<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(target)
        target = "".join(sorted(list(target)))
        stickers2 = []
        MAX_MASK = (1 << N) - 1

        for s in stickers:
            v = defaultdict(int)
            for c in s:
                if c in target:
                    v[c] += 1
            k = 0
            for i, c in enumerate(target):
                if c in v:
                    k |= 1 << (N - i - 1)
            stickers2.append((k, v))

        @cache
        def dp(idx=0, mask=0):
            if mask == MAX_MASK:
                return 0

            if idx == len(stickers2):
                return math.inf

            k, v = stickers2[idx]
            v2 = defaultdict(int)
            if mask | k == mask:
                return dp(idx + 1, mask)

            new_mask = mask
            for i in range(N):
                if not mask & (1 << (N - i - 1)) and v2[target[i]] < v[target[i]]:
                    v2[target[i]] += 1
                    new_mask |= 1 << (N - i - 1)

            r = min(1 + dp(idx, new_mask), dp(idx + 1, mask))
            if r < math.inf:
                return r

            return r

        r = dp()
        return r if r != math.inf else -1

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