<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 count(vector<int>& a, vector<int>& nums, int l1, int r1, int l2, int r2, vector<int>& ans) {
        int j=l2;
        for(int i=l1; i<=r1; i++) {
            while(j<=r2 && nums[a[j]] < nums[a[i]]) {
                j++;
            }
            ans[a[i]] += (j-l2);
        }
    }
    
    void merge(vector<int>& a, vector<int>& nums, int l1, int r1, int l2, int r2) {
        int i=l1, j=l2;
        vector<int> acc;
        while(i<=r1 && j<=r2) {
            if(nums[a[i]] <= nums[a[j]]) {
                acc.push_back(a[i]);
                i++;
            } else {
                acc.push_back(a[j]);
                j++;
            }
        }
        
        while(i<=r1) {
            acc.push_back(a[i]);
            i++;
        }
        
        while(j<=r2) {
            acc.push_back(a[j]);
            j++;
        }
        
        for(int i=l1, j=0; i<=r2; i++,j++) {
            a[i] = acc[j];
        }
    }
    
    void mergeSort(vector<int>& a, vector<int>& nums, int l, int r, vector<int>& ans) {
        if(l >= r) {
            return;
        }
        
        int mid = l + (r-l)/2;
        mergeSort(a, nums, l, mid, ans);
        mergeSort(a, nums, mid+1, r, ans);
        
        // Count the answer
        count(a, nums, l, mid, mid+1, r, ans);
        
        merge(a, nums, l, mid, mid+1, r);
    }
    
    vector<int> countSmaller(vector<int>& nums) {
        int n = nums.size();
        vector<int> a(n, 0), ans(n, 0);
        for(int i=0; i<n; i++) {
            a[i] = i;
        }
        
        mergeSort(a, nums, 0, n-1, ans);
        
        return ans;
    }
};
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