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        divisors, groups, sizes = {}, {}, {}\n\n        # Find all divisors of the numbers in the list\n        for num in A:\n            added = False\n\n            for i in range(2, max(int(math.sqrt(num)) + 1, 4)):\n                if num % i == 0:\n                    added = True\n\n                    # Found two divisors\n                    # First is i\n                    if i not in divisors:\n                        divisors[i] = set()\n                    divisors[i].add(num)\n\n                    # Second is num divided by i\n                    if (num_i := int(num / i)) > 1:\n                        if num_i not in divisors:\n                            divisors[num_i] = set()\n                        divisors[num_i].add(num)\n\n            if not added:\n\n                # This is a prime number\n                if num not in divisors:\n                    divisors[num] = set()\n                divisors[num].add(num)\n\n        # Union function\n        def union(node1: int, node2: int) -> None:\n            parent1 = find(node1)\n            parent2 = find(node2)\n\n            # Check if these nodes already belong to the same parent\n            if parent1 == parent2:\n                return\n            elif parent1 < parent2:\n\n                # Union to the smallest parent 1\n                groups[parent2] = parent1\n                sizes[parent1] = sizes[parent1] + sizes[parent2]\n\n            else:\n                # Union to the smallest parent 2\n                groups[parent1] = parent2\n                sizes[parent2] = sizes[parent1] + sizes[parent2]\n\n        # Find function\n        def find(node: int) -> int:\n\n            # If this node hasn't been created yet\n            if node not in groups:\n                groups[node] = node\n                sizes[node] = 1\n                return node\n\n            # Check if this node is also the parent (final node)\n            if groups[node] == node:\n                return node\n\n            # Apply path compression\n            groups[node] = find(groups[node])\n\n            # Return the parent\n            return groups[node]\n\n        # Union-find algorithm to union all groups with common divisor\n        for _, common_numbers in list(divisors.items()):\n            num1 = random.sample(common_numbers, 1)[0]\n\n            for num2 in common_numbers:\n                if num1 != num2:\n                    union(num1, num2)\n\n        return max(list(sizes.values()), default=1)\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: