<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]:
        
        class Pair:
            def __init__(self, val, index) -> None:
                self.val = val
                self.index = index
        
        def sort(array, low, high):
            if low < high:
                mid = low + (high-low)//2
                sort(array, low, mid)
                sort(array, mid+1, high)
                merge(array, low, mid, high)


        def merge(array, low, mid, high):
            for i in range(low, high+1):
                temp[i] = array[i]

            i, j = low, mid+1
            while i <= mid and j <= high:
                if temp[i].val <= temp[j].val:
                    array[low] = temp[i]
                    # record how many numbers are smaller than the current i
                    counter[array[low].index] += j - (mid + 1)
                    i += 1
                else:
                    array[low] = temp[j]
                    j += 1
                low += 1

            while i <= mid:
                array[low] = temp[i]
                counter[array[low].index] += j - (mid + 1)
                i += 1
                low += 1

            while j <= high:
                array[low] = temp[j]
                j += 1
                low += 1


        temp = [0] * len(nums)
        counter = [0] * len(nums)

        array = [Pair(nums[i], i) for i in range(len(nums))]

        sort(array, 0, len(nums)-1)

        return counter
52688