<p>You are given an array of strings <code>products</code> and a string <code>searchWord</code>.</p>

<p>Design a system that suggests at most three product names from <code>products</code> after each character of <code>searchWord</code> is typed. Suggested products should have common prefix with <code>searchWord</code>. If there are more than three products with a common prefix return the three lexicographically minimums products.</p>

<p>Return <em>a list of lists of the suggested products after each character of </em><code>searchWord</code><em> is typed</em>.</p>

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

<pre>
<strong>Input:</strong> products = [&quot;mobile&quot;,&quot;mouse&quot;,&quot;moneypot&quot;,&quot;monitor&quot;,&quot;mousepad&quot;], searchWord = &quot;mouse&quot;
<strong>Output:</strong> [[&quot;mobile&quot;,&quot;moneypot&quot;,&quot;monitor&quot;],[&quot;mobile&quot;,&quot;moneypot&quot;,&quot;monitor&quot;],[&quot;mouse&quot;,&quot;mousepad&quot;],[&quot;mouse&quot;,&quot;mousepad&quot;],[&quot;mouse&quot;,&quot;mousepad&quot;]]
<strong>Explanation:</strong> products sorted lexicographically = [&quot;mobile&quot;,&quot;moneypot&quot;,&quot;monitor&quot;,&quot;mouse&quot;,&quot;mousepad&quot;].
After typing m and mo all products match and we show user [&quot;mobile&quot;,&quot;moneypot&quot;,&quot;monitor&quot;].
After typing mou, mous and mouse the system suggests [&quot;mouse&quot;,&quot;mousepad&quot;].
</pre>

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

<pre>
<strong>Input:</strong> products = [&quot;havana&quot;], searchWord = &quot;havana&quot;
<strong>Output:</strong> [[&quot;havana&quot;],[&quot;havana&quot;],[&quot;havana&quot;],[&quot;havana&quot;],[&quot;havana&quot;],[&quot;havana&quot;]]
<strong>Explanation:</strong> The only word &quot;havana&quot; will be always suggested while typing the search word.
</pre>

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

<ul>
	<li><code>1 &lt;= products.length &lt;= 1000</code></li>
	<li><code>1 &lt;= products[i].length &lt;= 3000</code></li>
	<li><code>1 &lt;= sum(products[i].length) &lt;= 2 * 10<sup>4</sup></code></li>
	<li>All the strings of <code>products</code> are <strong>unique</strong>.</li>
	<li><code>products[i]</code> consists of lowercase English letters.</li>
	<li><code>1 &lt;= searchWord.length &lt;= 1000</code></li>
	<li><code>searchWord</code> consists of lowercase English letters.</li>
</ul>

class Trie:
    def __init__(self, products: Optional[List[str]]):
        self.nodes = {}
        self.word = False

        if products:
            for product in products:
                cur = self
                for char in product:
                    if char not in cur.nodes:
                        cur.nodes[char] = Trie(None)
                    cur = cur.nodes[char]
                cur.word = True
    
    def __repr__(self) -> str:
        return f"nodes={self.nodes}, word={self.word}"
    
    def find(self, char: str) -> Optional[Self]:
        if char in self.nodes:
            return self.nodes[char]
        return None
    
    def list(self, prefix: str, result: List[str]) -> None:
        if len(result) == 3:
            return
        if self.word:
            result.append(prefix)
        for node in sorted(self.nodes.keys()):
            new_prefix = prefix + node
            new_node = self.nodes[node]
            new_node.list(new_prefix, result)
    

class Solution:
    def suggestedProducts(self, products: List[str], searchWord: str) -> List[List[str]]:
        self.trie = Trie(products)
        cur = self.trie
        result = []
        prefix = ""

        for i, char in enumerate(searchWord):
            cur = None if cur is None else cur.find(char)
            new_result = []

            if cur:
                prefix += char
                cur.list(prefix, new_result)
            result.append(new_result)
        
        return result

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