<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>

// can be done with brute force O(n ^ 2) 
#include<ext/pb_ds/assoc_container.hpp>
#include<ext/pb_ds/tree_policy.hpp>
using namespace __gnu_pbds;
template<class T> using oset = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
class Solution {
public:
    int getCount(vector<int> rating) {
        int n = rating.size();
        oset<pair<int, int>> los, ros;
        for(int i = 0; i < n; i++) {
            if(i == 0) los.insert({rating[i], i});
            else ros.insert({rating[i], i});
        }
        int ans = 0;
        for(int i = 1; i < n - 1; i++) {
            int val = rating[i];
            ros.erase({val, i});
            auto it = los.upper_bound({val, -1});
            int left, right;
            if(it == los.end()) left = los.size();
            else left = los.order_of_key(*it);
            auto itt = ros.upper_bound({val, -1});
            if(itt == ros.end()) right = 0;
            else right = ros.size() - ros.order_of_key(*itt);
            ans += left * right;
            los.insert({val, i});
        }
        return ans;
    }
    int numTeams(vector<int>& rating) {
        int type1 = getCount(rating);
        reverse(rating.begin(), rating.end());
        int type2 = getCount(rating);
        return type1 + type2;
    }
};
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