<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 {
public:
    typedef long long ll;
    unordered_map<string,ll>mp;
    ll dp[65536][60];
    ll maxi=LONG_LONG_MAX;
    ll solve(ll val,ll i,vector<vector<string>>&nums){
        if(i>=nums.size()){
            if(val==0)return 0;
            return maxi;
        }
        if(dp[val][i]!=-1)return dp[val][i];
        ll ans=maxi,n=val;
        for(auto&j:nums[i]){
            if((n>>mp[j])&1)n^=(1<<(mp[j]));
        }
        ll it=solve(n,i+1,nums);
        if(it!=maxi){
            it|=(1ll<<i);
            if(__builtin_popcountll(it)<__builtin_popcountll(ans))ans=it;
        }
        it=solve(val,i+1,nums);
        if(it!=maxi && __builtin_popcountll(it)<__builtin_popcountll(ans))ans=it;
        return dp[val][i]=ans;
    } 
    vector<int> smallestSufficientTeam(vector<string>&skills, vector<vector<string>>& people){
        memset(dp,-1,sizeof(dp));
        for(int i=0;i<skills.size();i++)mp[skills[i]]=i;
        ll val=pow(2,skills.size())-1;
        ll res=solve(val,0,people);
        vector<int>ans;
        for(ll i=0;i<64;i++){
            if((res>>i)&1)ans.push_back(i);
        }
        return ans;
    }
};
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