<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:
    def countSmaller(self, nums: List[int]) -> List[int]:
        n = len(nums)
        arr = [[v, k] for k, v in enumerate(nums)]
        result = [0] * n

        def merge_sort(arr, left, right):
            if left >= right - 1:
                return

            mid = (left + right) // 2
            merge_sort(arr, left, mid)
            merge_sort(arr, mid, right)
            merge(arr, left, right, mid)

        def merge(arr, left, right, mid):
            temp = []
            i, j = left, mid
            while i < mid or j < right:
                if j >= right or (i < mid and arr[i][0] <= arr[j][0]):
                    temp.append(arr[i])
                    result[arr[i][1]] += j - mid
                    i += 1
                else:
                    temp.append(arr[j])
                    j += 1

            for i in range(left, right):
                arr[i] = temp[i - left]

        merge_sort(arr, 0, n)
        return result
                


2012