<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:
        p=10**9+7
        ord_a=ord('a')
        l=len(evil)
        dup=[]
        for i in range(1, l):
            if evil[i:]==evil[:l-i]:
                dup.append(i)
        lend=len(dup)
        def count(s):
            tmp_ct=0
            bd=1
            ind=n
            without_s=[]
            for i in range(n):
                tmp_ct*=26
                if bd:
                    tmp_ct+=ord(s[i])-ord_a
                if i>=l-1 and ind>i-l and evil<s[i-l+1:i+1]:
                    tmp_ct-=1
                if i>=l:
                    tmp_ct-=without_s[i-l]
                if i>=l-1:
                    if s[i-l+1:i+1]==evil:
                        bd=0
                        ind=i
                tmp_ct%=p
                tmp_with_s=0
                for j in range(lend):
                    d=dup[j]
                    if i>=d:
                        tmp_with_s+=without_s[i-d]
                    if i>=d-1 and ind>i-d and evil[:d]<s[i-d+1:i+1]:
                        tmp_with_s+=1
                without_s.append(tmp_ct-tmp_with_s)
            return tmp_ct, bd
        str_ct1, bd1=count(s1)
        str_ct2, bd2=count(s2)
        return (str_ct2-str_ct1+bd2)%p
        
16800