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        parent = [i for i in range(len(A))]\n        rank = [0 for i in range(len(A))]\n        \n        def prime_factors(n):\n            for i in range(2, int(math.sqrt(n))+1):\n                if n % i == 0:\n                    return prime_factors(n//i) | set([i])\n            return set([n])\n            # primes = set()\n            # d = 2\n            # while d <= sqrt(n):\n                # if n % d == 0:\n                    # primes.add(d)\n                    # n //= d\n                # else:    \n                    # d += 1\n            # if n > 1:\n                # primes.add(n)\n            # return primes        \n                    \n        def find(n):    \n            p = parent[n]\n            if p == n:\n                return p\n            parent[n] = find(parent[n])\n            return parent[n]\n\n        def merge(n1, n2):\n            r1 = find(n1)\n            r2 = find(n2)\n            \n            if r1 == r2:\n                return\n            \n            if rank[r1] < rank[r2]:\n                parent[r1] = r2\n            elif rank[r1] > rank[r2]:\n                parent[r2] = r1\n            else:    \n                parent[r1] = r2\n                rank[r2] += 1\n                \n        prime_indeces = defaultdict(list)\n        for i, n in enumerate(A):\n            primes = prime_factors(n)\n            for p in primes:\n                prime_indeces[p].append(i)\n            \n        print(prime_indeces)    \n        # print(parent)\n        for p, indeces in list(prime_indeces.items()):\n            for i in range(len(indeces)-1):\n                # print('merging', A[indeces[i]], A[indeces[i+1]])\n                merge(indeces[i], indeces[i+1])\n                # print(parent)        \n                \n                \n        count_map = dict()\n        best = 0        \n        \n        for i in parent:\n            i = find(i)\n            if i in count_map:\n                count_map[i] += 1\n            else:\n                count_map[i] = 1\n                \n            best = max(best, count_map[i])\n        # print(count_map)    \n            \n        return best\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: 9363