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 = 'import math\n\nclass Solution:\n    \n    def __init__(self):\n        self.prime_divisors_cache = {}\n    \n    def prime_divisors(self, x, i=2):\n        if x in self.prime_divisors_cache:\n            return self.prime_divisors_cache[x]\n        while i * i <= x:\n            if x % i != 0:\n                i += 1\n                if i > 3:\n                    i += 1\n            else:\n                self.prime_divisors_cache[x] = set([i]) | self.prime_divisors(x // i, i)\n                return self.prime_divisors_cache[x]\n    \n        res = set()\n        if x > 1:\n            res.add(x)\n        \n        self.prime_divisors_cache[x] = res\n        return self.prime_divisors_cache[x]\n            \n            \n    def largestComponentSize(self, A: List[int]) -> int:\n        # related if NOT coprime\n        \n        # we can keep associated a list of prime factors with each set \n        \n        # integers in A are unique\n        # form a disjoint set structure\n        # node label -> parent\n        parent = dict()\n        # representative label -> size of set\n        size = dict()\n        # keep track of list of representatives for ease\n        reps = set()\n        \n        def getRep(x):\n            # compress path to parent\n            while parent[x] != x:\n                x, parent[x] = parent[x], parent[parent[x]]\n            return x\n        \n        # def getSize(x):\n        #     return size[getRep(x)]\n            \n        def add(x):\n            parent[x] = x\n            size[x] = 1\n            reps.add(x)\n        \n        def merge(x, y):\n            x = getRep(x)\n            y = getRep(y)\n            if x == y:\n                return\n            if size[x] < size[y]:\n                x, y = y, x\n            size[x] += size.pop(y)\n            parent[y] = x\n            reps.remove(y)\n        \n        # prime -> list of numbers it divides\n        prime2dividend = {}\n        for x in A:\n            add(x)\n            for p in self.prime_divisors(x):\n                if not p in prime2dividend:\n                    prime2dividend[p] = [x]\n                else:\n                    prime2dividend[p].append(x)\n        \n        for _, xs in list(prime2dividend.items()):\n            # guaranteed to be one\n            first = xs.pop()\n            for x in xs:\n                merge(first, x)\n        \n        return max([size[rep] for rep in reps])\n        \n        \n        \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: 10840