<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 {
    vector<int> str_to_tokens(string s) {
        vector<int> res(26, 0);
        for (char c: s) res[c-'a']++;
        return res;
    }
public:
    int minStickers(vector<string>& stickers, string target) {
        vector<int> tokens_target = str_to_tokens(target);
        vector<vector<int>> tokens_stickers;
        vector<int> tokens_sum(26, 0);
        for (string sticker: stickers) {
            tokens_stickers.push_back(str_to_tokens(sticker));
            for (int i = 0; i < 26; i++) {
                tokens_sum[i] += tokens_stickers.back()[i];
            }
        }
        for (int i = 0; i < 26; i++) {
            if ((tokens_sum[i]) == 0 && (tokens_target[i]) > 0) {
                return -1;
            }
        }
        queue<vector<int>> q;
        q.push(vector<int>(26, 0));
        set<vector<int>> visited;
        visited.insert(vector<int>(26, 0));
        int res = 0;
        while (!q.empty() && res < 15) {
            res++;
            int n_this_layer = q.size(); 
            //cout << n_this_layer << endl;
            for (int i_this_layer = 0; i_this_layer < n_this_layer; i_this_layer++) {
                vector<int> now = q.front();
                q.pop();
                for (vector<int>& tokens_sticker: tokens_stickers) {
                    vector<int> next(now);
                    bool is_target = true;
                    for (int i = 0; i < 26; i++) {
                        next[i] += tokens_sticker[i];
                        next[i] = min(next[i], tokens_target[i]);
                        is_target = is_target && (next[i] == tokens_target[i]);
                    }
                    if (is_target) return res;
                    if (visited.find(next) == visited.end()) {
                        visited.insert(next);
                        q.push(next);
                    }
                }
            }
        }
        return 0;
    }
};
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