<p>You are given an integer <code>n</code>.</p>

<p>A string <code>s</code> is called <strong>good </strong>if it contains only lowercase English characters <strong>and</strong> it is possible to rearrange the characters of <code>s</code> such that the new string contains <code>&quot;leet&quot;</code> as a <strong>substring</strong>.</p>

<p>For example:</p>

<ul>
	<li>The string <code>&quot;lteer&quot;</code> is good because we can rearrange it to form <code>&quot;leetr&quot;</code> .</li>
	<li><code>&quot;letl&quot;</code> is not good because we cannot rearrange it to contain <code>&quot;leet&quot;</code> as a substring.</li>
</ul>

<p>Return <em>the <strong>total</strong> number of good strings of length </em><code>n</code>.</p>

<p>Since the answer may be large, return it <strong>modulo </strong><code>10<sup>9</sup> + 7</code>.</p>

<p>A <strong>substring</strong> is a contiguous sequence of characters within a string.</p>

<div class="notranslate" style="all: initial;">&nbsp;</div>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> n = 4
<strong>Output:</strong> 12
<strong>Explanation:</strong> The 12 strings which can be rearranged to have &quot;leet&quot; as a substring are: &quot;eelt&quot;, &quot;eetl&quot;, &quot;elet&quot;, &quot;elte&quot;, &quot;etel&quot;, &quot;etle&quot;, &quot;leet&quot;, &quot;lete&quot;, &quot;ltee&quot;, &quot;teel&quot;, &quot;tele&quot;, and &quot;tlee&quot;.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> n = 10
<strong>Output:</strong> 83943898
<strong>Explanation:</strong> The number of strings with length 10 which can be rearranged to have &quot;leet&quot; as a substring is 526083947580. Hence the answer is 526083947580 % (10<sup>9</sup> + 7) = 83943898.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= n &lt;= 10<sup>5</sup></code></li>
</ul>

class Solution:
    def stringCount(self, n: int) -> int:
        """
        - only need 1 l, 2 e's, 1 t
        - need length of at least 4
        - every other letter can be a - z, i.e. 26 characters
        - 4 letters are locked in
            - can be in any position
            - i.e. n * (n - 1) * (n - 2) * (n - 3)
        - l can go in s positions

        """
        def dfs(n, l, e, t):
            if n == 0:
                return 0 if sum([l, e, t]) else 1
            if (n, l, e, t) in dp:
                return dp[(n, l, e, t)]
            dp[(n, l, e, t)] = (dfs(n - 1, l, e, t) * 23 +
                                dfs(n - 1, max(0, l - 1), e, t) +
                                dfs(n - 1, l, max(0, e - 1), t) + 
                                dfs(n - 1, l, e, max(0, t - 1))) % mod
            return dp[(n, l, e, t)]    
        dp = {}
        mod = 10 ** 9 + 7
        return dfs(n, 1, 2, 1) % mod
308100