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

        table = list()
        for w in words:
            conc_w = w + "$" + target
            # print(conc_w)
            table.append(z_algo(conc_w)[(len(w)+1):])
        # for t in table:
        #     print(t)
        max_table = [0 for _ in target]
        for i in range(len(target)):
            max_table[i] = max([table[k][i] for k in range(len(words))])
        print(max_table)
        # res = [float("inf") for _ in target]
        # for i in range(len(target)):
        #     max_count = 0
        #     for t in table:
        #         if 

        # return 0

        steps = 0
        curr_end = 0
        farthest = 0
        n = len(max_table)
        for i, e in enumerate(max_table):
            farthest = max(farthest, i + e)
            if i == curr_end:
                steps += 1
                curr_end = farthest
                if curr_end >= n:
                    break
            # print(i, e, farthest, curr_end, steps)

        if curr_end < n:
            return -1
        return steps
22909