<p>Given the strings <code>s1</code> and <code>s2</code> of size <code>n</code> and the string <code>evil</code>, return <em>the number of <strong>good</strong> strings</em>.</p>

<p>A <strong>good</strong> string has size <code>n</code>, it is alphabetically greater than or equal to <code>s1</code>, it is alphabetically smaller than or equal to <code>s2</code>, and it does not contain the string <code>evil</code> as a substring. Since the answer can be a huge number, return this <strong>modulo</strong> <code>10<sup>9</sup> + 7</code>.</p>

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

<pre>
<strong>Input:</strong> n = 2, s1 = &quot;aa&quot;, s2 = &quot;da&quot;, evil = &quot;b&quot;
<strong>Output:</strong> 51 
<strong>Explanation:</strong> There are 25 good strings starting with &#39;a&#39;: &quot;aa&quot;,&quot;ac&quot;,&quot;ad&quot;,...,&quot;az&quot;. Then there are 25 good strings starting with &#39;c&#39;: &quot;ca&quot;,&quot;cc&quot;,&quot;cd&quot;,...,&quot;cz&quot; and finally there is one good string starting with &#39;d&#39;: &quot;da&quot;.&nbsp;
</pre>

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

<pre>
<strong>Input:</strong> n = 8, s1 = &quot;leetcode&quot;, s2 = &quot;leetgoes&quot;, evil = &quot;leet&quot;
<strong>Output:</strong> 0 
<strong>Explanation:</strong> All strings greater than or equal to s1 and smaller than or equal to s2 start with the prefix &quot;leet&quot;, therefore, there is not any good string.
</pre>

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

<pre>
<strong>Input:</strong> n = 2, s1 = &quot;gx&quot;, s2 = &quot;gz&quot;, evil = &quot;x&quot;
<strong>Output:</strong> 2
</pre>

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

<ul>
	<li><code>s1.length == n</code></li>
	<li><code>s2.length == n</code></li>
	<li><code>s1 &lt;= s2</code></li>
	<li><code>1 &lt;= n &lt;= 500</code></li>
	<li><code>1 &lt;= evil.length &lt;= 50</code></li>
	<li>All strings consist of lowercase English letters.</li>
</ul>

class Solution {
public:
    
    #define ll long long
    int mod = 1e9 + 7;

    ll solve(string & s1, string & s2,int pos,bool ok1, bool ok2,int k,vector<int> & pre,
     vector<vector<vector<vector<int>>>> & dp,string & evil){
        if(evil.size() == k){return 0;}
        if(pos == s1.size()){
            return 1;
        }

        if(dp[pos][ok1][ok2][k] != -1){
            return dp[pos][ok1][ok2][k];
        }
        
        int c1 = s1[pos]-'a';
        int c2 = s2[pos]-'a';

        ll ans = 0;
        for(int i=0; i<26; i++){
            int k1 = k;
            
            bool ok3 = ok1 , ok4 =ok2;

            if(i<c1 && !ok3){continue;}
            if(i>c2 && !ok4){continue;}

            if(i>c1){ok3=1;}
            if(i<c2){ok4=1;}
            
            char ch = i+'a';
            while(k1!=0 && evil[k1]!=ch){
                k1 = pre[k1-1];
            }
            if(ch == evil[k1]){k1++;}

            ans += solve(s1,s2,pos+1,ok3,ok4,k1,pre,dp,evil);
            ans %= mod;
        }
        return  dp[pos][ok1][ok2][k] = ans;
    }
    
    vector<int> prefix(string & s){
          vector<int> pre(s.size(),0);

          int k = 0;
          for(int i=1; i<s.size(); i++){
               while(k!=0 && s[i]!= s[k]){
                k = pre[k-1];
               }
               if(s[i] == s[k]) k++;

               pre[i] = k;
          }

          return pre;
    }

    int findGoodStrings(int n, string s1, string s2, string evil) {
         vector<vector<vector<vector<int>>>> dp(n,vector<vector<vector<int>>>(2,vector<vector<int>>(2,
         vector<int>(evil.size(),-1))));

         vector<int> pre = prefix(evil);

         return solve(s1,s2,0,0,0,0,pre,dp,evil);

    }
};
10600