<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(vector <pair <int,int>> &nums,int start,int mid,int end,vector <int> &greater_left,vector <int> &greater_right,vector <int> &smaller_left,vector <int> &smaller_right)
    {
        int i=start,j=mid+1;
        
        vector <pair <int,int>> temp;
        
        while(i<=mid && j<=end)
        {
            if(nums[i].first < nums[j].first)
            {
                greater_right[nums[i].second]+=end-j+1;
                int t=j;
                while(t<=end)
                {
                smaller_left[nums[t].second]=smaller_left[nums[t].second]+1;
                t++;
                }
                temp.push_back(nums[i++]);

            }
            else
            {
                
                
                
                if(nums[i].first!=nums[j].first)
                {
                    
                    int t=i;
                    while(t<=mid)
                    {
                    smaller_right[nums[t].second]++;
                    t++;
                    }
                    greater_left[nums[j].second]+=mid-i+1;
                }
                
                
                temp.push_back(nums[j++]);
            }
        }
        
        
        
        while(i<=mid)
        {
            //smaller_right[i]+=end-mid;
            temp.push_back(nums[i++]);
        }
        
        
        while(j<=end)
        {
            //smaller_left[j]+=mid-start+1;
            temp.push_back(nums[j++]);
        
        }
        
        
        
        
        
        for(int index=start;index<=end;index++)
        {
            nums[index]=temp[index-start];
        }
      
    }
    void mergeSort(vector <pair <int,int>> &nums,int start,int end,vector <int> &greater_left,vector <int> &greater_right,vector <int> &smaller_left,vector <int> &smaller_right)
    {
        if(start>=end) return;
        int mid=start+(end-start)/2;
        
        mergeSort(nums,start,mid,greater_left,greater_right,smaller_left,smaller_right);
        
        mergeSort(nums,mid+1,end,greater_left,greater_right,smaller_left,smaller_right);
        
        merge(nums,start,mid,end,greater_left,greater_right,smaller_left,smaller_right);
    }
    int numTeams(vector<int>& rating) {
        
        
        int size=rating.size();
        
        
        vector <pair <int,int>> nums;
        
        
        
        for(int i=0;i<size;i++)
        {
            nums.push_back({rating[i],i});
        }
        
        
        int ans=0;
        
        vector <int> greater_left(size);
        vector <int> greater_right(size);
        vector <int> smaller_left(size);
        
        vector <int> smaller_right(size);
        mergeSort(nums,0,size-1,greater_left,greater_right,smaller_left,smaller_right);
        
        
        for(int i=0;i<size;i++)
        {
            ans+=(smaller_left[i]*greater_right[i])+(greater_left[i]*smaller_right[i]);
        }
        return ans;
        
        
        
        
    }
};
22670