<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(object):
    def minStickers(self, stickers, target):
        m = len(stickers)
        mp = [[0]*26 for y in range(m)] 
        for i in range(m):
            for c in stickers[i]:
                mp[i][ord(c)-ord('a')] += 1    
        dp = {}
        dp[""] = 0
        
        def helper(dp, mp, target):
            if target in dp:
                return dp[target]
            n = len(mp)
            tar = [0]*26
            for c in target:
                tar[ord(c)-ord('a')] += 1   
            ans = inf
            for i in range(n):
                if mp[i][ord(target[0])-ord('a')] == 0:
                    continue
                s = ''
                for j in range(26):
                    if tar[j] > mp[i][j]:
                        s += chr(ord('a')+j)*(tar[j] - mp[i][j]) 
                tmp = helper(dp, mp, s)
                if (tmp != -1): 
                    ans = min(ans, 1+tmp)    
            dp[target] = -1 if ans == inf else ans
            return dp[target]
                
        return helper(dp, mp, target)
17016