<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:
    @lru_cache(None)
    def __dfs(self, i: int, t: int) -> int | float: 
        if t == (1<<len(self.target))-1: return 0
        if i == len(self.stickrs): return float("inf")

        res = self.__dfs(i+1, t)
        newt = t
        for s in self.stickrs[i]:
            for j, c in enumerate(self.target):
                if newt & (1<<j): continue
                if c == s:
                    newt |= (1<<j)
                    break
        if newt != t: res = min(res, 1+self.__dfs(i, newt))

        return res

    def minStickers(self, stickers: List[str], target: str) -> int:
        self.stickrs: list[str] = list()
        targetSet: set[str] = set(target)
        self.target: str = target

        t_count = collections.Counter(target)
        A = [collections.Counter(sticker) & t_count
             for sticker in stickers]

        for i in range(len(A) - 1, -1, -1):
            if any(A[i] == A[i] & A[j] for j in range(len(A)) if i != j):
                A.pop(i)

        self.stickrs = ["".join(s_count.elements()) for s_count in A]

        # for sticker in stickers:
        #     s = ""
        #     for c in sticker:
        #         if c in targetSet:
        #             s = f"{s}{c}"
        #     self.stickrs.append(s)
        # self.stickrs = list(set(self.stickrs))

        res = self.__dfs(0, 0)
        return res if res != float("inf") else -1
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