1])\n        \n        return max(Counter([uf.find(i) for i in range(n)]).values())\n# class Dis_set_node:\n#     def __init__(self):\n#         self.parent = None\n#         self.size = 1\n        \n# class Dis_set:\n#     def __init__(self):\n#         self.forest = {}\n        \n#     def addSet(self, node, key):\n#         self.forest[key] = node\n        \n#     def find(self, p):\n#         while self.forest[p].parent is not None:\n#             self.forest[p].parent = self.forest[self.forest[p].parent].parent\n#             p = self.forest[p].parent\n        \n#         return p\n    \n#     def union(self, x, y):\n#         x = self.find(x)\n#         y = self.find(y)\n        \n#         if x != y:\n#             if self.forest[x].size < self.forest[y].size:\n#                 x, y = y, x\n            \n#             self.forest[y].parent = x\n#             self.forest[x].size += self.forest[y].size\n            \n\n# class Solution:\n#     def largestComponentSize(self, A: List[int]) -> int:\n#         prime_factors = {key:value for key, value in zip([n for n in A], [[] for _ in range(len(A))])}\n        \n#         up_to = max(A)\n        \n#         primes = set()\n#         comps = set()\n        \n#         for i in range(2, up_to + 1):\n#             if i not in comps:\n#                 primes.add(i)\n#                 comp = i * 2\n                \n#                 if i in prime_factors:\n#                         prime_factors[i].append(i)\n                \n#                 while comp <= up_to:\n#                     comps.add(comp)\n                    \n#                     if comp in prime_factors:\n#                         prime_factors[comp].append(i)\n                        \n#                     comps.add(comp)\n#                     comp += i \n        \n#         djus = Dis_set()\n        \n#         for p in primes:\n#             djus.addSet(Dis_set_node(), p)\n            \n#         for pf in prime_factors.values():\n#             if not pf:\n#                 continue\n            \n#             for p1, p2 in zip(pf, pf[1:]):\n#                 djus.forest[djus.find(p1)].size += 1\n#                 djus.union(p1, p2)\n                \n            \n#         print([node.size for node in djus.forest.values()])\n        \n        \n        \n        # print(self.prime_factors)\n        \n#         groups = []\n        \n#         for n in A:\n#             i = 0\n#             to_merge = []\n            \n#             while i < len(groups):\n#                 if groups[i][0] & (self.prime_factors[n]):\n#                     to_merge.append(groups.pop(i))\n#                 else:\n#                     i += 1\n                    \n#             to_add = [self.prime_factors[n], 1]\n            \n            \n#             for merge in to_merge:\n#                 to_add = [merge[0] | to_add[0], merge[1] + to_add[1]]\n                    \n                \n#             groups.append(to_add)\n            \n\n                \n\n#         return max(groups, key=lambda x:x[1])[1]\n        \n        \n                \n#     def seive(self, up_to):\n#         primes = set()\n#         comps = set()\n        \n#         for i in range(2, up_to + 1):\n#             if i not in comps:\n#                 primes.add(i)\n#                 comp = i * 2\n                \n#                 if i in self.prime_factors:\n#                         self.prime_factors[i].add(i)\n                \n#                 while comp <= up_to:\n#                     comps.add(comp)\n                    \n#                     if comp in self.prime_factors:\n#                         self.prime_factors[comp].add(i)\n                        \n#                     comps.add(comp)\n#                     comp += i\n        \n#         return primes\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: 12914