<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>

#include <ext/pb_ds/assoc_container.hpp> 
#include <ext/pb_ds/tree_policy.hpp> 
using namespace __gnu_pbds; 
#define ordered_set tree<int, null_type,less<int>, rb_tree_tag,tree_order_statistics_node_update>

class Solution {
    
public:
    vector<int>smallnum(vector<int>& a){
        ordered_set s;
        vector<int>ans;
        int n = a.size();
        ans.push_back(0);
        s.insert(a[n-1]);
        for(int i = n-2;i>=0;i--){
            ans.push_back(s.order_of_key(a[i]));
            s.insert(a[i]);
        }
        reverse(ans.begin(),ans.end());
        return ans;
    } 

    vector<int>smallnuml(vector<int>& a){
        ordered_set s;
        vector<int>ans;
        int n = a.size();
        ans.push_back(0);
        s.insert(a[0]);
        for(int i = 1;i<n;i++){
            ans.push_back(s.order_of_key(a[i]));
            s.insert(a[i]);
        }
        return ans;
    } 

    int numTeams(vector<int>& rating) {
        ios_base::sync_with_stdio(false);cin.tie(NULL);cout.tie(NULL);
        int n=rating.size();
        vector<int>sr=smallnum(rating);
        vector<int>sl=smallnuml(rating);
        int ans=0;
        for(int i=1;i<n-1;i++){
            // left bigger and right smaller
            ans+=((i-sl[i])*sr[i]);
        }
        for(int i=1;i<n-1;i++){
            // left smaller and right bigger
            int cnt1,cnt2;
            cnt1=sl[i];
            cnt2=(n-i-1-sr[i]);
            ans+=(sl[i]*(n-i-1-sr[i]));
        }
        return ans;
    }
};
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