<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 merge(self, nums, low, mid, high, n, count):
        i, j = low, mid + 1
        temp = []
        right = mid + 1

        # The counting should be performed before merging the arrays
        for left in range(low, mid + 1):
            while right <= high and nums[left][0] > nums[right][0]:
                right += 1
            count[nums[left][1]] += (right - (mid + 1))

        while i <= mid and j <= high:
            if nums[i][0] <= nums[j][0]:
                temp.append(nums[i])
                i += 1
            else:
                temp.append(nums[j])
                j += 1
        
        while i <= mid:
            temp.append(nums[i])
            i += 1
        
        while j <= high:
            temp.append(nums[j])
            j += 1

        # Copy the sorted array into the original array
        for k in range(len(temp)):
            nums[low + k] = temp[k]

    def mergeSort(self, nums, l, h, n, count):
        if l >= h:
            return
        mid = l + (h - l) // 2
        self.mergeSort(nums, l, mid, n, count)
        self.mergeSort(nums, mid + 1, h, n, count)
        self.merge(nums, l, mid, h, n, count)

    def countSmaller(self, arr):
        n = len(arr)
        count = [0] * n
        nums = [(arr[i], i) for i in range(n)]
        self.mergeSort(nums, 0, n - 1, n, count)
        return count
2331