<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 TrieNode:
    def __init__(self):
        self.children={}
        self.end=False
class Trie:
    def __init__(self):
        self.root=TrieNode()
    
    def insert(self,product):
        current=self.root
        for letter in product:
            if letter not in current.children:
                current.children[letter]=TrieNode()
            current=current.children[letter]
        current.end=True
        
    
    def search(self,prefix,products):
        #return list of 3 lexico words with a prefix
        current=self.root
        for letter in prefix:
            if letter not in current.children:
                return []
            current=current.children[letter]
        #return the three lexico sorted ones
        #DFS code
        print(current.children,prefix)
        answer=[]
        lst=[]
        def top3(node,string):
            #base case
            nonlocal lst,answer
            if node.end==True:
                temp=lst[:]
                answer.append(prefix+"".join(temp))
            for child in node.children:
                lst.append(child)
                top3(node.children[child],lst)
                lst.pop()        
        top3(current,lst)
        if len(answer)>3:
            return(answer[:3])
        return answer
        





class Solution:
    def suggestedProducts(self, products: List[str], searchWord: str) -> List[List[str]]:
        #do the lexico sort
        products=sorted(products)


        #construct a trie of products
        Trieobj=Trie()
        for product in products:
            Trieobj.insert(product)
        
        #traerse serachWord and return 3 lexico
        output=[]
        for letter in range(len(searchWord)):
            output.append(Trieobj.search(searchWord[:letter+1],products))
        return output

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