<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> ans, index;
    void merge(vector<int> &nums, int s, int mid, int e){

        vector<int> left,right;
        for(int i=s; i<=mid; i++){
            left.push_back(index[i]);
        }
        for(int i=mid+1; i<=e; i++){
            right.push_back(index[i]);
        }

        int i=0, j=0, k=s;
        int n=left.size(), m=right.size();
        while(i<n && j<m){
            if(nums[left[i]]>nums[right[j]]){
                ans[left[i]]+=(m-j);
                index[k++]=left[i++];
            }else{
                index[k++]=right[j++];
            }
        }
        while(i<n){
            index[k++]=left[i++];
        }
        while(j<m){
            index[k++]=right[j++];
        }
        return;
    }

    void mergeSort(vector<int> &v, int s, int e){
        if(s>=e){
            return;
        }
        int mid=(s+e)>>1;
        mergeSort(v,s,mid);
        mergeSort(v,mid+1,e);
        merge(v,s,mid,e);
    }

    vector<int> countSmaller(vector<int>& nums) {
        vector<pair<int,int>> v;
        int n = nums.size();
        index.resize(n);
        for(int i=0; i<n; i++){
            index[i]=i;
        }

        ans.resize(n,0);
        mergeSort(nums,0,n-1);
        return ans;
    }
};
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