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 = '# https://www.tutorialspoint.com/largest-component-size-by-common-factor-in-cplusplus\n\nfrom collections import defaultdict as dd\n\ndef find(parent,num) :\n\n    if parent[num]==-1 :\n        return num\n    else :\n        parent[num] = find(parent,parent[num])\n    \n    return parent[num]\n\ndef union(parent,u,v) :\n    par_u = find(parent,u)\n    par_v = find(parent,v)\n    if par_u != par_v :\n        parent[par_v] = par_u\n        \nclass Solution:\n    def largestComponentSize(self, a: List[int]) -> int:\n        ans=0\n        n=len(a)\n        parent=[-1]*100001\n        \n        for i in range(n) :\n            x=a[i]\n            \n            for j in range(2, int(x**0.5)+1) :\n                \n                if x%j == 0 :\n                    \n                    union(parent,j,x)\n                    union(parent,x//j,x)\n                               \n        count = dd(int)    \n        for i in range(len(a)) :\n            par = find(parent,a[i])\n            count[par]+=1\n            ans=max(ans,count[par])\n\n        return ans\n                    \n# from collections import defaultdict as dd\n\n# def find(parent,num) :\n\n#     if parent[num]==-1 :\n#         return num\n#     else :\n#         parent[num] = find(parent,parent[num])\n    \n#     return parent[num]\n\n# def union(parent,rank,u,v) :\n#     par_u = find(parent,u)\n#     par_v = find(parent,v)\n    \n#     if par_u == par_v :\n#         return \n    \n#     if rank[par_u] >= rank[par_v] :\n#         parent[par_v] = par_u\n#         rank[par_u] += rank[par_v]\n\n#     else :\n#         parent[par_u] = par_v\n#         rank[par_v] += rank[par_u]\n        \n\n# class Solution:\n#     def largestComponentSize(self, a: List[int]) -> int:\n#         ans=0\n#         n=len(a)\n#         parent=[-1]*n\n#         rank=[1]*n\n        \n#         factor = dd(int)\n        \n#         for i in range(n) :\n#             x=a[i]\n            \n#             for j in range(2, int(x**0.5)+1) :\n                \n#                 if x%j == 0 :\n#                     if factor[j] :\n#                         union(parent,rank,factor[j],i)\n                        \n#                     else :\n#                         factor[j]=i\n                        \n#                     if factor[x//j] :\n#                         union(parent,rank,factor[x//j],i)\n\n#                     else :\n#                         factor[x//j]=i\n                            \n#             if factor[x] :\n#                 union(parent,rank,factor[x],i)\n#             else :\n#                 factor[x]=i\n                \n#             ans = max(ans,rank[find(parent,i)])\n            \n#         return ans\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: 806618