<p>There are <code>n</code> couples sitting in <code>2n</code> seats arranged in a row and want to hold hands.</p>

<p>The people and seats are represented by an integer array <code>row</code> where <code>row[i]</code> is the ID of the person sitting in the <code>i<sup>th</sup></code> seat. The couples are numbered in order, the first couple being <code>(0, 1)</code>, the second couple being <code>(2, 3)</code>, and so on with the last couple being <code>(2n - 2, 2n - 1)</code>.</p>

<p>Return <em>the minimum number of swaps so that every couple is sitting side by side</em>. A swap consists of choosing any two people, then they stand up and switch seats.</p>

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

<pre>
<strong>Input:</strong> row = [0,2,1,3]
<strong>Output:</strong> 1
<strong>Explanation:</strong> We only need to swap the second (row[1]) and third (row[2]) person.
</pre>

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

<pre>
<strong>Input:</strong> row = [3,2,0,1]
<strong>Output:</strong> 0
<strong>Explanation:</strong> All couples are already seated side by side.
</pre>

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

<ul>
	<li><code>2n == row.length</code></li>
	<li><code>2 &lt;= n &lt;= 30</code></li>
	<li><code>n</code> is even.</li>
	<li><code>0 &lt;= row[i] &lt; 2n</code></li>
	<li>All the elements of <code>row</code> are <strong>unique</strong>.</li>
</ul>

class dsu:
    def __init__(self,n):
        self.parent = [0]*(n)
        self.size = [1]*(n)
        self.count = n
        for i in range(n):
            self.parent[i] = i
    def find(self,x):
        if  x != self.parent[x]:
            self.parent[x] = self.find(self.parent[x])
        return self.parent[x]
    def union(self,p1,p2):
        u1 = self.find(p1)
        u2 = self.find(p2)
        if u1 == u2:
            return
        if self.size[u1] > self.size[u2]:
            self.size[u1] += self.size[u2]
            self.parent[u2] = u1
        else:
            self.size[u2] += self.size[u1]
            self.parent[u1] = u2
        self.count -= 1
        return 

class Solution:
    def minSwapsCouples(self, row: List[int]) -> int:
        ds = dsu(len(row)//2) 
        n = len(row)//2
        for i in range(n):
            a = row[2*i]//2
            b = row[2*i+1]//2
            ds.union(a,b)
        return  n - ds.count

16500