<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 convert_str_to_num(s: str) -> int:
            return ord(s) - ord("a")
        
        num1, num2, evil_num = list(map(convert_str_to_num, s1)), tuple(map(convert_str_to_num, s2)), tuple(map(convert_str_to_num, evil))
        def prefix_function(tup: tuple) -> List[int]:
            l = len(tup)
            lps = [0 for _ in range(l)]
            for i in range(1, l):
                j = lps[i - 1]
                while j > 0 and tup[i] != tup[j]: j = lps[j - 1]
                if tup[i] == tup[j]: j += 1
                lps[i] = j
            return lps

        kmp = prefix_function(evil_num)

        @cache
        def dp(pos: int, tight: True, match_number: int, num: tuple) -> int:
            if match_number == len(evil_num): return 0
            if pos == n: return 1
            res = 0
            bound = num[pos] if tight else 26
            for i in range(bound + 1):
                if i == 26: continue
                new_tight = i == bound
                j = match_number
                while j > 0 and evil_num[j] != i:
                    j = kmp[j - 1]
                if evil_num[j] == i: j += 1
                res = (res + dp(pos + 1, new_tight, j, num))
            return res % mod

        i = n - 1
        while i >= 0 and num1[i] == 0:
            num1[i] = 25
            i -= 1
        if i >= 0: num1[i] -= 1
        else: return dp(0, True, 0, num2) % mod
        
        return (dp(0, True, 0, num2) - dp(0, True, 0, tuple(num1))) % mod
25000