<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 Solution:
    def minValidStrings(self, words: List[str], target: str) -> int:
        def most_common_prefix(target, start = 0):
            in_list = words.copy()
            max_num = 0
            for word in words:
                i = 0
                while i < min(len(target) - start, len(word)):
                    if target[start + i] == word[i]:
                        i += 1
                    else:
                        break
                max_num = max(max_num, i)
            return max_num
        def update(target, start_list, pos):
            start_list.reverse()
            max_more = 0
            for start in start_list:
                a_slice = target[start:pos]
                for word in words:
                    more = 0
                    if len(word) > len(a_slice):
                        if word[:len(a_slice)] == a_slice:
                            while pos + more < len(target) and len(a_slice) + more < len(word):
                                if word[len(a_slice) + more] == target[pos + more]:
                                    more += 1
                                else:
                                    break
                    max_more = max(max_more, more)
                max_more = max(max_more, more)
            return max_more

        count = 0
        start = 0
        a_list = [0] * len(target)
        least_start = 0
        while start < len(target):
            #print('least_start =', least_start)
            #print('start =', start)
            num = most_common_prefix(target, start = start)
            #print('pre_num = ', num)
            count += 1
            if count > 1 and start != least_start:
                num += update(target, list(range(least_start, start)), start + num)
            #print('post_num = ', num)
            if num == 0:
                return -1
            elif start + num == len(target):
                return count
            else:
                for i in range(start, start + num):
                    a_list[i] = count
                
                least_start = start + 1
                start += num    
            
        return count
19438