<p>In a project, you have a list of required skills <code>req_skills</code>, and a list of people. The <code>i<sup>th</sup></code> person <code>people[i]</code> contains a list of skills that the person has.</p>

<p>Consider a sufficient team: a set of people such that for every required skill in <code>req_skills</code>, there is at least one person in the team who has that skill. We can represent these teams by the index of each person.</p>

<ul>
	<li>For example, <code>team = [0, 1, 3]</code> represents the people with skills <code>people[0]</code>, <code>people[1]</code>, and <code>people[3]</code>.</li>
</ul>

<p>Return <em>any sufficient team of the smallest possible size, represented by the index of each person</em>. You may return the answer in <strong>any order</strong>.</p>

<p>It is <strong>guaranteed</strong> an answer exists.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<pre><strong>Input:</strong> req_skills = ["java","nodejs","reactjs"], people = [["java"],["nodejs"],["nodejs","reactjs"]]
<strong>Output:</strong> [0,2]
</pre><p><strong class="example">Example 2:</strong></p>
<pre><strong>Input:</strong> req_skills = ["algorithms","math","java","reactjs","csharp","aws"], people = [["algorithms","math","java"],["algorithms","math","reactjs"],["java","csharp","aws"],["reactjs","csharp"],["csharp","math"],["aws","java"]]
<strong>Output:</strong> [1,2]
</pre>
<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= req_skills.length &lt;= 16</code></li>
	<li><code>1 &lt;= req_skills[i].length &lt;= 16</code></li>
	<li><code>req_skills[i]</code> consists of lowercase English letters.</li>
	<li>All the strings of <code>req_skills</code> are <strong>unique</strong>.</li>
	<li><code>1 &lt;= people.length &lt;= 60</code></li>
	<li><code>0 &lt;= people[i].length &lt;= 16</code></li>
	<li><code>1 &lt;= people[i][j].length &lt;= 16</code></li>
	<li><code>people[i][j]</code> consists of lowercase English letters.</li>
	<li>All the strings of <code>people[i]</code> are <strong>unique</strong>.</li>
	<li>Every skill in <code>people[i]</code> is a skill in <code>req_skills</code>.</li>
	<li>It is guaranteed a sufficient team exists.</li>
</ul>

class Solution:
    def smallestSufficientTeam(self, req_skills: List[str], people: List[List[str]]) -> List[int]:
        skill_bits = {s:1<<i for (i, s) in enumerate(req_skills)}
        skill_mask = (1 << len(req_skills)) - 1

        #print(skill_mask)

        people_hash = {i: 0 for i in range(len(people))}
        for i in range(len(people)):
            p = people[i]
            bits = 0
            for s in p:
                bits |= skill_bits[s]
            
            people_hash[i] = bits
        
        dp = {}
        
        def calc(pi, cbits):
            nonlocal dp
            nonlocal people_hash
            nonlocal skill_mask
            nonlocal people

            if pi >= len(people):
                return (1 << 65) - 1
            
            if cbits == skill_mask:
                return 0

            if (pi, cbits) in dp:
                return dp[(pi, cbits)]
            
            if (cbits | people_hash[pi]) == skill_mask:
                dp[(pi, cbits)] = 1 << pi
                return 1 << pi
            
            ps = calc(pi + 1, cbits)
            ns = (1 << 65) - 1

            if people_hash[pi] != 0 and cbits | people_hash[pi] != cbits:
                ns = calc(pi + 1, cbits | people_hash[pi])
                if ns != (1 << 65) - 1:
                    ns |= 1 << pi
            
            if ps.bit_count() < ns.bit_count():
                res = ps
            else:
                res = ns
            
            dp[(pi, cbits)] = res
            return res

            
        
        resb = calc(0, 0)

        res = []
        for i in range(len(people)):
            if 1 << i & resb != 0:
                res.append(i)
        
        return res
65907