<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) {
        vector<int> t_freq(26, 0);
        for (const auto &c : target) {
            t_freq[c-'a']++;
        }

        vector<vector<int>> s_freq(stickers.size(), vector<int>(26, 0));
        for (int i = 0; i<stickers.size(); i++) {
            for (const auto &c : stickers[i]) {
                s_freq[i][c-'a']++;
            }
        }

        unordered_map<string, int> seen;
        queue<vector<int>> next;
        int step = 1;
        next.push(t_freq);
        seen[target] = 1;
        
        while(next.size()) {
            int size = next.size();

            for (int i = 0; i<size; i++) {
                auto curr = next.front();
                next.pop();

                for (const auto &s : s_freq) {
                    auto copy = curr;
                    string remain = "";

                    for (int j = 0; j<26; j++) {
                        if (copy[j]-s[j] > 0) {
                            remain += string(copy[j]-s[j], 'a'+j);
                        }
                    }
                    
                    if (remain == "") {
                        return step;
                    }
                    if (seen[remain]) {
                        continue;
                    }
                    seen[remain] = 1;

                    vector<int> temp(26, 0);
                    for (const auto &c : remain) {
                        temp[c-'a']++;
                    }
                    next.push(temp);
                }
            }
            step++;
        }
        return -1;
    }
};
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