<p>Two strings, <code>X</code> and <code>Y</code>, are considered similar if either they are identical or we can make them equivalent by swapping at most two letters (in distinct positions) within the string <code>X</code>.</p>

<p>For example, <code>&quot;tars&quot;</code>&nbsp;and <code>&quot;rats&quot;</code>&nbsp;are similar (swapping at positions <code>0</code> and <code>2</code>), and <code>&quot;rats&quot;</code> and <code>&quot;arts&quot;</code> are similar, but <code>&quot;star&quot;</code> is not similar to <code>&quot;tars&quot;</code>, <code>&quot;rats&quot;</code>, or <code>&quot;arts&quot;</code>.</p>

<p>Together, these form two connected groups by similarity: <code>{&quot;tars&quot;, &quot;rats&quot;, &quot;arts&quot;}</code> and <code>{&quot;star&quot;}</code>.&nbsp; Notice that <code>&quot;tars&quot;</code> and <code>&quot;arts&quot;</code> are in the same group even though they are not similar.&nbsp; Formally, each group is such that a word is in the group if and only if it is similar to at least one other word in the group.</p>

<p>We are given a list <code>strs</code> of strings where every string in <code>strs</code> is an anagram of every other string in <code>strs</code>. How many groups are there?</p>

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

<pre>
<strong>Input:</strong> strs = [&quot;tars&quot;,&quot;rats&quot;,&quot;arts&quot;,&quot;star&quot;]
<strong>Output:</strong> 2
</pre>

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

<pre>
<strong>Input:</strong> strs = [&quot;omv&quot;,&quot;ovm&quot;]
<strong>Output:</strong> 1
</pre>

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

<ul>
	<li><code>1 &lt;= strs.length &lt;= 300</code></li>
	<li><code>1 &lt;= strs[i].length &lt;= 300</code></li>
	<li><code>strs[i]</code> consists of lowercase letters only.</li>
	<li>All words in <code>strs</code> have the same length and are anagrams of each other.</li>
</ul>

class Solution:
    def numSimilarGroups(self, strs: List[str]) -> int:
        strs = list(set(strs))
        groups = [(i, 1) for i in range(len(strs))]
        def find(i):
            if groups[i][0] != i:
                g = find(groups[i][0])
                groups[i] = (g, groups[i][1])
                return g
            else: return i

        def union(i, j):
            group_i = find(i)
            group_j = find(j)
            if group_i == group_j: return
            if groups[group_i][1] > groups[group_j][1]:
                groups[group_j] = (group_i, groups[group_j][1])
                groups[group_i] = (group_i, groups[group_i][1] + groups[group_j][1])
            else:
                groups[group_i] = (group_j, groups[group_i][1])
                groups[group_j] = (group_j, groups[group_i][1] + groups[group_j][1])

        all_numbers = {s : i for i, s in enumerate(strs)}

        for index, s in enumerate(strs):
            for i in range(len(s)):
                for j in range(i + 1, len(s)):
                    neighbor = s[:i] + s[j] + s[i + 1:j] + s[i] + s[j + 1:]
                    if neighbor not in all_numbers: continue
                    union(index, all_numbers[neighbor])

        for i in range(len(strs)):
            find(i)
        return len(set(g[0] for g in groups))
17000