<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 defaultdict, deque
from typing import List

class Solution:
    def minStickers(self, stickers: List[str], target: str) -> int:
        # Count the frequency of characters in the target
        target_count = defaultdict(int)
        for ch in target:
            target_count[ch] += 1
        
        # Create a list of sticker character counts
        sticker_counts = []
        for sticker in stickers:
            count = defaultdict(int)
            for ch in sticker:
                count[ch] += 1
            sticker_counts.append(count)
        
        # BFS initialization
        queue = deque([(target_count, 0)])  # (remaining target, number of stickers used)
        visited = set()
        visited.add(tuple(sorted(target_count.items())))  # Add the initial target state to visited
        
        # BFS loop
        while queue:
            current_target, steps = queue.popleft()
            
            # Check if the current target is fully covered (i.e., all character counts are 0)
            if all(value == 0 for value in current_target.values()):
                return steps
            
            # Try applying each sticker
            for sticker in sticker_counts:
                new_target = current_target.copy()
                for ch, count in sticker.items():
                    if ch in new_target:
                        new_target[ch] = max(0, new_target[ch] - count)  # Reduce target characters
                
                new_target_tuple = tuple(sorted(new_target.items()))
                
                # Only add to the queue if this state hasn't been visited
                if new_target_tuple not in visited:
                    visited.add(new_target_tuple)
                    queue.append((new_target, steps + 1))
        
        # If no solution found, return -1
        return -1

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