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 UnionFind:\n    def __init__(self, n):\n        self.p = []\n        self.size = [1] * n\n        for i in range(n):\n            self.p.append(i)\n        self.max_union_size = 1\n        \n    def union(self, X, Y):\n        px, py = self.find(X), self.find(Y)\n        if px == py:\n            return\n        elif self.size[px] < self.size[py]:\n            self.p[px] = py\n            self.size[py] += self.size[px]\n            self.max_union_size = max(self.max_union_size, self.size[py])\n        else:\n            self.p[py] = px\n            self.size[px] += self.size[py]\n            self.max_union_size = max(self.max_union_size, self.size[px])\n\n    def find(self, X): \n        if self.p[X] != X:\n            self.p[X] = self.find(self.p[X])\n        return self.p[X]\n    \nclass Solution:\n    def largestComponentSize(self, A: List[int]) -> int:\n        def get_prime_factors(num):\n            n = num\n            d = 2\n            while d * d <= n:\n                if n % d == 0:\n                    yield d\n                while n % d == 0:\n                    n //= d\n                d += 1\n            if n > 1:\n                yield n\n        \n        factors_to_nums = collections.defaultdict(list)\n        for i, a in enumerate(A):\n            for f in get_prime_factors(a):\n                factors_to_nums[f].append(i) # save the index of the number in A, which is easier to generate UF\n        \n        uf = UnionFind(len(A))\n        for idx_of_num in factors_to_nums.values():\n            for i in range(1, len(idx_of_num)):\n                uf.union(idx_of_num[0], idx_of_num[i])\n        \n        return uf.max_union_size\n\n''' \n# lingnan 写的DisjointSet，还没有看\nclass DisjointSet:\n    def __init__(self, n):\n        self.parent = [-1] * n\n        self.max_size = 1\n    \n    \n    def find(self, x):\n        root = x\n        while self.parent[root] >= 0:\n            if self.parent[self.parent[root]] >= 0:\n                self.parent[root] = self.parent[self.parent[root]]\n            root = self.parent[root]\n        return root\n    \n    \n    def union(self, x, y):\n        x_root = self.find(x)\n        y_root = self.find(y)\n        \n        if x_root != y_root:\n            if self.parent[x_root] > self.parent[y_root]:\n                x_root, y_root = y_root, x_root\n            \n            self.parent[x_root] += self.parent[y_root]\n            self.parent[y_root] = x_root\n            self.max_size = max(self.max_size, -self.parent[x_root])\n    \n\nclass Solution:\n    def largestComponentSize(self, A: List[int]) -> int:\n        def get_prime_factors(num):\n            n = num\n            d = 2\n            while d * d <= n:\n                if n % d == 0:\n                    yield d\n                while n % d == 0:\n                    n //= d\n                d += 1\n            if n > 1:\n                yield n\n        \n        f_to_i = collections.defaultdict(list)\n        for i, a in enumerate(A):\n            for f in get_prime_factors(a):\n                f_to_i[f].append(i)\n        \n        ds = DisjointSet(len(A))\n        for indexes in f_to_i.values():\n            for i in range(1, len(indexes)):\n                ds.union(indexes[0], indexes[i])\n        \n        return ds.max_size\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: 8054