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 defaultdict\n\nclass UnionFind:\n    def __init__(self, length):\n        self.parent = list(range(length))\n        self.size = [1] * length\n        \n    def find(self,i):\n        if self.parent[i] == i:\n            return i\n        if self.parent[i] != i:\n            return self.find(self.parent[i])\n\n    # A utility function to do union of two subsets\n    def union(self,x,y):\n        x_set, y_set = self.find(x), self.find(y)\n        if x_set == y_set:\n            return\n        self.parent[x_set] = y_set\n        self.size[y_set] += self.size[x_set]\n        self.size[x_set] = 0\n\nclass Solution:\n    def largestComponentSize(self, A: List[int]) -> int:\n        # brute force is look at each node and see if we can connect it to every other node\n        # after we are done connecting, we check every node and see keep track of longest path\n        \n        if len(A) <= 0:\n            return 0\n        \n        '''# key: node value\n        # values: list of connected components\n        nodes = defaultdict(list)\n        \n        gcf_cache = {}\n        def greatest_common_factor(a, b):\n            if (a,b) in gcf_cache:\n                return gcf_cache[(a,b)]\n            \n            if (b,a) in gcf_cache:\n                return gcf_cache[(b,a)]\n            \n            # euclidean algo\n            # Everything divides 0  \n            if (a == 0): \n                return b \n            if (b == 0): \n                return a \n\n            # base case \n            if (a == b): \n                return a \n\n            # a is greater \n            if (a > b): \n                gcf = greatest_common_factor(a-b, b)\n                gcf_cache[(a,b)] = gcf\n                gcf_cache[(b,a)] = gcf\n                return gcf\n            gcf = gcd(a, b-a)\n            gcf_cache[(a,b)] = gcf\n            gcf_cache[(b,a)] = gcf\n            return gcf\n        \n        def dfs(node):\n            visited = set()\n            stack = [(node,0)]\n            max_path = -float('inf')\n            while(stack):\n                current_node, current_path = stack.pop()\n                if current_node:\n                    visited.add(current_node)\n                    current_path += 1\n                    max_path = max(max_path, current_path)\n                    neighbors = nodes[current_node]\n\n                    for i in range(len(neighbors)):\n                        if neighbors[i] not in visited:\n                            stack.append((neighbors[i], current_path))\n            return max_path\n        \n        for i in range(len(A)):\n            for j in range(i+1, len(A)):\n                gcf = greatest_common_factor(A[i], A[j])\n                if gcf > 1:\n                    nodes[A[i]].append(A[j])\n                    nodes[A[j]].append(A[i])\n        \n        result = 1\n        for i in nodes.keys():\n            path = dfs(i)\n            print(path)\n            result = max(result, dfs(i))\n        return result'''\n        \n        # try union find\n        # reference: https://leetcode.com/problems/largest-component-size-by-common-factor/discuss/200643/Python-1112-ms-beats-100-Union-Find-and-Prime-factor-decomposition-with-Optimization\n        def primeFactors(n):\n            out = set()\n            while n % 2 == 0: \n                out.add(2)\n                n //= 2\n            for i in range(3, int(math.sqrt(n))+1, 2): \n                while n % i== 0: \n                    out.add(i) \n                    n //= i \n            if n > 2: \n                out.add(n)\n            return out\n        \n        uf = UnionFind(len(A))\n        \n        primeToIndex = {} \n        for i,a in enumerate(A):\n            primes = primeFactors(a)\n            for p in primes:\n                if p in primeToIndex:\n                    uf.union(i, primeToIndex[p])\n                primeToIndex[p] = i\n        return max(uf.size)\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: 7758