<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:

    int M=1e9+7;

    int dp[502][52][2][2];

    int solve(vector<int>&lps,string &s1,string &s2,string &evil,int idx,int match,bool min,bool max){
            
            if(match==evil.size())return 0;
            if(idx==s1.size())return 1; 

            if(dp[idx][match][min][max]!=-1)return dp[idx][match][min][max];

            char lb;
            char ub;

            if(min){
                lb=s1[idx];
            }else{
                lb='a';
            }

            if(max){
                ub=s2[idx];
            }else{
                ub='z';
            }

            int ans=0;

          for(char c=lb;c<=ub;c++){

             int j=match;

             while(j>0 && c!=evil[j]){
                j=lps[j-1];
             }

             if(evil[j]==c)j++;

             ans=(ans+solve(lps,s1,s2,evil,idx+1,j,min & (c==lb),max & (c==ub)))%M;

          }

          return dp[idx][match][min][max] =ans;  
 

    }

    int findGoodStrings(int n, string s1, string s2, string evil) {
        
         int m=evil.size();

         vector<int>lps(m);

         lps[0]=0;
         int len=0;
           int i=1;

          while(i<m){

               if(evil[i]==evil[len]){
                  len++;
                  lps[i]=len;
                  i++;
               }else{

                  if(len!=0){
                    len=lps[len-1];
                  }else{
                    lps[i]=0;
                    i++;
                  }

               }

          }
 
          memset(dp,-1,sizeof dp);

          int ans=solve(lps,s1,s2,evil,0,0,1,1);

          return ans;


          
    }
};
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