<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:
    def findGoodStrings(self, n: int, s1: str, s2: str, evil: str) -> int:
        m = len(evil)
        kmp = [0]*m
        j = 0
        for i in range(1,m):
            while j and evil[i]!=evil[j]:
                j = kmp[j-1]
            if evil[i] == evil[j]:
                j += 1
            kmp[i] = j

        @cache
        def dp(i,j,tight1,tight2):
            if j == m:return 0
            if i == n:
                return 1
            a1 = ord('a')
            a2 = ord('z')
            if tight1:
                a1 = ord(s1[i])
            if tight2:
                a2 = ord(s2[i])
            res = 0
            for k in range(a1,a2+1):
                newl = chr(k)
                nevil = 0
                nt1 = False
                nt2 = False
                nj = j
                while nj and evil[nj]!=newl:
                    nj = kmp[nj-1]
                if newl == evil[nj]:
                    nj += 1
                if k == a1:
                    nt1 = True
                if k == a2:
                    nt2 = True
                if j+nevil<m:
                    res += dp(i+1,nj,tight1 and nt1,tight2 and nt2)
            return res % (10**9+7)
        return dp(0,0,True,True) % (10**9+7)
                
        
22100