<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 SegmentTreeNode:
    def __init__(self, low, high):
        self.low = low
        self.high = high
        self.left = None
        self.right = None
        self.cnt = 0
        
class Solution: 
    def _build(self, left, right):
        root = SegmentTreeNode(self.nums[left], self.nums[right])
        if left == right:
            return root
        
        mid = (left+right)//2
        root.left = self._build(left, mid)
        root.right = self._build(mid+1, right)
        return root
    
    def _update(self, root, val):
        if not root:
            return 
        if root.low <= val <= root.high:
            root.cnt += 1
            self._update(root.left, val)
            self._update(root.right, val)
            
    def _query(self, root, lower, upper):
        if lower <= root.low and root.high <= upper:
            return root.cnt
        if upper < root.low or root.high < lower:
            return 0
        return self._query(root.left, lower, upper) + self._query(root.right, lower, upper)
    
    def countSmaller(self, nums: List[int]) -> List[int]:
        nums = nums[::-1]
        self.nums = sorted(list(set(nums)))
        root = self._build(0, len(self.nums)-1)  if nums else None
        
        res = []
        for n in nums:
            res.append(self._query(root,float('-inf'),n-1)) 
            self._update(root, n)
        return res[::-1]
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