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        amax = max(A)\n        plist = [2]\n        for k in range(3, int(sqrt(amax)) + 2, 2):\n            for p in plist:\n                if p * p > k:\n                    plist.append(k)\n                    break\n                if k % p == 0: break\n            else:\n                plist.append(k)\n        pset = set(plist)\n        amax //= 2\n        n = n1 = n2 = len(A)\n        k = 0\n        while k < n1:\n            x = A[k]\n            if x in pset:\n                n1 -= 1\n                n2 -= 1\n                A[k] = A[n1]\n                A[n2] = x\n                continue\n            if x < plist[-1]:\n                k += 1\n                continue\n            prime = True\n            for p in plist:\n                if p * p > x: break\n                if x % p == 0:\n                    prime = False\n                    break\n            if not prime:\n                k += 1\n            else:\n                n1 -= 1\n                A[k] = A[n1]\n                if x <= amax:\n                    n2 -= 1\n                    A[n2] = x\n        ans = 1\n        left = n - n2 + n1\n        while left > ans and n1 > 0:\n            n1 -= 1\n            x = A[n1]\n            found = False\n            k = 0\n            while k < n1:\n                y = A[k]\n                p = math.gcd(x, y)\n                if p > 1:\n                    found = True\n                    n1 -= 1\n                    A[k] = A[n1]\n                    while p > 1:\n                        y //= p\n                        p = math.gcd(y, p)\n                    x *= y\n                else:\n                    k += 1\n                if k == n1 and found:\n                    found = False\n                    k = 0\n            k = n - 1\n            while k >= n2:\n                if x % A[k] == 0:\n                    A[k] = A[n2]\n                    n2 += 1\n                else:\n                    k -= 1\n            k = n - n2 + n1\n            ans = max(ans, left - k)\n            left = k\n        return ans'
_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: 6470