<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) {
        int n=stickers.size();
        int m = target.length();
        int N = (1<<m);
        int dp[N];
        for(int i=1;i<N;i++)
            dp[i]=-1;
        dp[0]=0;
        for(int i=0;i<N;i++){
            if(dp[i]==-1) continue;
            set<int> pos[26];
            
            for(int j=0;j<n;j++){
                for(int j=0;j<m;j++){
                    if((i&(1<<j))==0){
                        pos[target[j]-'a'].insert(j);
                    }
                }
                int mask=i;
                for(int k=0;k<stickers[j].length();k++){
                    int c = stickers[j][k]-'a';
                    if(!pos[c].empty()){
                        int idx = *pos[c].begin();
                        pos[c].erase(pos[c].begin());
                        mask+=((1<<idx));
                    }
                }
                if((dp[mask]==-1 || dp[mask]>dp[i]+1))
                    dp[mask]=1 + dp[i];
            }
        }
        return dp[N-1];
    }
};
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