<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 SegmentTree:
    def __init__(self, data, default=0, func=max):
        """initialize the segment tree with data"""
        self._default = default
        self._func = func
        self._len = len(data)
        self._size = _size = 1 << (self._len - 1).bit_length()

        self.data = [default] * (2 * _size)
        self.data[_size:_size + self._len] = data
        for i in reversed(range(_size)):
            self.data[i] = func(self.data[i + i], self.data[i + i + 1])

    def __delitem__(self, idx):
        self[idx] = self._default

    def __getitem__(self, idx):
        return self.data[idx + self._size]

    def __setitem__(self, idx, value):
        idx += self._size
        self.data[idx] = value
        idx >>= 1
        while idx:
            self.data[idx] = self._func(self.data[2 * idx], self.data[2 * idx + 1])
            idx >>= 1

    def __len__(self):
        return self._len

    def query(self, start, stop):
        """func of data[start, stop)"""
        start += self._size
        stop += self._size

        res_left = res_right = self._default
        while start < stop:
            if start & 1:
                res_left = self._func(res_left, self.data[start])
                start += 1
            if stop & 1:
                stop -= 1
                res_right = self._func(self.data[stop], res_right)
            start >>= 1
            stop >>= 1

        return self._func(res_left, res_right)

    def __repr__(self):
        return "SegmentTree({0})".format(self.data)


class Solution:
    def countSmaller(self, nums: List[int]) -> List[int]:
        count = [0] * (2 * int(1e4) + 1)


        st = SegmentTree(count, default= 0, func = lambda x,y : x + y)

        output = [0]


        offset = int(1e4)

        st[nums[-1] + offset] += 1

        for i in range(len(nums)-2, -1, -1):
            num = nums[i]
            output.append(st.query(0, num + offset ))
            st[num + offset] += 1

        return output[::-1]
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