<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) {
        constexpr int invalid = -1;
        const int n_stickers = static_cast<int>(stickers.size());
        const int n_target = static_cast<int>(target.size());
        const int n_layouts = (1 << n_target);
        long letter_to_stickers[26] = {};
        int dp[32768];
        
        for (int i_sticker = 0; i_sticker < n_stickers; ++i_sticker)
            for (const char c : stickers[i_sticker])
                letter_to_stickers[c - 'a'] |= (1L << i_sticker);
        std::memset(dp, invalid, sizeof(dp));
        dp[0] = 0;
        for (int layout = 0; layout < n_layouts; ++layout)
        {
            if (dp[layout] == invalid)
                continue;
            int letter = -1;
            for (int i_target = 0; i_target < n_target; ++i_target)
            {
                if (!((layout >> i_target) & 1)
                &&  (letter_to_stickers[target[i_target] - 'a'] != 0))
                {
                    letter = target[i_target] - 'a';
                    break;
                }
            }
            if (letter == -1) break;
            for(int i_sticker = 0; i_sticker < n_stickers; ++i_sticker)
            {
                if (((letter_to_stickers[letter] >> i_sticker) & 1) == 0)
                    continue;
                int next_layout = layout;
                for (const char c_sticker : stickers[i_sticker])
                {
                    for (int i_target = 0; i_target < n_target; ++i_target)
                    {
                        if ((target[i_target] == c_sticker)
                        &&  (((next_layout >> i_target) & 1) == 0))
                        {
                            next_layout |= (1 << i_target);
                            break;
                        }
                    }
                }
                dp[next_layout] = (dp[next_layout] == invalid)
                                    ?(dp[layout] + 1)
                                    :std::min(dp[next_layout], dp[layout] + 1);
            }
        }
        return dp[n_layouts - 1];
    }
};
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