<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:

    vector<int> computeLPS(string& str) { // Longest Prefix also Suffix
        int n = str.size();
        vector<int> lps = vector<int>(n);
        for (int i = 1, j = 0; i < n; i++) {
            while (j > 0 && str[i] != str[j]) j = lps[j - 1];
            if (str[i] == str[j]) lps[i] = ++j;
        }
        return lps;
    }

    int solve(int i, int j, bool leftbound, bool rightbound, string &evil, string &s, string &name, int n, vector<int>& lps,vector<vector<vector<vector<int>>>> &dp){
        if(j == evil.size()){
            return 0;
        }
        if(i == n){
            return 1;
        }
        if(dp[i][j][leftbound][rightbound] != -1){
            return dp[i][j][leftbound][rightbound];
        }

        char st = leftbound ? s[i] : 'a';
        char ed = rightbound ? name[i] : 'z';

        int ans = 0;
        for(char c = st ; c <= ed ; c++){
            int ind = j;
            while(ind > 0 && evil[ind] != c){
                ind = lps[ind - 1];
            }
            if(evil[ind] == c){
                ind++;
            }
            ans = (ans + solve(i + 1, ind, leftbound && (c == st) , rightbound && (c == ed), evil, s, name, n, lps, dp)) % (1000000007);
        }
        return dp[i][j][leftbound][rightbound] = ans;
    }

    int findGoodStrings(int n, string s1, string s2, string evil) {
        int m = evil.size(); 
        vector<vector<vector<vector<int>>>> dp(n + 1, vector<vector<vector<int>>> (m + 1, vector<vector<int>> (2, vector<int> (2, -1))));
        vector<int> lps = computeLPS(evil);
        int ans = solve(0, 0, 1, 1, evil, s1, s2, n, lps, dp);
        return ans;
    }
};
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