<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 isItPossible(self, word1: str, word2: str) -> bool:
        counts1 = {}
        counts2 = {}

        for char1 in word1:
            if char1 not in counts1:
                counts1[char1] = 0
            counts1[char1] += 1

        for char2 in word2:
            if char2 not in counts2:
                counts2[char2] = 0
            counts2[char2] += 1

        count1 = len(counts1)
        count2 = len(counts2)

        if abs(count1 - count2) > 2:
            return False

        solos1 = {char for char in counts1 if counts1[char] == 1}
        solos2 = {char for char in counts2 if counts2[char] == 1}

        for char1 in counts1:
            for char2 in counts2:

                newcount1 = count1
                newcount2 = count2

                if char1 != char2:
                    if char1 in solos1:
                        newcount1 -= 1
                    if char2 in solos2:
                        newcount2 -= 1

                    if char1 not in counts2:
                        newcount2 += 1
                    if char2 not in counts1:
                        newcount1 += 1

                if newcount1 == newcount2:
                    return True
                

        return False
        
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