<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>

#define FOR(i, n) for(int i=0; i<n; i++)
#define IFOR(i, a, n) for(int i=a; i<n; i++)

class Solution {
public:
    int rec(int n, vector<vector<int>> &smp, int target_mask, string &target, int ind, int mask, vector<vector<int>> &memo) {
        if(ind >= n) {
            if(mask == target_mask) return 0;
            else return -1;
        }
        if(mask == target_mask) return 0;

        if(memo[ind][mask] != -10) return memo[ind][mask];

        int nt = rec(n, smp, target_mask, target, ind+1, mask, memo);
        int tsz = target.size();
        int cnt = 0;
        vector<int> mp = smp[ind];
        int nm = mask;
        FOR(i, tsz) {
            if((mask&(1<<i)) == 0) {
                if(mp[target[i]-'a'] > 0) {
                    mp[target[i]-'a']--;
                    cnt++;
                    nm = nm|(1<<i);
                }
            }
        }

        if(cnt > 0) {
            int idx = rec(n, smp, target_mask, target, ind, nm, memo);
            if(idx != -1) {
                if(nt == -1) nt = 1+idx;
                else nt = min(nt, 1+idx);
            }
        }
        memo[ind][mask] = nt;
        return nt;
    }

    int minStickers(vector<string>& stickers, string target) {
        int n = stickers.size();
        vector<vector<int>> smp(n, vector<int>(26, 0));
        FOR(i, n) {
            for(auto it: stickers[i]) smp[i][it-'a']++;
        }

        vector<vector<int>> msmp;
        FOR(i, n) {
            for(auto it: target) {
                if(smp[i][it-'a'] > 0) {
                    msmp.push_back(smp[i]);
                    break;
                }
            }
        }

        int target_mask = 0;
        FOR(i, target.size()) target_mask += pow(2, i);

        vector<vector<int>> memo(n+2, vector<int>(target_mask+2, -10));
        int ans = rec(msmp.size(), msmp, target_mask, target, 0, 0, memo);
        return ans;
    }
};
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