<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:
    void printBit(int val){
        for(int i = 14; i >=0 ; i--){
            if((val& (1<<i)) == 0)cout<<0;
            else cout<<1;
        }
        cout<<" ";
    }
    int calc(vector<string>& stickers, string target, int mask, int pos,vector<vector<int>>&dp){
        int allset = (1 << target.length())-1;

        if((mask ^ allset) == 0)return 0;
        if(pos >= stickers.size()){
            if((mask ^ allset) == 0)return 0;
            return 1e9;
        }

        if(dp[mask][pos] != -1)return dp[mask][pos];

        int take = 1e9;
        int newMask = mask;
        for(int i = 0; i < stickers[pos].length(); i++){
            for(int j = 0; j < target.length(); j++){
                if(stickers[pos][i] != target[j])continue;
                if((newMask & (1 << j)) != 0)continue;
                newMask |= (1 <<j);
                break;
            }
        }

        if(newMask != mask){
            take = 1 + calc(stickers,target,newMask,pos,dp);
        }
        int noTake = calc(stickers,target, mask,pos+1,dp);
        return  dp[mask][pos] = min(take,noTake);
    }

    int minStickers(vector<string>& stickers, string target) {
        vector<vector<int>> dp((1 << target.length()), vector<int> (stickers.size(),-1));
        int ans = calc(stickers,target,0,0,dp);
        if(ans >= 1e9)ans = -1;
        return ans;
    }
};
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