<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) {
        vector<int> result(nums.size());
        vector<int> indexes(nums.size());
        iota(begin(indexes), end(indexes), 0);
        sort(result, nums, indexes, 0, nums.size() - 1);
        return result;
    }

    void sort(vector<int>& result, vector<int>& nums, vector<int>& indexes, int lo, int hi) {
        if (hi - lo < 2) {
            if (nums[indexes[lo]] > nums[indexes[hi]]) {
                swap(indexes[lo], indexes[hi]);
                result[indexes[hi]]++;
            }
            return;
        }
        
        int mid = (hi + lo) / 2;
        sort(result, nums, indexes, lo, mid);
        sort(result, nums, indexes, mid+1, hi);
        vector<int> temp;
        temp.reserve(hi-lo);

        int i = lo, j = mid + 1, smallers = 0;

        while (i <= mid || j <= hi) {
            if (j > hi || i <= mid && nums[indexes[i]] <= nums[indexes[j]]) {
                result[indexes[i]] += smallers;
                temp.push_back(indexes[i++]);
            }
            else {
                smallers++;
                temp.push_back(indexes[j++]);
            }
        }

        for (int i = 0; i < temp.size(); i++)
            indexes[lo++] = temp[i];
    }
};

auto init = []() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    cout.tie(nullptr);
    return 'c';
}();

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