<p>You are given an integer array of unique positive integers <code>nums</code>. Consider the following graph:</p>

<ul>
	<li>There are <code>nums.length</code> nodes, labeled <code>nums[0]</code> to <code>nums[nums.length - 1]</code>,</li>
	<li>There is an undirected edge between <code>nums[i]</code> and <code>nums[j]</code> if <code>nums[i]</code> and <code>nums[j]</code> share a common factor greater than <code>1</code>.</li>
</ul>

<p>Return <em>the size of the largest connected component in the graph</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2018/12/01/ex1.png" style="width: 500px; height: 97px;" />
<pre>
<strong>Input:</strong> nums = [4,6,15,35]
<strong>Output:</strong> 4
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2018/12/01/ex2.png" style="width: 500px; height: 85px;" />
<pre>
<strong>Input:</strong> nums = [20,50,9,63]
<strong>Output:</strong> 2
</pre>

<p><strong class="example">Example 3:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2018/12/01/ex3.png" style="width: 500px; height: 260px;" />
<pre>
<strong>Input:</strong> nums = [2,3,6,7,4,12,21,39]
<strong>Output:</strong> 8
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= nums.length &lt;= 2 * 10<sup>4</sup></code></li>
	<li><code>1 &lt;= nums[i] &lt;= 10<sup>5</sup></code></li>
	<li>All the values of <code>nums</code> are <strong>unique</strong>.</li>
</ul>

class Solution {
public:
    int N;
    vector<int> prime;
    vector<vector<int>> cf;
    vector<int> num_state;
    vector<bool> isPrime;

    void sieve(int n){
        isPrime.assign(n+1, 1);
        isPrime[0]=isPrime[1]=0;
        int&& n_sqrt=int(sqrt(n));
        for(int i=2; i<=n_sqrt; i++){
            if (isPrime[i]){
                for(int j=i*i ; j<=n; j+=i) { isPrime[j]=0;}
            }
        }
        prime.reserve((int)(n/log(n)));
        for(int i=2; i<=n; i++)
            if (isPrime[i]) {prime.push_back(i);}
    }

    void cfpath(vector<int>& nums, int M) {
        num_state.assign(M + 1, 0);
        cf.resize(M + 1, vector<int>());

        for (int x : nums)
            num_state[x] = 1;

        for (int p : prime) {
            if (num_state[p] != 1) {num_state[p] = -1;}
            for (int i = p * 2; i <= M; i += p) {
                if (num_state[i] == 1) {
                    cf[i].push_back(p);
                    cf[p].push_back(i);
                }
            }
        }
    }

    void dfs(int i, int& sz) {
        if (num_state[i] == 1) { sz++;}
        num_state[i] = 2;
        for (int x : cf[i]) {
            if (num_state[x] == 1 || num_state[x] == -1) { dfs(x, sz);}
        }
    }

    int largestComponentSize(vector<int>& nums) {
        N = nums.size();
        int M = *max_element(nums.begin(), nums.end());
        sieve(M);
        cfpath(nums, M);
        int res = 0;
        for (int i : nums) {
            if (num_state[i] == 1) {
                int sz = 0;
                dfs(i, sz);
                res = max(res, sz);
            }
        }
        return res;
    }
};
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