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 Solution:\n    def largestComponentSize(self, A: List[int]) -> int:\n        \n        # union find\n        '''\n        def gcd(a, b):    \n            if b==0:\n                return a\n            return gcd(b, a%b)\n        '''\n        def find(u):  # pass compresson\n            if p[u]==-1:\n                return u\n            p[u]=find(p[u])\n            return p[u]\n            \n        def union(u, v):\n            u = find(u)\n            v = find(v)\n            \n            if u!=v:\n                if r[u]>r[v]:\n                    p[v] = u\n                elif r[u]<r[v]:\n                    p[u] = v\n                else:\n                    p[v]=u\n                    r[u]+=1\n        '''\n        def sieve(x):\n            \n            num = [True]*(x+1)\n            \n            k = 2\n            while k*k<=x:\n                if num[k]:\n                    i = k*k\n                    while i<=x:\n                        num[i] = False\n                        i += k\n                k+=1        \n                \n            for i in range(2, x+1):\n                if num[i]:\n                    pr.append(i)\n            \n        '''         \n        n = len(A)\n        \n        m = max(A)+1\n        \n        #pr = []\n        #sieve(m-1)\n        #l = len(pr)\n            \n        p = [-1]*m\n        r = [0]*m\n    \n        for i in range(n):\n            # prime factorization\n            factor = 2\n            num = A[i]\n            while num>=factor*factor:  # here\n                if num%factor==0:\n                    num//=factor\n                    union(A[i], factor)\n                else:\n                    factor+=1\n            union(A[i], num)    # here\n    \n            ################\n            #j = 0\n            #while j<l and pr[j]<=A[i]:\n            #    if A[i]%pr[j]==0:\n            #        union(A[i], pr[j])\n            #    j+=1\n            ##################\n            #j = 2\n            #while j*j<=A[i]:\n            #    if A[i]%j==0:\n            #        union(A[i], j)\n            #        union(A[i], A[i]//j)\n            #    j+=1    \n                \n        \n        s = [0]*m    \n        for i in range(n):    \n            s[find(A[i])]+=1\n         \n        return max(s)\n        \n        '''\n        # dfs   TLE\n        \n        def gcd(a, b):    \n            if b==0:\n                return a\n            return gcd(b, a%b)\n        \n        def dfs(u):\n            y = 1\n            for v in adj[u]:\n                if not vis[v]:\n                    vis[v] = True\n                    y += dfs(v)\n            \n            return y\n        \n        \n        n = len(A)\n        \n        adj = [ [] for i in range(n) ]\n        \n        for i in range(n):\n            for j in range(i+1,n):\n                if gcd(A[i], A[j])>1:\n                    adj[i].append(j)\n                    adj[j].append(i)\n        \n        \n        \n        res = 0\n        \n        vis = [False]*n\n        \n        for i in range(n):\n            \n            if not vis[i]:\n                vis[i] = True\n                res = max(res, dfs(i))\n        \n        return res\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: 7484