<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[51][1LL<<15];

    int cal(int i, vector<vector<int>> &arr, string &target, int mask) {
        if (mask == (1 << target.size()) - 1)
            return 0;

        if (i >= arr.size())
            return 1e9;

         if(dp[i][mask]!=-1) return dp[i][mask];
        vector<int> mp = arr[i];
        int curr_mask = mask;
            bool f = 0;

        for (int j = 0; j < target.size(); j++) {
            if (curr_mask & (1 << j)) {}
            else {
                if (mp[target[j] - 'a'] > 0) {
                    f = 1;
                    curr_mask |= (1 << j);
                    mp[target[j] - 'a']--;
                }
            }
        }

      int t = 1e9;
        if(f)
        t = 1 + cal(i, arr, target, curr_mask);
        int nt = cal(i + 1, arr, target, mask);

        return dp[i][mask] = min(t, nt);
    }

    int minStickers(vector<string>& stickers, string target) {
        int n = stickers.size();
        vector<vector<int>> vec;
                memset(dp , -1 , sizeof(dp));

        for (auto ele : stickers) {
            vector<int> mp(26, 0);
            for (auto e : ele)
                mp[e - 'a']++;
            vec.push_back(mp);
        }
        int val = cal(0, vec, target, 0);
        return val>=1e9?-1:val;
    }
};

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