<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 n;
    vector<string>s;
    string t;
    int dp[51][(1<<15)];
    int rec(int l,int mask){
        if(mask==(1<<n)-1)return 0;
        if(l==s.size())return 1e9;
        if(dp[l][mask]!=-1)return dp[l][mask];
        int ans=rec(l+1,mask);//skip this sticker
        vector<int>mp(26,0);
        for(int i=0;i<s[l].size();i++)mp[s[l][i]-'a']++;
        int flag=0;//check if we can insert the character
        for(int i=0;i<n;i++){
            if(mp[t[i]-'a']>0&&((mask>>(n-i-1))&1)==0){
                flag=1;
                break;
            }
        }
        if(flag){//we can insert this sticker
            int tmask=mask;
            for(int i=0;i<n;i++){
                if(mp[t[i]-'a']>0&&((tmask>>(n-i-1))&1)==0){
                    tmask|=(1<<(n-i-1));
                    mp[t[i]-'a']--;
                }
            }
            ans=min(ans,1+rec(l,tmask));
        }
        return dp[l][mask]=ans;
    }
    int minStickers(vector<string>& S, string tar) {
        s=S;
        t=tar;
        n=t.size();
        memset(dp,-1,sizeof(dp));
        return (rec(0,0)>=1e9?-1:rec(0,0));
    }
};
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