<p>There are <code>n</code> soldiers standing in a line. Each soldier is assigned a <strong>unique</strong> <code>rating</code> value.</p>

<p>You have to form a team of 3 soldiers amongst them under the following rules:</p>

<ul>
	<li>Choose 3 soldiers with index (<code>i</code>, <code>j</code>, <code>k</code>) with rating (<code>rating[i]</code>, <code>rating[j]</code>, <code>rating[k]</code>).</li>
	<li>A team is valid if: (<code>rating[i] &lt; rating[j] &lt; rating[k]</code>) or (<code>rating[i] &gt; rating[j] &gt; rating[k]</code>) where (<code>0 &lt;= i &lt; j &lt; k &lt; n</code>).</li>
</ul>

<p>Return the number of teams you can form given the conditions. (soldiers can be part of multiple teams).</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> rating = [2,5,3,4,1]
<strong>Output:</strong> 3
<strong>Explanation:</strong> We can form three teams given the conditions. (2,3,4), (5,4,1), (5,3,1). 
</pre>

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

<pre>
<strong>Input:</strong> rating = [2,1,3]
<strong>Output:</strong> 0
<strong>Explanation:</strong> We can&#39;t form any team given the conditions.
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> rating = [1,2,3,4]
<strong>Output:</strong> 4
</pre>

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

<ul>
	<li><code>n == rating.length</code></li>
	<li><code>3 &lt;= n &lt;= 1000</code></li>
	<li><code>1 &lt;= rating[i] &lt;= 10<sup>5</sup></code></li>
	<li>All the integers in <code>rating</code> are <strong>unique</strong>.</li>
</ul>

class Solution {
public:
  int call(vector<int> &rating)
    {
        int n = rating.size();
        set<int> s,p;
        for(int i = 0; i < n; i++) s.insert(rating[i]);
        
        int ans = 0;
        for(auto a : rating)
        {
            s.erase(s.find(a));
            // Count elements smaller than a in p
            int h = distance(p.begin(), p.lower_bound(a));
            // Count elements greater than a in s
            int k = distance(s.upper_bound(a), s.end());
            //cout<<h<<" "<<k<<endl;
            ans += (h*k);
            p.insert(a);
        }
        return ans;
    }
    
    int numTeams(vector<int>& rating) 
    {    
        int h = call(rating);
        reverse(rating.begin(), rating.end());
        cout<<endl;
        int k = call(rating);
        return h+k;
        
    }

#if 0
    int solve(vector<int>& rating)
    {
        int ans = 0;
        for (int i = 0; i < rating.size(); i++) 
        {
            int l = 0;
            for (int j = i - 1; j >= 0; j--) l += rating[i] > rating[j];
            for (int j = i + 1; j < rating.size(); j++) ans += rating[i] < rating[j] ? l : 0;
        }
        return ans;
    }
    
    int numTeams(vector<int>& rating) 
    {
        int h = solve(rating);
        reverse(begin(rating), end(rating));
        int k = solve(rating);
        return h + k;
    }
    #endif
};
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