<p>Given an integer array <code>nums</code>, return<em> an integer array </em><code>counts</code><em> where </em><code>counts[i]</code><em> is the number of smaller elements to the right of </em><code>nums[i]</code>.</p>

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

<pre>
<strong>Input:</strong> nums = [5,2,6,1]
<strong>Output:</strong> [2,1,1,0]
<strong>Explanation:</strong>
To the right of 5 there are <b>2</b> smaller elements (2 and 1).
To the right of 2 there is only <b>1</b> smaller element (1).
To the right of 6 there is <b>1</b> smaller element (1).
To the right of 1 there is <b>0</b> smaller element.
</pre>

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

<pre>
<strong>Input:</strong> nums = [-1]
<strong>Output:</strong> [0]
</pre>

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

<pre>
<strong>Input:</strong> nums = [-1,-1]
<strong>Output:</strong> [0,0]
</pre>

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

<ul>
	<li><code>1 &lt;= nums.length &lt;= 10<sup>5</sup></code></li>
	<li><code>-10<sup>4</sup> &lt;= nums[i] &lt;= 10<sup>4</sup></code></li>
</ul>

class Solution {
public:
    void mergeSort(vector < vector <int> > &cp,vector < vector <int> > &aux, int start, int mid, int end)
    {
        for(int i = start; i <= end; i++)
        {
            aux[i] = cp[i];
        }

        int swap = 0;

        int i = start;
        int j = mid + 1;
        int index = start;
        while(index <= end)
        {
            if(i > mid)
            {
                cp[index++] = aux[j++];
            }
            else if(j > end)
            {
                cp[index] = aux[i++];
                cp[index++][2] += swap;
            }
            else if(aux[i][0] > aux[j][0])
            {
                swap++;
                cp[index++] = aux[j++];
            }
            else
            {
                cp[index] = aux[i++];
                cp[index++][2] += swap;
            }
        }
        
    }

    void mergeRec(vector < vector <int> > &cp,vector < vector <int> > &aux, int start, int end)
    {
        if(start >= end ) return;

        int mid = (start + end) / 2;
        mergeRec(cp, aux, start, mid);
        mergeRec(cp, aux, mid + 1, end);

        mergeSort(cp, aux, start, mid, end);
        return;
    }

    vector<int> countSmaller(vector<int>& nums) {
        int n = nums.size();
        vector < vector <int> > cp (n, vector <int> (3));
        vector < vector <int> > aux (n, vector <int> (3));

        for(int i = 0; i < n; i++)
        {
            cp[i] = {nums[i], i, 0};
            aux[i] = {nums[i], i, 0};
        }
        mergeRec(cp, aux, 0, n-1);

        vector <int> cpp(n);

        for(int i = 0; i < n; i++)
        {
            cpp[cp[i][1]] = cp[i][2];
        }
        return cpp;
    }
};
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