<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 Node:
    __slots__ = 'son','fail','len'
    def __init__(self,len=0):
        self.son = [None]*26
        self.fail = None
        self.len = len
class AC:
    def __init__(self):
        self.root = Node()
    def put(self,s:str)->None:
        cur = self.root
        for char in s:
            char = ord(char) - ord('a')
            if cur.son[char] is None:
                 cur.son[char] = Node(cur.len+1)
            cur = cur.son[char]
    def build_fail(self)->None:
        self.root.fail= self.root
        q = deque()
        for i, son in enumerate(self.root.son):
            if son is None:
                self.root.son[i]=self.root
            else:
                son.fail = self.root
                q.append(son)
        while q:
            cur=q.popleft()
            for i,son in enumerate(cur.son):
                if son is None:
                    cur.son[i]=cur.fail.son[i]
                    continue
                son.fail = cur.fail.son[i]
                q.append(son)
class Solution:
    def minValidStrings(self, words: List[str], target: str) -> int:
        ac = AC()
        for w in words:
            ac.put(w)
        ac.build_fail()
        n = len(target)
        f = [0]*(n+1)
        cur = root= ac.root
        for i,c in enumerate(target,1):
            cur = cur.son[ord(c)-ord('a')]
            if cur is root:
                return -1
            f[i]= f[i-cur.len]+1
        return f[n]
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