<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(int left, int mid, int right, vector<pair<int, int>>& v, vector<int>& cnt) {
        int ls = mid - left + 1;
        int rs = right - mid;
        vector<pair<int, int>> lef(ls);
        vector<pair<int, int>> rig(rs);

        for (int i = 0; i < ls; i++) {
            lef[i] = v[left + i];
        }

        for (int i = 0; i < rs; i++) {
            rig[i] = v[mid + 1 + i];
        }

        int i = 0, j = 0, k = left;
        while (i < ls && j < rs) {
            if (lef[i].first <= rig[j].first) {
                cnt[lef[i].second] += j;
                v[k++] = lef[i++];
            } else {
                v[k++] = rig[j++];
            }
        }

        while (i < ls) {
            cnt[lef[i].second] += j;
            v[k++] = lef[i++];
        }

        while (j < rs) {
            v[k++] = rig[j++];
        }
    }

    void func(int left, int right, vector<pair<int, int>>& v, vector<int>& cnt) {
        if (left >= right) return;
        int mid = left + (right - left) / 2;
        func(left, mid, v, cnt);
        func(mid + 1, right, v, cnt);
        merge(left, mid, right, v, cnt);
    }

    vector<int> countSmaller(vector<int>& nums) {
        vector<pair<int, int>> v;
        for (int i = 0; i < nums.size(); i++) v.push_back({nums[i], i});
        vector<int> cnt(nums.size(), 0);
        func(0, nums.size() - 1, v, cnt);
        return cnt;
    }
};
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