<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>

from collections import Counter
class Solution:
    def minStickers(self, stickers: List[str], target: str) -> int:
        tot=[]
        for s in stickers:
            tot.append(Counter(s))
        hs={}
        def rec(i,targ):
            if (i,targ) in hs:
                return hs[(i,targ)]
            if targ=="":
                hs[(i,targ)]=0
                return 0
            if i>=len(stickers):
                return float(inf)
            best=float(inf)
            high=0
            counts=Counter(targ)
            for x in tot[i]:
                high=max(counts[x],high)
            best=min(rec(i+1,targ),best)
            for j in range(1,high+1):
                newt=""
                for x in counts:
                    newt+=max(counts[x]-j*tot[i][x],0)*x
                best=min(rec(i+1,"".join(sorted(newt)))+j,best)
            hs[(i,targ)]=best
            return best
        sorted(target)
        x= rec(0,"".join(sorted(target)))
        print(hs)
        if x==float(inf):
            return -1
        return x





                    

        
        

        
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