<p>You are given an integer array <code>nums</code>, and you can perform the following operation <strong>any</strong> number of times on <code>nums</code>:</p>

<ul>
	<li>Swap the positions of two elements <code>nums[i]</code> and <code>nums[j]</code> if <code>gcd(nums[i], nums[j]) &gt; 1</code> where <code>gcd(nums[i], nums[j])</code> is the <strong>greatest common divisor</strong> of <code>nums[i]</code> and <code>nums[j]</code>.</li>
</ul>

<p>Return <code>true</code> <em>if it is possible to sort </em><code>nums</code><em> in <strong>non-decreasing</strong> order using the above swap method, or </em><code>false</code><em> otherwise.</em></p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> nums = [7,21,3]
<strong>Output:</strong> true
<strong>Explanation:</strong> We can sort [7,21,3] by performing the following operations:
- Swap 7 and 21 because gcd(7,21) = 7. nums = [<u><strong>21</strong></u>,<u><strong>7</strong></u>,3]
- Swap 21 and 3 because gcd(21,3) = 3. nums = [<u><strong>3</strong></u>,7,<u><strong>21</strong></u>]
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> nums = [5,2,6,2]
<strong>Output:</strong> false
<strong>Explanation:</strong> It is impossible to sort the array because 5 cannot be swapped with any other element.
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> nums = [10,5,9,3,15]
<strong>Output:</strong> true
We can sort [10,5,9,3,15] by performing the following operations:
- Swap 10 and 15 because gcd(10,15) = 5. nums = [<u><strong>15</strong></u>,5,9,3,<u><strong>10</strong></u>]
- Swap 15 and 3 because gcd(15,3) = 3. nums = [<u><strong>3</strong></u>,5,9,<u><strong>15</strong></u>,10]
- Swap 10 and 15 because gcd(10,15) = 5. nums = [3,5,9,<u><strong>10</strong></u>,<u><strong>15</strong></u>]
</pre>

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

<ul>
	<li><code>1 &lt;= nums.length &lt;= 3 * 10<sup>4</sup></code></li>
	<li><code>2 &lt;= nums[i] &lt;= 10<sup>5</sup></code></li>
</ul>

class UnionFind:
    
    def __init__(self, n): 
        self.parent = list(range(n))
        self.rank = [1] * n
        
    def find(self, p): 
        if p != self.parent[p]: 
            self.parent[p] = self.find(self.parent[p])
        return self.parent[p]

    def union(self, p, q):
        prt, qrt = self.find(p), self.find(q)
        if prt == qrt: return False 
        if self.rank[prt] > self.rank[qrt]: prt, qrt = qrt, prt
        self.parent[prt] = qrt
        self.rank[qrt] += self.rank[prt]
        return True 
        

class Solution:
    def gcdSort(self, nums: List[int]) -> bool:
        m = max(nums)
        uf = UnionFind(m+1)
        
        seen = set(nums)
        
        # modified sieve of eratosthenes
        sieve = [1]*(m+1)
        sieve[0] = sieve[1] = 0
        for k in range(m//2 + 1): 
            if sieve[k]: 
                for x in range(2*k, m+1, k): 
                    sieve[x] = 0
                    if x in seen: uf.union(k, x)
        return all(uf.find(x) == uf.find(y) for x, y in zip(nums, sorted(nums)))
808