<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:
        MOD = 10**9 + 7

        def kmp_table(pattern):
            table = [0] * len(pattern)
            j = 0
            for i in range(1, len(pattern)):
                while j > 0 and pattern[i] != pattern[j]:
                    j = table[j - 1]
                if pattern[i] == pattern[j]:
                    j += 1
                table[i] = j
            return table

        def dp(pos, tight1, tight2, evil_matched):
            if evil_matched == len(evil):
                return 0
            if pos == n:
                return 1
            if (pos, tight1, tight2, evil_matched) in memo:
                return memo[(pos, tight1, tight2, evil_matched)]

            low = s1[pos] if tight1 else 'a'
            high = s2[pos] if tight2 else 'z'
            result = 0

            for char in range(ord(low), ord(high) + 1):
                char = chr(char)
                new_tight1 = tight1 and (char == s1[pos])
                new_tight2 = tight2 and (char == s2[pos])
                j = evil_matched
                while j > 0 and char != evil[j]:
                    j = kmp[j - 1]
                if char == evil[j]:
                    j += 1
                result = (result + dp(pos + 1, new_tight1, new_tight2, j)) % MOD

            memo[(pos, tight1, tight2, evil_matched)] = result
            return result

        kmp = kmp_table(evil)
        memo = {}
        return dp(0, True, True, 0)
21400