<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 TreeNode:
    def __init__(self, start, end, val, left, right):
        self.start = start
        self.end = end
        self.val = val
        self.left = left
        self.right = right
class SegmentTree:
    def __init__(self, k):
        def build(start, end):
            if start == end:
                return TreeNode(start, end, 0, None, None)
            mid = start + (end - start) // 2
            left = build(start, mid)
            right = build(mid+1, end)
            return TreeNode(start, end, left.val+right.val, left, right)
        self.root = build(0, k)

    def update(self, rank):
        def updateRank(root, rank):
            root.val += 1
            if root.start == root.end == rank:
                return
            mid = root.start + (root.end - root.start) // 2
            if rank <= mid:
                updateRank(root.left, rank)
            else:
                updateRank(root.right, rank)

        updateRank(self.root, rank)
    def query(self, rank):
        if rank < 0:
            return 0
        def queryRank(root, start, end):
            if root.start == start and root.end == end:
                return root.val
            mid = root.start + (root.end - root.start) // 2
            if end <= mid:
                return queryRank(root.left, start, end)
            elif start > mid:
                return queryRank(root.right, start, end)
            return queryRank(root.left, start, mid) + queryRank(root.right, mid+1, end)
        return queryRank(self.root, 0, rank)

class Solution:
    def countSmaller(self, nums: List[int]) -> List[int]:
        unique_order_nums = sorted(list(set(nums)))
        ranks = {unique_order_nums[i]:i for i in range(len(unique_order_nums))}
        tree = SegmentTree(len(unique_order_nums))
        res = []
        for num in reversed(nums):
            tree.update(ranks[num])
            res.append(tree.query(ranks[num]-1))
        return reversed(res)

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