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

<p>A string <code>x</code> is called <strong>valid</strong> if <code>x</code> is a <span data-keyword="string-prefix">prefix</span> of <strong>any</strong> string in <code>words</code>.</p>

<p>Return the <strong>minimum</strong> number of <strong>valid</strong> strings that can be <em>concatenated</em> to form <code>target</code>. If it is <strong>not</strong> possible to form <code>target</code>, return <code>-1</code>.</p>

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

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">words = [&quot;abc&quot;,&quot;aaaaa&quot;,&quot;bcdef&quot;], target = &quot;aabcdabc&quot;</span></p>

<p><strong>Output:</strong> <span class="example-io">3</span></p>

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

<p>The target string can be formed by concatenating:</p>

<ul>
	<li>Prefix of length 2 of <code>words[1]</code>, i.e. <code>&quot;aa&quot;</code>.</li>
	<li>Prefix of length 3 of <code>words[2]</code>, i.e. <code>&quot;bcd&quot;</code>.</li>
	<li>Prefix of length 3 of <code>words[0]</code>, i.e. <code>&quot;abc&quot;</code>.</li>
</ul>
</div>

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

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">words = [&quot;abababab&quot;,&quot;ab&quot;], target = &quot;ababaababa&quot;</span></p>

<p><strong>Output:</strong> <span class="example-io">2</span></p>

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

<p>The target string can be formed by concatenating:</p>

<ul>
	<li>Prefix of length 5 of <code>words[0]</code>, i.e. <code>&quot;ababa&quot;</code>.</li>
	<li>Prefix of length 5 of <code>words[0]</code>, i.e. <code>&quot;ababa&quot;</code>.</li>
</ul>
</div>

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

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">words = [&quot;abcdef&quot;], target = &quot;xyz&quot;</span></p>

<p><strong>Output:</strong> <span class="example-io">-1</span></p>
</div>

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

<ul>
	<li><code>1 &lt;= words.length &lt;= 100</code></li>
	<li><code>1 &lt;= words[i].length &lt;= 5 * 10<sup>3</sup></code></li>
	<li>The input is generated such that <code>sum(words[i].length) &lt;= 10<sup>5</sup></code>.</li>
	<li><code>words[i]</code> consists only of lowercase English letters.</li>
	<li><code>1 &lt;= target.length &lt;= 5 * 10<sup>3</sup></code></li>
	<li><code>target</code> consists only of lowercase English letters.</li>
</ul>

class TrieNode(object):
    def __init__(self, val=None):
        self.val = val
        self.nx = {}
        self.is_end = False
    
    def __getitem__(self, key):
        return self.nx[key]
    
    def __setitem__(self, key, val):
        self.nx[key] = val
    
    def __contains__(self, key):
        return key in self.nx
        
class Trie(object):
    def __init__(self):
        self.head = TrieNode()
        
    def insert(self, word):
        curr = self.head

        for letter in word:
            if letter not in curr:
                curr[letter] = TrieNode(letter)
            curr = curr[letter]
        
        curr.is_end = True
    
    def prefix_match(self, word, start):
        res = []
        curr = self.head
        
        for i in range(start, len(word)):
            letter = word[i]
            
            if letter not in curr:
                break
            res.append(i)
            curr = curr[letter]
        return list(reversed(res))
    
from functools import lru_cache


def wb(s, words):
    tr = Trie()
    n = len(s)
    
    for word in words:
        tr.insert(word)
    
    @lru_cache(maxsize=None)
    def solve(idx):
        mini = -1
        for end_idx in tr.prefix_match(s, idx):
            if end_idx == n - 1:
                # we made the whole word
                return 1
            
            r = solve(end_idx + 1)
            if r != -1:
                r += 1
                mini = r if mini == -1 else min(r, mini)
        return mini
    
    return solve(0)


class Solution:
    def minValidStrings(self, words: List[str], target: str) -> int:
        return wb(target, words)
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