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 Solution1:\n    def largestComponentSize(self, A):\n        if not A: return 0\n        def findAndCompact(l, i): # require i >= 0\n            if l[i] == i: return i\n            p = l[i]\n            if p >= 0 and l[p] == p: return p\n            while p >= 0 and l[p] != p:\n                p = l[p]\n            root = p\n            \n            # compact\n            p = i\n            while p >= 0 and l[p] != p:\n                t = l[p]\n                l[p] = root\n                p = t\n            return root\n        \n        slist = [-1] * len(A)\n        d = {} # record prime->(root of union-find set)\n        for i in range(len(A)):\n            n = A[i]\n            has_factor = False\n            for j in range(2, int(sqrt(n)) + 1):\n                if n % j == 0:\n                    has_factor = True\n                    k = n // j\n                    #print(n, j, k)\n                    ri = -1 if slist[i] < 0 else findAndCompact(slist, slist[i])\n                    rj = -1 if j not in d else findAndCompact(slist, d[j])\n                    rk = -1 if k not in d else findAndCompact(slist, d[k])\n                    if ri < 0 and rj < 0 and rk < 0:\n                        slist[i] = d[j] = d[k] = i\n                    else:\n                        mm = min([item for item in (ri, rj, rk) if item >= 0])\n                        if slist[i] >= 0: slist[ri] = mm\n                        if j in d: slist[rj] = mm\n                        if k in d: slist[rk] = mm\n                        slist[i] = d[j] = d[k] = mm\n            if not has_factor: #prime\n                if A[i] not in d: slist[i] = d[A[i]] = i\n                else: slist[i] = d[A[i]]\n            #print(slist, d)\n        \n        for i in range(len(A)): findAndCompact(slist, i)\n        #print('### ', slist)\n        cc = Counter(slist)\n        m = cc.most_common(2)\n        return m[0][1] if m[0][0] != -1 else m[1][1]\n    \nclass DSU:\n    def __init__(self, N):\n        self.p = list(range(N))\n\n    def find(self, x):\n        n = self.p[x]\n        while n >= 0 and self.p[n] != n:\n            n = self.p[n]\n        root = n\n        # compact\n        n = x\n        while n >= 0 and self.p[n] != n:\n            t = self.p[n]\n            self.p[n] = root\n            n= t\n        return root\n\n    def union(self, x, y):\n        xr, yr = self.find(x), self.find(y)\n        self.p[xr] = yr\n\nclass Solution:\n    def primes_set(self,n):\n        for i in range(2, int(math.sqrt(n))+1):\n            if n % i == 0:\n                return self.primes_set(n//i) | set([i])\n        return set([n])\n\n    def largestComponentSize(self, A):\n        n = len(A)\n        UF = DSU(n)\n        primes = defaultdict(list)\n        for i, num in enumerate(A):\n            pr_set = self.primes_set(num)\n            for q in pr_set: primes[q].append(i)\n\n        for _, indexes in primes.items():\n            for i in range(len(indexes)-1):\n                UF.union(UF.find(indexes[i]), UF.find(indexes[i+1]))\n\n        return max(Counter([UF.find(i) for i in range(n)]).values())"
_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: 12916