<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:
    void merge(int l, int m, int r,vector<pair<int,int>>&arr, vector<int>&count)
    {
        int n = r-l+1;
        vector<pair<int,int>> merged(n);
        int i=l,j=m+1,k=0;
        
        while(i<=m and j<=r)
        {
            if(arr[i].first<arr[j].first)
            {
                count[arr[i].second] += r-j+1;
                merged[k]=arr[i],i++,k++;
            }
                
            else
                merged[k]=arr[j],j++,k++;
        }
        
        while(i<=m)
            merged[k]=arr[i],i++,k++;
        
        while(j<=r)
            merged[k]=arr[j],j++,k++;
        
        for(int b=0;b<n;b++)
            arr[b+l]=merged[b];
    }

    void mergeSort(int l, int r, vector<pair<int,int>>&v, vector<int>&count)
    {
        if(l>=r)
            return;
        int mid = (l+r)/2;
        mergeSort(l,mid,v,count);
        mergeSort(mid+1,r,v,count);
        merge(l,mid,r,v,count);
    }

    vector<int> countLarger(int n, vector<int>&arr)
    {
        vector<int> count(n);
        vector<pair<int,int>> v(n);
        for(int i = 0;i<n;i++)
            v[i]={arr[i],i};
        mergeSort(0,n-1,v,count);
        return count;
    }

    int numTeams(vector<int>& rating) {
        int n = rating.size();
        vector<int> countGreaterRight = countLarger(n,rating);
     
        reverse(rating.begin(),rating.end());
        vector<int> countGreaterLeft = countLarger(n,rating);
        reverse(countGreaterLeft.begin(),countGreaterLeft.end());
        int ans = 0;
        for(int i=1;i<n-1;i++)
        {
            int right = countGreaterRight[i];
            int left = countGreaterLeft[i];
            ans+=(right)*(i-left);
            ans+=(left)*((n-i-1)-right);
        }
        return ans;
    }
};
20553