<p>You are given two <strong>0-indexed</strong> strings <code>word1</code> and <code>word2</code>.</p>

<p>A <strong>move</strong> consists of choosing two indices <code>i</code> and <code>j</code> such that <code>0 &lt;= i &lt; word1.length</code> and <code>0 &lt;= j &lt; word2.length</code> and swapping <code>word1[i]</code> with <code>word2[j]</code>.</p>

<p>Return <code>true</code> <em>if it is possible to get the number of distinct characters in</em> <code>word1</code> <em>and</em> <code>word2</code> <em>to be equal with <strong>exactly one</strong> move. </em>Return <code>false</code> <em>otherwise</em>.</p>

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

<pre>
<strong>Input:</strong> word1 = &quot;ac&quot;, word2 = &quot;b&quot;
<strong>Output:</strong> false
<strong>Explanation:</strong> Any pair of swaps would yield two distinct characters in the first string, and one in the second string.
</pre>

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

<pre>
<strong>Input:</strong> word1 = &quot;abcc&quot;, word2 = &quot;aab&quot;
<strong>Output:</strong> true
<strong>Explanation:</strong> We swap index 2 of the first string with index 0 of the second string. The resulting strings are word1 = &quot;abac&quot; and word2 = &quot;cab&quot;, which both have 3 distinct characters.
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> word1 = &quot;abcde&quot;, word2 = &quot;fghij&quot;
<strong>Output:</strong> true
<strong>Explanation:</strong> Both resulting strings will have 5 distinct characters, regardless of which indices we swap.
</pre>

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

<ul>
	<li><code>1 &lt;= word1.length, word2.length &lt;= 10<sup>5</sup></code></li>
	<li><code>word1</code> and <code>word2</code> consist of only lowercase English letters.</li>
</ul>

class Solution:
    def make_freq_count(self, word):
        freq = {}
        for char in word:
            self.try_add(freq, char)
        return freq

    def try_remove(self, freq, char):
        freq[char] -=1
        if freq[char] == 0:
            del freq[char]
    
    def try_add(self, freq, char):
        if char in freq:
            freq[char] += 1
        else:
            freq[char] = 1

    def swap(self, freq1, freq2, char1, char2):
        self.try_remove(freq1, char1)
        self.try_add(freq2, char1)
        
        self.try_remove(freq2, char2)
        self.try_add(freq1, char2)

    def check_swap(self, word1_freq, word2_freq, char1, char2):
        self.swap(word1_freq, word2_freq, char1, char2)

        if self.keys_equal(word1_freq, word2_freq):
            return True

        self.swap(word1_freq, word2_freq, char2, char1)
        

    def keys_equal(self, freq1, freq2):
        return len(freq1.keys()) == len(freq2.keys())


    def isItPossible(self, word1: str, word2: str) -> bool:
        word1_freq = self.make_freq_count(word1)
        word2_freq = self.make_freq_count(word2)

        keys1 = list(word1_freq.keys())
        keys2 = list(word2_freq.keys())

        for char1 in keys1:
            for char2 in keys2:
                if self.check_swap(word1_freq, word2_freq, char1, char2):
                    return True

        return False
        
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