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 = '\nclass Primes:\n    def __init__(self):\n        M = ceil(sqrt(100000))+1\n        isPrime = [True] * M\n        k = 2\n        while k < M:\n            n=2\n            while k*n < M:\n                isPrime[k*n] = False               \n                n += 1\n            k += 1\n            while k < M and not isPrime[k]:\n                k += 1\n            \n        self.primes = [k for k in range(2,M) if isPrime[k]]\n        \n\n\nclass Solution:\n    primes = Primes().primes       \n        \n    def largestComponentSize(self, A: List[int]) -> int:        \n             \n        def getPrimeFactors(a):\n            ans = []\n            for p in Solution.primes:\n                if p*p > a: break\n                if a%p==0:\n                    ans.append(p)\n                    while True:\n                        a = a // p\n                        if a%p != 0: break\n            if a > 1:\n                ans.append(a)\n            return ans\n        \n        N = len(A) \n        D = defaultdict(list)\n        for k in range(N):\n            a = A[k]\n            ap = getPrimeFactors(a)\n            for p in ap:\n                D[p].append(k)\n        dsu = DSU(N)\n        for p,indexList in list(D.items()):            \n            n = len(indexList)\n            for i in range(n-1):\n                dsu.union(indexList[i],indexList[i+1])\n        return max(dsu.size)\n    \n    \nclass DSU: # Disjoint Set Union data structure\n    \n    def __init__(self, size):\n        self.size = [1] * (size+1)\n        self.parent = [i for i in range(size+1)]\n        \n        \n    def find(self, i):\n        \n        # Path halving... replaces only every other parent pointer with grandparent\n        # was fastest at 976ms\n        while self.parent[i] != i:\n            i = self.parent[i] = self.parent[self.parent[i]]\n        return i\n            \n        \n        # Path splitting way... let to 980ms... replacing every parent with grandparent\n        ##while self.parent[i] != i:\n        ##    i, self.parent[i] = self.parent[i], self.parent[self.parent[i]]\n        ##return i\n        \n        # The simplest recursive way... led to 1012ms\n        ##if i != self.parent[i]:\n        ##    self.parent[i] = self.find(self.parent[i])\n        ##return self.parent[i]\n    \n    def union(self, i,j):\n        i = self.find(i)\n        j = self.find(j)\n        \n        if i == j: \n            return i\n        \n        if self.size[i] > self.size[j]:\n            i,j = j,i\n            \n        self.parent[i] = j\n        self.size[j] += self.size[i]\n        \n        \n        return j\n\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: 8054