<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:
    // Merge Sort
    vector<int> mergeSort(vector<int>& nums, vector<int>& counts, int l, int r)
    {
        if(l == r)
        {
            return {l};
        }
        int mid = (l + r) / 2;
        auto left = mergeSort(nums, counts, l, mid);
        auto right = mergeSort(nums, counts, mid+1, r);
        int i = 0, j = 0, r_size = right.size();
        vector<int> merged;
        while(i < left.size() && j < right.size())
        {
            if(nums[left[i]] > nums[right[j]])
            {
                merged.push_back(left[i]);
                counts[left[i]] += r_size - j;
                i++;
            }
            else
            {
                merged.push_back(right[j]);
                j++;
            }
        }
        while(i < left.size())
        {
            merged.push_back(left[i]);
            i++;
        }
        while(j < right.size())
        {
            merged.push_back(right[j]);
            j++;
        }
        return merged;
    }
    vector<int> countSmaller(vector<int>& nums) {
        vector<int> counts(nums.size(), 0);
        mergeSort(nums, counts, 0, nums.size() - 1);
        return counts;
    }
};
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