<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<vector<int>>entry;
    unordered_map<string,int>dp;
public:
    int minStickers(vector<string>& stickers, string target) {
        if(target.empty())
            return 0;
        if(stickers.empty())
            return -1;
        for(const auto&s:stickers){
            entry.push_back(getMask(s));
        }
        auto ret = dfs(target);
        return ret == INT_MAX?-1:ret;
    }
    
    int dfs(const string&target){
        if(target.empty())
            return 0;
        if(dp.count(target))
            return dp[target];
        auto mask = getMask(target);
        int ret = INT_MAX;
        for(const auto&s:entry){
            if(!s[target[0]-'a'])
                continue;
            auto cur = mask;
            int i;
            string nex;
            for(i = 0;i<26;i++){
                cur[i] -= min(cur[i], s[i]);
                nex += string(cur[i], 'a'+i);
            }
            if(nex.size() == target.size())
                continue;
            ret = min((long)ret, (long)1+dfs(nex));
        }
        return dp[target] = ret;
    }
    
    vector<int>getMask(const string& s){
        vector<int>ret(26, 0);
        for(const auto&c:s){
            ret[c-'a']++;
        }
        return ret;
    }
};
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