<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>

import heapq

# https://tjkendev.github.io/procon-library/python/string/z-algorithm.html
def z_algo(S):
    N = len(S)
    A = [0]*N
    i = 1; j = 0
    A[0] = l = len(S)
    while i < l:
        while i+j < l and S[j] == S[i+j]:
            j += 1
        if not j:
            i += 1
            continue
        A[i] = j
        k = 1
        while l-i > k < j - A[k]:
            A[i+k] = A[k]
            k += 1
        i += k; j -= k
    return A

INF = 10**9
class Solution:
    def minValidStrings(self, words: List[str], target: str) -> int:
        n = len(target)
        m = len(words)
        tmp = []
        for i in range(m):
            tmp.append(z_algo(words[i]+target))
        #print(tmp)
        dp = [INF for _ in range(n)]
        deq = [(0, 0)]
        while deq:
            d, i = heapq.heappop(deq)
            i = -i
            k = 0
            for j in range(m):
                k = max(k, min(len(words[j]), tmp[j][len(words[j])+i]))
            for kk in range(k):
                if dp[i+kk]>d+1:
                    dp[i+kk] = d+1
                    if i+kk==n-1:
                        return dp[i+kk]
                    heapq.heappush(deq, (dp[i+kk], -(i+kk+1)))
            #print(dp)

        return -1 if dp[n-1]==INF else dp[n-1]
36105