<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 {
public:

    int minCharacters(string a, string b) {
        int m= a.size();
        int n= b.size();
        sort(a.begin(),a.end());
        sort(b.begin(),b.end());
        vector<int> pref_a(26), pref_b(26), suff_a(26), suff_b(26);
        vector<int>cnt_a(26,0), cnt_b(26,0);
        for(auto it:a){
            cnt_a[it-'a']++;
        } 
        for(auto it:b){
            cnt_b[it-'a']++;
        }

        pref_a[0]=cnt_a[0];
        pref_b[0]=cnt_b[0];
        suff_a[25]=cnt_a[25];
        suff_b[25]= cnt_b[25];
        for(int i=1;i<26;i++){
            pref_a[i]= pref_a[i-1]+ cnt_a[i];
            pref_b[i]= pref_b[i-1]+ cnt_b[i];
            suff_a[25-i]= suff_a[26-i]+ cnt_a[25-i];
            suff_b[25-i]= suff_b[26-i]+ cnt_b[25-i];
        }
        int cnt=INT_MAX;
        for(int i=0;i<26;i++){
            cnt= min(cnt, m+n-cnt_a[i]-cnt_b[i]);
        }
        for(int i=25;i>=1;i--){
            cnt= min(cnt, pref_b[i-1]+suff_a[i]);
        }
        for(int i=25;i>=1;i--){
            cnt= min(cnt, pref_a[i-1]+suff_b[i]);
        }

        return cnt;
    }
};
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