<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(vector<int> &nums, int low, int high, vector<int> &hash, vector<int> &indexes)
{
    int mid = (low + high) / 2;
    int i = low, j = mid + 1;
    vector<int> fake;
    int small = 0;
    while (i <= mid && j <= high)
    {
        if(nums[indexes[i]] > nums[indexes[j]])
        {
            while (j <= high && (nums[indexes[i]] > nums[indexes[j]]))
            {
                fake.push_back(indexes[j++]);
                small++;
            }
            hash[indexes[i]]+=small;
            fake.push_back(indexes[i++]);
        }
        else
        {
            hash[indexes[i]]+=small;
            fake.push_back(indexes[i++]);
        }
    }

    while(i<=mid)
    {
        hash[indexes[i]]+=small;
        fake.push_back(indexes[i++]);
    }

    while (j<=high)
    {
        fake.push_back(indexes[j++]);
    }

    for(int k = low;k<=high;k++) indexes[k] = fake[k-low];
}

void helper(vector<int> &nums, int low, int high, vector<int> &hash, vector<int> &indexes)
{
    if (low >= high)
        return;
    int mid = (low + high) / 2;
    helper(nums, low, mid, hash, indexes);
    helper(nums, mid + 1, high, hash, indexes);
    merge(nums, low, high, hash, indexes);
}

vector<int> countSmaller(vector<int> &nums)
{
    int n = nums.size();
    if(n==1) return {0};
    int low = 0, high = n-1;
    vector<int> hash(n,0), indexes(n);
    for(int i = 0;i<n;i++) indexes[i] = i;
    helper(nums,low,high,hash,indexes);
    return hash;
}
};
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