<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 __dfs(self, i: int, t: int, stickrs: list[str], target: str, dp: dict[tuple[int, int], int]) -> int | float: 
        if t == (1<<len(target))-1: return 0
        if i == len(stickrs): return float("inf")
        if (i, t) in dp: return dp[(i, t)]

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

        dp[(i, t)] = res
        return res

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

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

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