<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<int> res(n, 0);
        vector<pair<int, int>> indexedNums(n);

        for (int i = 0; i < n; ++i) {
            indexedNums[i] = {nums[i], i};
        }

        mergesort(indexedNums, res);
        return res;
    }

private:
    void mergesort(vector<pair<int, int>>& nums, vector<int>& res) {
        int n = nums.size();
        if (n <= 1)
            return;

        int mid = n / 2;
        vector<pair<int, int>> left(nums.begin(), nums.begin() + mid);
        vector<pair<int, int>> right(nums.begin() + mid, nums.end());

        mergesort(left, res);
        mergesort(right, res);

        merge(left, right, nums, res);
    }

    void merge(vector<pair<int, int>>& left, vector<pair<int, int>>& right,
               vector<pair<int, int>>& nums, vector<int>& res) {
        int i = 0, j = 0, k = 0;
        int leftCount = 0;

        while (i < left.size() && j < right.size()) {
            if (left[i].first <= right[j].first) {
                nums[k] = left[i];
                res[left[i].second] += leftCount;
                i++;
            } else {
                nums[k] = right[j];
                leftCount++;
                j++;
            }
            k++;
        }

        while (i < left.size()) {
            nums[k] = left[i];
            res[left[i].second] += leftCount;
            i++;
            k++;
        }

        while (j < right.size()) {
            nums[k] = right[j];
            j++;
            k++;
        }
    }
};
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