<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>4</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>4</sup></code></li>
	<li><code>target</code> consists only of lowercase English letters.</li>
</ul>

class ACNode(dict):
    def __init__(self):
        super().__init__()
        self.suffix_link = None
        self.depth = 0

class ACMatcher:
    def __init__(self, patterns):
        self.trie = ACNode()
        for pattern in patterns:
            spot = self.trie
            depth = 0
            for c in pattern:
                depth += 1
                if c not in spot:
                    spot[c] = ACNode()
                spot = spot[c]
                spot.depth = depth
        queue = deque([self.trie])
        while queue:
            parent = queue.popleft()
            for c in parent:
                suffix_link = parent.suffix_link
                spot = parent[c]
                while suffix_link is not None and c not in suffix_link:
                    suffix_link = suffix_link.suffix_link
                if suffix_link is None:
                    suffix_link = self.trie
                else:
                    suffix_link = suffix_link[c]
                spot.suffix_link = suffix_link
                queue.append(spot)

    def agree(self, text):
        spot = self.trie
        result = []
        for c in text:
            while spot is not None and c not in spot:
                spot = spot.suffix_link
            spot = spot[c] if spot else self.trie
            result.append(spot.depth)
        return result

class Solution:
    def minValidStrings(self, words: List[str], target: str) -> int:
        agree = ACMatcher(words).agree(target)
        i = len(target)-1
        count = 0
        while i >= 0 and agree[i]:
            i -= agree[i]
            count += 1
        return count if i == -1 else -1
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