<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)
        self.arr = [[v, i] for i, v in enumerate(nums)]
        self.temp = [[0, 0] for _ in range(n)]
        self.count = [0] * n
        self.sort(0, n-1)
        return self.count

    def sort(self, left, right):
        if right == left: return
        mid = (left + right) // 2
        self.sort(left, mid)
        self.sort(mid+1, right)
        self.merge(left, right, mid)
    
    def merge(self, left, right, mid):
        for i in range(left, right+1):
            self.temp[i] = self.arr[i]

        i, j = left, mid+1

        for p in range(left, right+1):
            if i == (mid + 1):
                self.arr[p] = self.temp[j]
                j += 1
            elif j == (right+1):               
                self.arr[p] = self.temp[i]
                self.count[self.arr[p][1]] += j - mid - 1
                i += 1
            elif self.temp[i][0] > self.temp[j][0]:
                self.arr[p] = self.temp[j]
                j += 1
            else:
                self.arr[p] = self.temp[i]
                self.count[self.arr[p][1]] += j - mid - 1
                i += 1
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