<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>

struct DSU {
    vector<int> f;

    DSU(int n) {
        f.resize(n);
        iota(f.begin(), f.end(), 0);
    }

    int find(int x) {
        while (x != f[x]) {
            x = f[x] = f[f[x]];
        } return x;
    }

    void merge(int x, int y) {
        x = find(x); y = find(y);
        if (x != y) f[y] = x;
    }
};

class Solution {
public:
    int numSimilarGroups(vector<string>& strs) {
        int n = strs.size();

        auto identical = [&](int i, int j) -> bool {
            int n1 = strs[i].size();
            if (n1 != strs[j].size()) return 0;

            int diff = 0;
            vector<int> freq(26, 0);
            for (int k = 0; k < n1; k++) {
                ++freq[strs[i][k] - 'a'], --freq[strs[j][k] - 'a'];
                diff += (strs[i][k] != strs[j][k]);
            }

            if (diff == 0 || diff == 2)
                return accumulate(begin(freq), end(freq), 0) == 0;
            return 0;
        };

        DSU dsu(n);
        for (int i = 0; i < n - 1; i++)
            for (int j = i + 1; j < n; j++)
                if (identical(i, j)) dsu.merge(i, j);

        set<int> st;
        for (int i = 0; i < n; i++)
            st.insert(dsu.find(i));
        return st.size();
    }
};
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