<p>We are given <code>n</code> different types of <code>stickers</code>. Each sticker has a lowercase English word on it.</p>

<p>You would like to spell out the given string <code>target</code> by cutting individual letters from your collection of stickers and rearranging them. You can use each sticker more than once if you want, and you have infinite quantities of each sticker.</p>

<p>Return <em>the minimum number of stickers that you need to spell out </em><code>target</code>. If the task is impossible, return <code>-1</code>.</p>

<p><strong>Note:</strong> In all test cases, all words were chosen randomly from the <code>1000</code> most common US English words, and <code>target</code> was chosen as a concatenation of two random words.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> stickers = [&quot;with&quot;,&quot;example&quot;,&quot;science&quot;], target = &quot;thehat&quot;
<strong>Output:</strong> 3
<strong>Explanation:</strong>
We can use 2 &quot;with&quot; stickers, and 1 &quot;example&quot; sticker.
After cutting and rearrange the letters of those stickers, we can form the target &quot;thehat&quot;.
Also, this is the minimum number of stickers necessary to form the target string.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> stickers = [&quot;notice&quot;,&quot;possible&quot;], target = &quot;basicbasic&quot;
<strong>Output:</strong> -1
Explanation:
We cannot form the target &quot;basicbasic&quot; from cutting letters from the given stickers.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>n == stickers.length</code></li>
	<li><code>1 &lt;= n &lt;= 50</code></li>
	<li><code>1 &lt;= stickers[i].length &lt;= 10</code></li>
	<li><code>1 &lt;= target.length &lt;= 15</code></li>
	<li><code>stickers[i]</code> and <code>target</code> consist of lowercase English letters.</li>
</ul>

class Solution:
    def minStickers(self, stickers: List[str], target: str) -> int:
        n = len(stickers)
        s = [[0] * 26 for _ in range(n)]
        td = [0] * 26

        for i, v in enumerate(stickers):
            for c in v:
                s[i][ord(c) - ord('a')] += 1
        
        for c in target:
            td[ord(c) - ord('a')] += 1

        @lru_cache(maxsize=None)
        def recur(tt, rem):
            t = list(tt)
            if rem == 0:
                return 0
            ans = float('inf')
            for w in s:
                count = 0
                hold = [0] * 26
                for i in range(26):
                    if t[i] and w[i]:
                        hold[i] = min(t[i], w[i])
                        t[i] -= hold[i]
                        count += hold[i]
                if count:
                    ans = min(ans, 1 + recur(tuple(t), rem - count))
                    for i in range(26):
                        t[i] += hold[i]

            return ans

        fans = recur(tuple(td), len(target))
        return fans if fans != float('inf') else -1
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