<p>You are given two strings <code>a</code> and <code>b</code> that consist of lowercase letters. In one operation, you can change any character in <code>a</code> or <code>b</code> to <strong>any lowercase letter</strong>.</p>

<p>Your goal is to satisfy <strong>one</strong> of the following three conditions:</p>

<ul>
	<li><strong>Every</strong> letter in <code>a</code> is <strong>strictly less</strong> than <strong>every</strong> letter in <code>b</code> in the alphabet.</li>
	<li><strong>Every</strong> letter in <code>b</code> is <strong>strictly less</strong> than <strong>every</strong> letter in <code>a</code> in the alphabet.</li>
	<li><strong>Both</strong> <code>a</code> and <code>b</code> consist of <strong>only one</strong> distinct letter.</li>
</ul>

<p>Return <em>the <strong>minimum</strong> number of operations needed to achieve your goal.</em></p>

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

<pre>
<strong>Input:</strong> a = &quot;aba&quot;, b = &quot;caa&quot;
<strong>Output:</strong> 2
<strong>Explanation:</strong> Consider the best way to make each condition true:
1) Change b to &quot;ccc&quot; in 2 operations, then every letter in a is less than every letter in b.
2) Change a to &quot;bbb&quot; and b to &quot;aaa&quot; in 3 operations, then every letter in b is less than every letter in a.
3) Change a to &quot;aaa&quot; and b to &quot;aaa&quot; in 2 operations, then a and b consist of one distinct letter.
The best way was done in 2 operations (either condition 1 or condition 3).
</pre>

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

<pre>
<strong>Input:</strong> a = &quot;dabadd&quot;, b = &quot;cda&quot;
<strong>Output:</strong> 3
<strong>Explanation:</strong> The best way is to make condition 1 true by changing b to &quot;eee&quot;.
</pre>

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

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

class Solution:
    def minCharacters(self, a: str, b: str) -> int:
        m, n = len(a), len(b)
        res = m + n
        c1, c2 = [0] * 26, [0] * 26
        
        for c in a:
            c1[ord(c) - ord('a')] += 1
        for c in b:
            c2[ord(c) - ord('a')] += 1
        
        for i in range(26):
            res = min(res, m + n - c1[i] - c2[i])
            if i > 0:
                c1[i] += c1[i - 1]
                c2[i] += c2[i - 1]
            if i < 25:
                res = min(res, m - c1[i] + c2[i])
                res = min(res, n - c2[i] + c1[i])
        
        return res
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