With respect to a given <code>puzzle</code> string, a <code>word</code> is <em>valid</em> if both the following conditions are satisfied:
<ul>
	<li><code>word</code> contains the first letter of <code>puzzle</code>.</li>
	<li>For each letter in <code>word</code>, that letter is in <code>puzzle</code>.
	<ul>
		<li>For example, if the puzzle is <code>&quot;abcdefg&quot;</code>, then valid words are <code>&quot;faced&quot;</code>, <code>&quot;cabbage&quot;</code>, and <code>&quot;baggage&quot;</code>, while</li>
		<li>invalid words are <code>&quot;beefed&quot;</code> (does not include <code>&#39;a&#39;</code>) and <code>&quot;based&quot;</code> (includes <code>&#39;s&#39;</code> which is not in the puzzle).</li>
	</ul>
	</li>
</ul>
Return <em>an array </em><code>answer</code><em>, where </em><code>answer[i]</code><em> is the number of words in the given word list </em><code>words</code><em> that is valid with respect to the puzzle </em><code>puzzles[i]</code>.
<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> words = [&quot;aaaa&quot;,&quot;asas&quot;,&quot;able&quot;,&quot;ability&quot;,&quot;actt&quot;,&quot;actor&quot;,&quot;access&quot;], puzzles = [&quot;aboveyz&quot;,&quot;abrodyz&quot;,&quot;abslute&quot;,&quot;absoryz&quot;,&quot;actresz&quot;,&quot;gaswxyz&quot;]
<strong>Output:</strong> [1,1,3,2,4,0]
<strong>Explanation:</strong> 
1 valid word for &quot;aboveyz&quot; : &quot;aaaa&quot; 
1 valid word for &quot;abrodyz&quot; : &quot;aaaa&quot;
3 valid words for &quot;abslute&quot; : &quot;aaaa&quot;, &quot;asas&quot;, &quot;able&quot;
2 valid words for &quot;absoryz&quot; : &quot;aaaa&quot;, &quot;asas&quot;
4 valid words for &quot;actresz&quot; : &quot;aaaa&quot;, &quot;asas&quot;, &quot;actt&quot;, &quot;access&quot;
There are no valid words for &quot;gaswxyz&quot; cause none of the words in the list contains letter &#39;g&#39;.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> words = [&quot;apple&quot;,&quot;pleas&quot;,&quot;please&quot;], puzzles = [&quot;aelwxyz&quot;,&quot;aelpxyz&quot;,&quot;aelpsxy&quot;,&quot;saelpxy&quot;,&quot;xaelpsy&quot;]
<strong>Output:</strong> [0,1,3,2,0]
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= words.length &lt;= 10<sup>5</sup></code></li>
	<li><code>4 &lt;= words[i].length &lt;= 50</code></li>
	<li><code>1 &lt;= puzzles.length &lt;= 10<sup>4</sup></code></li>
	<li><code>puzzles[i].length == 7</code></li>
	<li><code>words[i]</code> and <code>puzzles[i]</code> consist of lowercase English letters.</li>
	<li>Each <code>puzzles[i] </code>does not contain repeated characters.</li>
</ul>

class Solution {
	int bits(string& s){
		int val = 0;
		for(auto c : s) val |= 1<<(c-'a');
		return val;
	}

	int count(int x){
		int cnt = 0;
		while(x){
			x &= x-1;
			cnt++;
		}
		return cnt;
	}

	int pack(int x, int i){
		int val = 0;
		while(i){
			int t = -x&x;
			if(i&1) val |= t;
			x -= t;
			i >>= 1;
		}
		return val;
	}
public:
	vector<int> findNumOfValidWords(vector<string>& words, vector<string>& puzzles) {
		unordered_map<int, int> hash;
		for(string& s : words){
			int val = bits(s);
			if (count(val) > 7) continue;
			if (hash.find(val) != hash.end()) hash[val]++;
			else hash[val]=1;
		}

		vector<int> res;
		for(string& s : puzzles){
			int first = 1<<(s[0]-'a');
			int target = bits(s)&~first;
			int cnt = 0;
			for(int i=0; i<(1<<6); i++){
				int val = pack(target, i) | first;
				auto it = hash.find(val);
				if(it != hash.end()) cnt += it->second;
			}

			res.push_back(cnt);
		}
		return res;
	}
};
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