<p>You are given a string <code>s</code> and an array of strings <code>words</code>. All the strings of <code>words</code> are of <strong>the same length</strong>.</p>

<p>A <strong>concatenated string</strong> is a string that exactly contains all the strings of any permutation of <code>words</code> concatenated.</p>

<ul>
	<li>For example, if <code>words = [&quot;ab&quot;,&quot;cd&quot;,&quot;ef&quot;]</code>, then <code>&quot;abcdef&quot;</code>, <code>&quot;abefcd&quot;</code>, <code>&quot;cdabef&quot;</code>, <code>&quot;cdefab&quot;</code>, <code>&quot;efabcd&quot;</code>, and <code>&quot;efcdab&quot;</code> are all concatenated strings. <code>&quot;acdbef&quot;</code> is not a concatenated string because it is not the concatenation of any permutation of <code>words</code>.</li>
</ul>

<p>Return an array of <em>the starting indices</em> of all the concatenated substrings in <code>s</code>. You can return the answer in <strong>any order</strong>.</p>

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

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">s = &quot;barfoothefoobarman&quot;, words = [&quot;foo&quot;,&quot;bar&quot;]</span></p>

<p><strong>Output:</strong> <span class="example-io">[0,9]</span></p>

<p><strong>Explanation:</strong></p>

<p>The substring starting at 0 is <code>&quot;barfoo&quot;</code>. It is the concatenation of <code>[&quot;bar&quot;,&quot;foo&quot;]</code> which is a permutation of <code>words</code>.<br />
The substring starting at 9 is <code>&quot;foobar&quot;</code>. It is the concatenation of <code>[&quot;foo&quot;,&quot;bar&quot;]</code> which is a permutation of <code>words</code>.</p>
</div>

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

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">s = &quot;wordgoodgoodgoodbestword&quot;, words = [&quot;word&quot;,&quot;good&quot;,&quot;best&quot;,&quot;word&quot;]</span></p>

<p><strong>Output:</strong> <span class="example-io">[]</span></p>

<p><strong>Explanation:</strong></p>

<p>There is no concatenated substring.</p>
</div>

<p><strong class="example">Example 3:</strong></p>

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">s = &quot;barfoofoobarthefoobarman&quot;, words = [&quot;bar&quot;,&quot;foo&quot;,&quot;the&quot;]</span></p>

<p><strong>Output:</strong> <span class="example-io">[6,9,12]</span></p>

<p><strong>Explanation:</strong></p>

<p>The substring starting at 6 is <code>&quot;foobarthe&quot;</code>. It is the concatenation of <code>[&quot;foo&quot;,&quot;bar&quot;,&quot;the&quot;]</code>.<br />
The substring starting at 9 is <code>&quot;barthefoo&quot;</code>. It is the concatenation of <code>[&quot;bar&quot;,&quot;the&quot;,&quot;foo&quot;]</code>.<br />
The substring starting at 12 is <code>&quot;thefoobar&quot;</code>. It is the concatenation of <code>[&quot;the&quot;,&quot;foo&quot;,&quot;bar&quot;]</code>.</p>
</div>

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

<ul>
	<li><code>1 &lt;= s.length &lt;= 10<sup>4</sup></code></li>
	<li><code>1 &lt;= words.length &lt;= 5000</code></li>
	<li><code>1 &lt;= words[i].length &lt;= 30</code></li>
	<li><code>s</code> and <code>words[i]</code> consist of lowercase English letters.</li>
</ul>

class Solution:
    def findSubstring(self, s: str, words: List[str]) -> List[int]:
        
        m = len(words)
        n = len(words[0])
        l = len(s)

        if l < m * n:
            return []

        sol = []
        wordsTrie = {}

        for word in words:
           self._insertWord(word, 0, wordsTrie)
        
        i = 0
        while self._count(s[i : i + n], 0, wordsTrie) == 0:
            i += 1
        
        sol += self._findSubstring(s, i, words, wordsTrie, m, n, l)
        
        for j in range(1, n):
            sol += self._findSubstring(s, i + j, words, wordsTrie, m, n, l)
        
        return sol
    
    def _findSubstring(self, s, i, words, wordsTrie, m, n, l):
        
        sTrie = {}
        sCount = 0
        sol = []
        
        while l - i >= (m - sCount) * n:
            
            word = s[i : i + n]
            count = self._count(word, 0, wordsTrie)
            
            if count > 0 and self._insertWord(word, 0, sTrie) > count:
                start = i - sCount * n
                while s[start : start + n] != word:
                    self._removeWord(s[start : start + n], 0, sTrie)
                    sCount -= 1
                    start += n
                self._removeWord(s[start : start + n], 0, sTrie)
            elif count > 0 and sCount + 1 == m:
                start = i - m * n + n
                sol.append(start)
                self._removeWord(s[start : start + n], 0, sTrie)
            elif count > 0:
                sCount += 1
            else:
                sTrie = {}
                sCount = 0

            i += n
        
        return sol

    def _insertWord(self, word, i, trie):

        if i == len(word):
            trie['count'] = trie.get('count', 0) + 1
            return trie['count']
        elif word[i] not in trie:
            trie[word[i]] = {}
        
        return self._insertWord(word, i + 1, trie[word[i]])
    
    def _removeWord(self, word, i, trie):

        if i == len(word):
            trie['count'] -= 1
            return
        
        self._removeWord(word, i + 1, trie[word[i]])
    
    def _count(self, word, i, trie):

        if i == len(word):
            return trie.get('count', 0)
        elif word[i] not in trie:
            return 0
        
        return self._count(word, i + 1, trie[word[i]])

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