<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:
    import math
    def minStickers(self, stickers: List[str], target: str) -> int:
        cnt = []
        for s in stickers:
            cnt.append(Counter(s))
        
        ctarget = Counter(target)
        target = [v for k,v in ctarget.items()]
        cand = []
        for group in cnt:
            cur = [group[k] for k in ctarget.keys()]
            cand.append(cur)
        
        for char in range(len(target)):
            count = 0
            for curcand in cand:
                count += curcand[char]
            if count == 0:
                return -1
        @cache
        def dfs(i, cur_target):
            cur_target = [int(n) for n in cur_target.split('_')]
            if sum(cur_target) == 0:
                return 0
            if i == len(cand) and sum(cur_target) != 0:
                return -1
            else:
                cur_cand = cand[i]
                res = inf
                maxtime = 0
                for char in range(len(target)):
                    if cur_cand[char]!=0:
                        maxtime = max(maxtime, math.ceil(cur_target[char]/cur_cand[char]))
                for choose_time in range(maxtime + 1):
                    
                    copycat = copy.deepcopy(cur_target)
                    for char in range(len(target)):
                        copycat[char] = max(0, copycat[char] - choose_time * cur_cand[char])
                    copycat = "_".join([str(n) for n in copycat])
                    q = dfs(i + 1, copycat)
                    if q != -1:
                        res = min(res, q + choose_time)
                return res
        targeter = "_".join([str(n) for n in target])
        return dfs(0, targeter)
                        

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