<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:
    vector<int> countSmaller(vector<int>& nums) {
        int n = nums.size();
        vector<pair<int,int>> arr;
        for(int i = 0; i < n; i++){
            arr.push_back({nums[i], i});
        }
        vector<int> counts(n, 0);
        mergeSort(0, n-1, counts, arr);
        return counts;
    }
    void mergeSort(int l, int r, vector<int>& counts, vector<pair<int,int>>& arr){
        if(l >= r) return;

        int m = l + (r - l) / 2;

        mergeSort(l, m, counts, arr);
        mergeSort(m+1, r, counts, arr);

        int j = m + 1;
        for(int i = l; i <= m; i++){

            while(j <= r and arr[j].first < arr[i].first) j++;
            counts[arr[i].second] += j-m-1;
        }

        merge(l, m, r, arr);
    }
    void merge(int l, int m, int r, vector<pair<int,int>>& arr){

        vector<pair<int,int>> left, right;
        for(int i = l; i <= m; i++) left.push_back(arr[i]);
        for(int i = m+1; i <= r; i++) right.push_back(arr[i]);

        int i = 0, j = 0, k = l;
        while(i < left.size() and j < right.size()){
            if(left[i].first <= right[j].first){
                arr[k++] = left[i++];
            }
            else arr[k++] = right[j++];
        }

        while(i < left.size()) arr[k++] = left[i++];
        while(j < right.size()) arr[k++] = right[j++];
    }
};
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