<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:
    vector<int> dp;
    int f(int mask, vector<string>& s, string &target){
        if(mask == (1 << target.size()) - 1) return 0;

        if(dp[mask] != -1) return dp[mask];

        int ans = 1e9;
        for(auto &e:s){
            vector<int> freq(26, 0);
            for(auto &x:e) freq[x - 'a']++;
            int m = 0;
            for(int i = 0; i < target.size(); i++){
                if(!((1 << i) & mask)){
                    if(freq[target[i] - 'a']){
                        freq[target[i] - 'a']--;
                        m |= (1 << i);
                    }
                }
            }
            if(m) ans = min(ans, 1 + f(mask | m, s, target));
        }
        return dp[mask] = ans;
    }
    int minStickers(vector<string>& s, string target) {
        map<char, int> cnt;
        for(auto &e:s) for(auto &r:e) cnt[r]++, cnt[r] = min(cnt[r], 1);
        for(auto &e:target){
            if(!cnt[e]) return -1;
        }
        dp.assign((1 << target.size()) + 1, -1);
        int ans = f(0, s, target);
        return ans == 1e9 ? -1 : ans;
    }
};
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