<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>

#include<bits/stdc++.h>
using namespace std;

const int mod = 1e9+7;

class Solution {
public:
    int dp[501][2][2][51];

    int genv(int ind, int tight1, int tight2, string &s1, string &s2, vector<vector<int>> &pos, int seen, int n) {
        if(seen == n) {
            return 0;
        }

        if(ind == s1.size()) {
            return 1;
        }

        if(dp[ind][tight1][tight2][seen] != -1) {
            return dp[ind][tight1][tight2][seen];
        }

        int ans = 0;
        if(tight1 == 1 && tight2 == 0) {
            for(int j = 0; j < 26; j++) {
                char c = 'a' + j;
                if(c < s2[ind]) {
                    ans = (ans + genv(ind+1, tight1, 1, s1, s2, pos, pos[seen][j], n)) % mod;
                } else if(c == s2[ind]) {
                    ans = (ans + genv(ind+1, tight1, tight2, s1, s2, pos, pos[seen][j], n)) % mod;
                }
            }
        }
        else if(tight1 == 0 && tight2 == 1) {
            for(int j = 0; j < 26; j++) {
                char c = 'a' + j;
                if(c > s1[ind]) {
                    ans = (ans + genv(ind+1, 1, tight2, s1, s2, pos, pos[seen][j], n)) % mod;
                } else if(c == s1[ind]) {
                    ans = (ans + genv(ind+1, 0, tight2, s1, s2, pos, pos[seen][j], n)) % mod;
                }
            }
        }
        else if(tight1 == 1 && tight2 == 1) {
            for(int j = 0; j < 26; j++) {
                ans = (ans + genv(ind+1, tight1, tight2, s1, s2, pos, pos[seen][j], n)) % mod;
            }
        }
        else if(tight1 == 0 && tight2 == 0) {
            for(int j = 0; j < 26; j++) {
                char c = 'a' + j;
                if(c > s1[ind]) {
                    if(c < s2[ind]) {
                        ans = (ans + genv(ind+1, 1, 1, s1, s2, pos, pos[seen][j], n)) % mod;
                    } else if(c == s2[ind]) {
                        ans = (ans + genv(ind+1, 1, 0, s1, s2, pos, pos[seen][j], n)) % mod;
                    }
                } else if(c == s1[ind]) {
                    if(c < s2[ind]) {
                        ans = (ans + genv(ind+1, 0, 1, s1, s2, pos, pos[seen][j], n)) % mod;
                    } else if(c == s2[ind]) {
                        ans = (ans + genv(ind+1, 0, 0, s1, s2, pos, pos[seen][j], n)) % mod;
                    }
                }
            }
        }

        return dp[ind][tight1][tight2][seen] = ans;
    }

    int findGoodStrings(int n, string s1, string s2, string evil) {
        int evilSize = evil.size();  // Fix variable for evil string size.
        vector<vector<int>> pos(evilSize + 1, vector<int>(26, 0));
        for(int i = 0; i <= evilSize; i++) {
            if(i == evilSize) break;
            string s = (i == 0) ? "" : evil.substr(0, i);

            for(int j = 0; j < 26; j++) {
                if(evil[i] == 'a' + j) {
                    pos[i][j] = i + 1;
                } else {
                    s += 'a' + j;
                    int maxi = -1;
                    int x = s.size() - 1;
                    for(int k = 0; k <= x; k++) {
                        int f = 0;
                        int cnt = x;
                        for(int k1 = k; k1 >= 0; k1--) {
                            if(s[cnt] != evil[k1]) {
                                f = 1;
                                break;
                            }
                            cnt--;
                        }
                        if(f == 0) {
                            maxi = max(maxi, k);
                        }
                    }
                    s.pop_back();
                    pos[i][j] = maxi + 1;
                }
            }
        }

        memset(dp, -1, sizeof(dp));
        return genv(0, 0, 0, s1, s2, pos, 0, evilSize);
    }
};  // End of Solution class


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