<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:
        stk, t, res = [], collections.defaultdict(int), [100]
        for s in stickers:
            cur = collections.defaultdict(int)
            for c in s:
                if c in target:
                    cur[c] += 1
            if cur:
                stk.append(cur)
        toDel = set()
        for i, m in enumerate(stk):
            keep = True
            for n in stk:
                if n == m:
                    continue
                dominated = True
                for k, v in m.items():
                    if k not in n or n[k] < v:
                        dominated = False
                        break
                if dominated:
                    keep = False
                    break
            if not keep:
                toDel.add(i)
        stk = [m for i, m in enumerate(stk) if i not in toDel]
        for c in target:
            t[c] += 1
        self.dfs(stk, t, res, 0, 0)
        return res[0] if res[0] != 100 else -1

    def dfs(self, stk, target, res, num, index):
        if index == len(stk):
            if sum(target.values()) == 0:
                res[0] = min(res[0], num)
            return
        if num > res[0]:
            return
        helpful, curStk = False, stk[index]
        for k, v in target.items():
            if v > 0 and k in curStk:
                helpful = True
                break
        if helpful:
            used = {}
            for k, v in curStk.items():
                if k in target and target[k] > 0:
                    consumption = min(v, target[k])
                    used[k] = consumption
                    target[k] -= consumption
            self.dfs(stk, target, res, num + 1, index)
            for k, v in used.items():
                target[k] += v
        self.dfs(stk, target, res, num, index + 1)

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