<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> const& stickers, string const& target) {
        int tcount[26]{};
        vector<vector<int>> scount(stickers.size(), vector<int>(26));
        for (char c : target) ++tcount[c-'a'];
        for (int i{}; i < stickers.size(); ++i) {
            for (char c : stickers[i]) ++scount[i][c-'a'];
        }
        int ret{recurse(scount, tcount, 0)};
        return ret == INT_MAX ? -1 : ret;
    }
private:
    unordered_map<string, int> s;
    int recurse(vector<vector<int>> const& scount, int *tcount, int i) {
        if (i == scount.size()) {
            for (int j{}; j < 26; ++j) if (tcount[j]) return INT_MAX;
            return 0;
        }
        string mem;
        for (int j{}; j < 26; ++j) mem.append(tcount[j], 'a'+j);
        mem += to_string(i);
        if (auto it{s.find(mem)}; it != s.end()) return it->second;
        int ans{recurse(scount, tcount, i+1)};
        int max_use{};
        for (int j{}; j < 26; ++j) {
            if (tcount[j] and scount[i][j]) max_use = max(max_use, (tcount[j] + scount[i][j] - 1) / scount[i][j]);
        }
        if (max_use == 0) return s[mem] = ans;
        int new_tcount[26];
        copy(tcount, tcount + 26, new_tcount);
        for (int use{1}; use <= max_use; ++use) {
            for (int j{}; j < 26; ++j) new_tcount[j] =
                max(0, new_tcount[j] - scount[i][j]);
            int ret{recurse(scount, new_tcount, i+1)};
            if (ret < INT_MAX) ans = min(ans, use + ret);
        }
        return s[mem] = ans;
    }
};
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