<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 dp[50][(1 << 16)];
    int f(int idx, int mask, vector<vector<int>> &stk, string &targ){
        int t = targ.length();
        int n = stk.size();
        if(mask == (1 << t) - 1) return 0;
        if(idx == n) return 1e9;

        // cout<<mask<<endl;
        if(dp[idx][mask] != -1) return dp[idx][mask];

        int ans = f(idx+1, mask, stk, targ);

        int newMask = mask;
        // cout<<"enter "<<idx<<" "<<mask<<endl;
        vector<int> tmp = stk[idx];
        for(int j=0; j<t; ++j){
            if((mask >> j)&1) continue;
            // cout<<j<<" ";
            if(tmp[targ[j] - 'a'] > 0) {
                // cout<<j<<" ";
                tmp[targ[j] - 'a']--;
                newMask =  newMask | (1 << j);
            }
            
        }
        // cout<<endl;


        if(newMask != mask){
            // cout<<"string "<<idx<<" o " <<mask<<" n "<<newMask<<endl;

            ans = min(ans, 1 + f(idx, newMask, stk, targ));
        }

        return dp[idx][mask] = ans;
    }
    int minStickers(vector<string>& stickers, string target) {
        int n = stickers.size();
        vector<vector<int>> stk(n, vector<int>(26));
        for(int i=0; i<n; ++i){
            for(auto &c : stickers[i]){
                stk[i][c-'a']++;
            }
        }
        memset(dp, -1, sizeof(dp));
        int ans = f(0, 0, stk, target);
        return ans >= 1e9 ? -1 : ans;
    }
};
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