<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 diffMatch(self, ele: str, target: str, parse: List[int]) -> List[int]:
        i = 0
        j = 0
        res = [len(target) + 1]*len(target)
        while j < len(target):
            if i == len(ele):
                i = parse[i - 1]
            if ele[i] == target[j]:
                if i != j:
                    res[j] = min(j - i - 1, res[j])
                else:
                    res[j] = -1
                i += 1
                j += 1
            else:
                if i != 0:
                    i = parse[i - 1]
                else:
                    res[j] = -2
                    j += 1
        # print(res)
        return res

    def match(self, ele: str) -> List[int]:
        res = [0] * len(ele)
        i = 0
        j = 1
        while j < len(ele):
            if ele[i] == ele[j]:
                res[j] = i + 1
                i += 1
                j += 1
            else:
                if i != 0:
                    i = res[i - 1]
                else:
                    j += 1
        # print(res)
        return res
        
        

    def minValidStrings(self, words: List[str], target: str) -> int:
        res = [len(target) + 1]*(len(target) + 1)
        res[0] = 0
        diffs = []
        for ele in words:
            match = self.match(ele)
            temp = self.diffMatch(ele, target, match)
            diffs.append(temp)
        # for temp in diffs:
        #     print(temp)
        # print("start")
        for i in range(len(target)):
            for temp in diffs:
                if temp[i] == -2:
                    continue
                if temp[i] == -1:
                    res[i + 1] = min(res[i + 1], 1 + res[0])    
                else:
                    res[i + 1] = min(res[i + 1], 1 + res[temp[i] + 1])
            # print(res)
        
        if res[-1] == len(target) + 1:
            return -1
        return res[-1]

        
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