<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 merge(vector<int>& ans, vector<pair<int,int>>& numsPair, int lo, int mid, int hi){
    vector<pair<int, int>> temp(hi-lo+1);
    int i = lo, j = mid+1, k = 0;
    while(i<=mid and j<=hi){
      if(numsPair[i].first <= numsPair[j].first) temp[k++] = numsPair[j++];
      else{
        ans[numsPair[i].second]+=hi-j+1;
        temp[k++] = numsPair[i++];
      }
    }
    while(i<=mid) temp[k++] = numsPair[i++];
    while(j<=hi) temp[k++] = numsPair[j++];
    for(int i=lo; i<=hi; i++) numsPair[i] = temp[i-lo];
  }
  void mergeSort(vector<int>& ans, vector<pair<int, int>>& numsPair, int lo, int hi){
    if(lo<hi){
      int mid = (lo+hi)/2;
      mergeSort(ans, numsPair, lo, mid);
      mergeSort(ans, numsPair, mid+1, hi);
      merge(ans, numsPair, lo, mid, hi);
    }
  }
  vector<int> countSmaller(vector<int>& nums) {
    int n = nums.size();
    vector<pair<int, int>> numsPair;
    for(int i=0;i<n;i++) numsPair.push_back({nums[i], i});
    vector<int> ans(n, 0);
    mergeSort(ans, numsPair, 0, n-1);
    return ans;      
  }
};
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