<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 {
public:
  int minStickers(vector<string>& stickers, string target) {
    vector<int> dp(1 << target.size(), -1);
    dp[0] = 0;

    int res = dfs((1 << target.size()) - 1, stickers, dp, target);
    return res > target.size() ? -1 : res;
  }

  int dfs(int mask, vector<string>& stickers, vector<int>& dp, string& target) {
    if (dp[mask] != -1) {
      return dp[mask];
    }
    dp[mask] = target.size() + 1;
    for (auto& sticker : stickers) {
      int left = mask;
      vector<int> cnt(26);
      for (char& c : sticker) {
        cnt[c - 'a']++;
      }
      for (int i = 0; i < target.size(); i++) {
        if ((mask >> i & 1) && cnt[target[i] - 'a'] > 0) {
          cnt[target[i] - 'a']--;
          left ^= 1 << i;
        }
      }
      if (left < mask) {
        dp[mask] = min(dp[mask], dfs(left, stickers, dp, target) + 1);
      }
    }
    return dp[mask];
  };
};

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