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 = "from collections import Counter, defaultdict, OrderedDict, deque\nfrom bisect import bisect_left, bisect_right\nfrom functools import reduce, lru_cache\nfrom typing import List\nimport itertools\nimport math\nimport heapq\nimport string\ntrue = True\nfalse = False\nMIN, MAX, MOD = -0x3f3f3f3f, 0x3f3f3f3f, 1000000007\n\n\n#\n# @lc app=leetcode id=952 lang=python3\n#\n# [952] Largest Component Size by Common Factor\n#\n# https://leetcode.com/problems/largest-component-size-by-common-factor/description/\n#\n# algorithms\n# Hard (30.37%)\n# Total Accepted:    18.1K\n# Total Submissions: 53.6K\n# Testcase Example:  '[4,6,15,35]'\n#\n# Given a non-empty\xa0array of unique positive integers A, consider the following\n# graph:\n#\n#\n# There are A.length nodes, labelled A[0] to A[A.length - 1];\n# There is an edge between A[i] and A[j]\xa0if and only if\xa0A[i] and A[j] share a\n# common factor greater than 1.\n#\n#\n# Return the size of the largest connected component in the graph.\n#\n#\n#\n#\n#\n#\n#\n# Example 1:\n#\n#\n# Input: [4,6,15,35]\n# Output: 4\n#\n#\n#\n#\n# Example 2:\n#\n#\n# Input: [20,50,9,63]\n# Output: 2\n#\n#\n#\n#\n# Example 3:\n#\n#\n# Input: [2,3,6,7,4,12,21,39]\n# Output: 8\n#\n#\n#\n# Note:\n#\n#\n# 1 <= A.length <= 20000\n# 1 <= A[i] <= 100000\n#\n#\n#\n#\n#\n#\nclass UF:\n    def __init__(self, n):\n        self.p = list(range(n))\n        self.size = [1] * n\n\n    def merge(self, x, y):\n        # Merge by size of set\n        px, py = self.find(x), self.find(y)\n        if px == py: return\n        if self.size[px] < self.size[py]:\n            self.p[px] = py\n            self.size[py] += self.size[px]\n        else:\n            self.p[py] = px\n            self.size[px] += self.size[py]\n\n    def find(self, x):\n        if x != self.p[x]:\n            self.p[x] = self.find(self.p[x])\n        return self.p[x]\n\n\nclass Solution:\n    def largestComponentSize(self, A: List[int]) -> int:\n        uf = UF(max(A) + 1)\n        for n in A:\n            for i in range(2, math.ceil(math.sqrt(n)) + 1):\n                if n % i == 0:\n                    uf.merge(n, i)\n                    uf.merge(n, max(n // i, 2))\n\n        return Counter(list(map(uf.find, A))).most_common()[0][1]\n\n\nsol = Solution()\n\nns = [2, 3, 6, 7, 4, 12, 21, 39]\nns = [1, 2, 3, 4, 5, 6, 7, 8, 9]\nns = [32, 5, 8, 11, 13, 78, 61, 16, 83, 22, 28, 93]\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: 11676