<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>

#define ll long long

bool dp[61][66000][61];
ll xf;

vector<int> res;
ll mn;

void find(int pos, int mask, int cnt, vector<int> &arr, vector< vector<ll> > &st, int n)
{

    if(pos == st.size())
    {
        if(mask == xf)
        {
            if(arr.size() < mn)
            {
                mn = arr.size();
                res = arr;
                return;
            }

            return;
        }

        return;
    }

    if(dp[pos][mask][cnt] != false)
        return;

    dp[pos][mask][cnt] = true;

    find(pos+1, mask, cnt, arr, st, n);

    for(int i=0; i<st[pos].size(); ++i)
    {   
        ll curr = st[pos][i];
        mask = mask | (1<<curr);
    }       

    arr.push_back(pos);
    find(pos+1, mask, cnt + 1, arr, st, n);
    arr.pop_back();
}


class Solution {
public:
    vector<int> smallestSufficientTeam(vector<string>& rs, vector<vector<string>>& p) {

       
        for(int i=0; i<61; ++i)
        {
            for(int j=0; j<66000; ++j)
            {
                for(int k=0; k<61; ++k)
                {
                    dp[i][j][k] = false;
                }
            }
        }

        mn = 1e9;

        unordered_map<string, int > m;
        int val = 0;

        for(int i=0; i<rs.size(); ++i)
        {
            m[rs[i]] = val;
            ++val;
        }

        vector< vector<ll> > st;

        for(int i=0; i<p.size(); ++i)
        {   
            vector<ll> arr;

            for(int j=0; j<p[i].size(); ++j)
            {   
                ll curr = m[ p[i][j] ];
                arr.push_back(curr);
            }

            st.push_back(arr);
        }

        int mask = 0;
        int n = rs.size();

        xf = pow(2, n) - 1;
        vector<int> arr;

        find(0, 0, 0, arr, st, n);

        return res;
    }
};





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