<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>

void merge(vector<pair<int,int>>&num , int low ,int mid , int high , vector<int>&result)
{
    int n1 = mid - low + 1;
    int n2 = high - mid;
    vector<pair<int,int>>L(n1);
    vector<pair<int,int>>R(n2);
    for(int i = 0; i < n1 ; i++)
    {
        L[i] = num[i + low];
    }
    for(int i = 0; i < n2 ; i++)
    {
        R[i] = num[mid + 1 + i];
    }
    int i = 0 , j = 0 , k = low;
    while(i < n1 && j < n2)
    {
        if(L[i].first <= R[j].first)
        {
            result[L[i].second] += j;
            num[k] = L[i];
            i++;
        }
        else
        {
            num[k] = R[j];
            j++;
        }
        k++;
    }
    while(i < n1)
    {
        result[L[i].second] += j;
        num[k] = L[i];
        k++;
        i++;
    }
    while(j < n2)
    {
        num[k++] = R[j++];
    }
}
void merge_sort(vector<pair<int,int>>&num, int low ,int high, vector<int>&result)
{
    if(low >= high) return;
    int mid = (high + low )/2;
    merge_sort(num , low ,mid , result);
    merge_sort(num, mid + 1, high , result);
    merge(num, low ,mid ,high, result);
}
class Solution {
public:
    vector<int> countSmaller(vector<int>& a) {
        int n = a.size();
        vector<int>result(n, 0);
        vector<pair<int,int>>num(n);
        for(int i = 0 ;i < n; i++)
        {
            num[i] = {a[i], i};
        }
        merge_sort(num, 0 , n - 1, result);
        return result;
    }
};
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