<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.parents = [i for i in range (n)]
        self.ranks = [0 for i in range (n)]
    def find(self, u):
        if self.parents[u] != u:
            self.parents[u] = self.find(self.parents[u])
            
        return self.parents[u]
    def union(self, u, v):
        par_u = self.find(u)
        par_v = self.find(v)
        if par_u == par_v:
            return 
        if self.ranks[par_u] <= self.ranks[par_v]:
            self.parents[par_u] = par_v
            if self.ranks[par_u] == self.ranks[par_v]:
                self.ranks[par_v] += 1
        else:
            self.parents[par_v] = par_u
class Solution:
    def gcdSort(self, nums: List[int]) -> bool:
        sorted_nums = sorted(nums)
        n = len(nums)
        
        union = UnionFind(max(nums) + 1)
        
        for i in range (n):
            max_val = int(nums[i] ** 0.5) + 1
            for j in range (2, max_val + 1):
                if nums[i] % j == 0:
                    union.union(nums[i], j)
                    if j != nums[i]:
                        union.union(nums[i], nums[i] // j)
                        
        for i in range (n):
            if union.find(nums[i]) != union.find(sorted_nums[i]):
                return False
            
        return True
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