<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<vector<int>>& nums_copy, vector<vector<int>>& aux, int first, int mid, int last) {
        for (int i = first; i <= last; i++) {
            aux[i] = nums_copy[i];
        }

        int inv_count = 0;
        int i = first, j = mid + 1;

        for (int k = first; k <= last; k++) {
            if (i > mid) {
                nums_copy[k] = aux[j++];
            } else if (j > last) {
                nums_copy[k] = aux[i];
                nums_copy[k][2] += inv_count;
                i++;
            } else if (aux[i][0] > aux[j][0]) {
                nums_copy[k] = aux[j++];
                inv_count++;
            } else {
                nums_copy[k] = aux[i];
                nums_copy[k][2] += inv_count;
                i++;
            }
        }
    }

    void merge_sort(vector<vector<int>>& nums_copy, vector<vector<int>>& aux, int first, int last) {
        if (first >= last) return;

        int mid = (first + last) / 2;
        merge_sort(nums_copy, aux, first, mid);
        merge_sort(nums_copy, aux, mid + 1, last);
        merge(nums_copy, aux, first, mid, last);
    }

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

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

        merge_sort(nums_copy, aux, 0, n - 1);

        vector<int> result(n);
        for (int i = 0; i < n; i++) {
            result[nums_copy[i][1]] = nums_copy[i][2];
        }

        return result;
    }
};

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