<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 {

	bool isPrime(int x) {
		if (x < 2) {
			return false;
		}
		if (x < 4) {
			return true;
		}
		if ((x % 2 == 0) || (x % 3 == 0)) {
			return false;
		}
		for (int i = 3; i * i <= x; i += 2) {
			if (x % i == 0) {
				return false;
			}
		}
		return true;
	}
public:
	void getFactors(int x, unordered_set<int>& facs) {
		facs.insert(x);
		int z = 2;
		while (z * z <= x) {
			if (x % z == 0) {
				facs.insert(z);
				x /= z;
			}
			else {
				z++;
			}
		}
		if (x > 1) {
			facs.insert(x);
		}
	}

	struct Item {
		int count{ 1 };
		unordered_set<int> facs;

		bool commonFacs(const Item& itm) const {
			for (auto n : itm.facs) {
				if (facs.find(n) != facs.end()) {
					return true;
				}
			}
			return false;
		}

		void unify(const Item& itm) {
			count += itm.count;
			facs.insert(itm.facs.begin(), itm.facs.end());
		}
	};

public:
	int largestComponentSize(vector<int>& nums) {
		std::sort(nums.begin(), nums.end(), std::greater<int>());
		if (nums.front() == nums.back()) {
			if (nums.back() == 1) {
				return 1;
			}
			if (isPrime(nums.back())) {
				return 1;
			}
			return nums.size();
		}
		while (nums.back() == 1) {
			nums.pop_back();
		}



		list<Item> items;
		Item item;
		for (auto n : nums) {
			items.push_back(item);
			getFactors(n, items.back().facs);
		}

		int mcount = 1;
		auto lastItm = items.begin();
		auto itm = items.begin();
		while (lastItm != items.end()) {
			if (lastItm->facs.size() < 2) {
				lastItm = std::next(lastItm);
				continue;
			}
			itm = lastItm;
			int count = itm->count;
			auto nitm = std::next(itm);
			while (nitm != items.end()) {
				if (itm->commonFacs(*nitm)) {
					itm->unify(*nitm);
					nitm = items.erase(nitm);
					if (itm->count > mcount) {
						mcount = itm->count;
					}
				}
				else {
					nitm = std::next(nitm);
				}
			}
			if (count < itm->count) {
				itm = lastItm;
			}
			else {
				lastItm = std::next(lastItm);
			}
		}

		return mcount;
	}
};
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