<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>

typedef long long ll;
class Solution {
public:
    vector<ll> getLPS(string& s){
        vector<ll> lps(s.size());
        for (ll i=1,len=0; i<s.size();){
            if (s[i] == s[len]){
                lps[i++] = ++len;
            }
            else if (len) len = lps[len-1];
            else lps[i++] = 0;
        }
        return lps;
    }
    ll mod = 1e9+7;
    ll dp[505][3][3][55];
    ll func(ll indx, ll flag1, ll flag2, ll len1, string& evil ,vector<ll>& lps, string& s1, string& s2){
        if (indx == s1.size()) return (len1!=evil.size());
        if (dp[indx][flag1][flag2][len1]!=-1) return dp[indx][flag1][flag2][len1];
        ll cnt = 0;
        int i = (flag1) ? s1[indx]-'a' : 0;
        int j = (flag2) ? s2[indx]-'a' : 25;
        for (int h=i; h<=j; h++){
            int y = len1;
            while (y>0 && evil[y]!=((char)('a' + h))){
                y = lps[y-1];
            }
            y=(evil[y] == ((char)('a' + h))) ? 1+y : 0;
            if (y == evil.size()) continue;
            cnt+=func(indx+1,flag1 & (h ==i),flag2 & (h == j),y,evil,lps,s1,s2);
            cnt%=mod;
        }
        return dp[indx][flag1][flag2][len1] = cnt;
    }
    int findGoodStrings(int n, string s1, string s2, string evil) {
        vector<ll> lps = getLPS(evil);
        memset(dp,-1,sizeof(dp));
        return func(0,1,1,0,evil,lps,s1,s2);
    }
};
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