<p>You are given an array of strings of the same length <code>words</code>.</p>

<p>In one <strong>move</strong>, you can swap any two even indexed characters or any two odd indexed characters of a string <code>words[i]</code>.</p>

<p>Two strings <code>words[i]</code> and <code>words[j]</code> are <strong>special-equivalent</strong> if after any number of moves, <code>words[i] == words[j]</code>.</p>

<ul>
	<li>For example, <code>words[i] = &quot;zzxy&quot;</code> and <code>words[j] = &quot;xyzz&quot;</code> are <strong>special-equivalent</strong> because we may make the moves <code>&quot;zzxy&quot; -&gt; &quot;xzzy&quot; -&gt; &quot;xyzz&quot;</code>.</li>
</ul>

<p>A <strong>group of special-equivalent strings</strong> from <code>words</code> is a non-empty subset of words such that:</p>

<ul>
	<li>Every pair of strings in the group are special equivalent, and</li>
	<li>The group is the largest size possible (i.e., there is not a string <code>words[i]</code> not in the group such that <code>words[i]</code> is special-equivalent to every string in the group).</li>
</ul>

<p>Return <em>the number of <strong>groups of special-equivalent strings</strong> from </em><code>words</code>.</p>

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

<pre>
<strong>Input:</strong> words = [&quot;abcd&quot;,&quot;cdab&quot;,&quot;cbad&quot;,&quot;xyzz&quot;,&quot;zzxy&quot;,&quot;zzyx&quot;]
<strong>Output:</strong> 3
<strong>Explanation:</strong> 
One group is [&quot;abcd&quot;, &quot;cdab&quot;, &quot;cbad&quot;], since they are all pairwise special equivalent, and none of the other strings is all pairwise special equivalent to these.
The other two groups are [&quot;xyzz&quot;, &quot;zzxy&quot;] and [&quot;zzyx&quot;].
Note that in particular, &quot;zzxy&quot; is not special equivalent to &quot;zzyx&quot;.
</pre>

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

<pre>
<strong>Input:</strong> words = [&quot;abc&quot;,&quot;acb&quot;,&quot;bac&quot;,&quot;bca&quot;,&quot;cab&quot;,&quot;cba&quot;]
<strong>Output:</strong> 3
</pre>

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

<ul>
	<li><code>1 &lt;= words.length &lt;= 1000</code></li>
	<li><code>1 &lt;= words[i].length &lt;= 20</code></li>
	<li><code>words[i]</code> consist of lowercase English letters.</li>
	<li>All the strings are of the same length.</li>
</ul>

class Solution {
public:
    bool is_linked(string a, string b)
    {
        
        int n=a.size();
        vector<int> ea(26,0), eb(26,0), oa(26,0), ob(26,0);

        for(int j=0;j<n;j++)
        {
            if(j%2==0)
            {
                ea[a[j]-'a']++;
                eb[b[j]-'a']++;
            }
            else
            {
                oa[a[j]-'a']++;
                ob[b[j]-'a']++;
            }
        }

        return (ea == eb) & (oa == ob);
    }


    string hashify(string a)
    {
        vector<int> oa(26,0), ea(26,0);
        int n=a.size();
        for(int j=0;j<n;j++)
        {
            if(j%2==0)
                ea[a[j]-'a']++;
            else
                oa[a[j] - 'a']++;
        }

        string ret="";
        for(int j=0;j<26;j++)
        {
            ret += to_string(j)+':'+to_string(oa[j])+':'+to_string(ea[j])+'|';
        }
        return ret;
    }

    int numSpecialEquivGroups(vector<string>& words) {
        int n=words.size();
        unordered_set<string> hash;
        for(auto st:words)
            hash.insert(hashify(st));
    
        return hash.size();
    }
};
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