<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 go(int mask, const string& target, const vector<string>& stickers, std::vector<int>& dp, const int& sz) const {
        if(mask == (1 << sz) - 1)   return 0;
        
        if(dp[mask] != -1)  return dp[mask];
        
        std::vector<int> can[26];
        for(int i = 0; i < target.length(); i ++) {
            if(mask & (1<<i))   continue;
            can[target[i] - 'a'].push_back(i);
        }
        int ans = 20;
        for(auto it : stickers) {
            std::vector<int> f(26, 0);
            for(auto ch : it)  f[ch - 'a'] ++;
            
            int nmask = mask;
            for(int i = 0; i < 26; i ++) {
                if(!f[i])   continue;
                int sz = can[i].size();
                for(int j = 0; j < min(f[i], sz); j ++)
                    nmask |= (1 << (can[i][j]));
            }
            if(nmask != mask)
                ans = min(ans, 1 + go(nmask, target, stickers, dp, sz));
        }
        return dp[mask] = ans;
    }
    int minStickers(vector<string>& stickers, string target) {
        const int sz = target.size();
        std::vector<int> dp(1<<sz, -1);
        
        const int ans = go(0, target, stickers, dp, sz);
        return (ans >= 20 ? -1 : ans);
    }
};
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