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 Primes:\n    def __init__(self, N):\n        self.N = N\n        self.primes = [0]*(N+1)\n        self.get_primes()\n    \n    def get_primes(self):\n        for i in range(2, self.N+1):\n            if self.primes[i]==0:\n                self.primes[i] = i\n                upto = self.N//i\n                for j in range(2, upto+1):\n                    if self.primes[i*j] == 0:\n                        self.primes[i*j] = i\n    \n    def __call__(self, n):\n        # num = n\n        if n<=2:\n            return {n}\n        p = []\n        while n>=2:\n            lp = self.primes[n]\n            p.append(lp)\n            n =  n//lp\n        # print(num,\\":\\", p)\n        return set(p)\n\nclass DisjointSet:\n    def __init__(self, primes):\n        self.primes = primes\n        self.count = 1\n        \n    def union(self, setB):\n        # print(\\"org:\\", self.primes)\n        # print(\\"union with:\\", setB.primes)\n        self.primes |= setB.primes\n        self.count += setB.count\n        # print(\\"after union:\\", self.primes)\n        \n        \n    \nclass Solution:\n    def largestComponentSize(self, A: List[int]) -> int:\n        disjoint_sets = []\n        Factors = Primes(max(A))\n        rank = [1]*(len(A)+1)\n        parent = [-1]*(len(A)+1)\n        m = dict()\n        curr_count = 0\n        \n        def get_parent(x):\n            if parent[x]==-1: return x\n            parent[x] = get_parent(parent[x])\n            # print(f\\"parent of {x} is {parent[x]}\\")\n            return parent[x]\n        \n        def union(x, y):\n            parx = get_parent(x)\n            pary = get_parent(y)\n            if parx==pary: return\n            if rank[parx]>=rank[pary]:\n                rank[parx] += rank[pary]\n                parent[pary] = parx\n            else:\n                rank[pary] += rank[parx]\n                parent[parx] = pary\n            # print(x,\\":\\",\\"parent\\", paar)\n        \n            \n        for i,val in enumerate(A):\n            # union = []\n            val_primes = Factors(val)\n            # for i, ds in enumerate(disjoint_sets):\n            #     diff_set = val_primes - ds.primes\n            #     if len(diff_set) < len(val_primes):\n            #         union.append(i)\n            #         val_primes = diff_set\n            # # if len(val_primes)>0:\n            # #     new_set = DisjointSet(val_primes)\n            # #     disjoint_sets.append(new_set)\n            # #     union.append(-1)\n            # temp_set = DisjointSet(val_primes)\n            # for ds in union:\n            #     temp_set.union(disjoint_sets[ds])\n            #     # disjoint_sets[union[-1]].union(disjoint_sets[ds])\n            #     # curr_count = max(curr_count, disjoint_sets[union[-1]].count)\n            # for ds in reversed(union):\n            #     disjoint_sets.pop(ds)\n            # disjoint_sets.append(temp_set)\n            \n            for prime in val_primes:\n                if prime in m:\n                    union(m[prime],i)\n                else:\n                    m[prime]=i\n                    # print(prime, \\":\\", i)\n        curr_count = max(rank)\n        return curr_count\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: 8710