<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:

    ''' 
    
    t:2
    h:2
    e:1
    a:1

    w:1
    i:1
    t:1
    h:1

    '''

    def minStickers(self, stickers: List[str], target: str) -> int:
        target = Counter(target)
        stickers = [Counter(x) for x in stickers]

        letters = set()
        for sticker in stickers:
            for l in sticker:
                letters.add(l)

        for k in target.keys():
            if k not in letters:
                return -1

        output = [math.inf]
        seen = {}
        total = 0

        for _, count in target.items():
            total += count

        def backtrack(curr, total, count):
            if total == 0:
                output[0] = min(count, output[0])
                return
            
            for sticker in stickers:
                removed, amount = spell(sticker, curr)
                key = tuple(curr.items())
                if key not in seen or seen[key] > count:
                    seen[key] = count
                    backtrack(curr, total - amount, count + 1)
                for l, c in removed.items():
                    curr[l] += c

        def spell(sticker, curr):
            removed = {}
            amount = 0
            for l, count in sticker.items():
                if curr[l] == 0:
                    continue
                to_rem = min(curr[l], count)
                removed[l] = to_rem
                amount += to_rem
                curr[l] -= to_rem

            return (removed, amount)

        backtrack(target, total, 0)

        return output[0]     
26886