<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]:

        ## BIT
        # m, M = min(nums), max(nums)
        # rng = M-m+1 # range
        
        # def update(i, v):
        #     i = i-m+1
        #     while i <= rng:
        #         bit[i] += v
        #         i += i & -i
        
        # def get_ps(i):
        #     i = i-m+1
        #     s = 0
        #     while i > 0:
        #         s += bit[i]
        #         i -= i & -i
        #     return s
        
        # bit = [0] * (rng+1)

        # for i in nums:
        #     update(i, 1)

        # counts = []
        # for i in nums:
        #     counts.append(get_ps(i-1))
        #     update(i, -1)
        
        # return counts

        
        ## Merge sort
        n = len(nums)

        def merge_sort(enum, i, j):
            if j <= i:
                return
            m = (i + j) // 2
            merge_sort(enum, i, m)
            merge_sort(enum, m+1, j)
            merged = []
            x, y = m, j
            while x >= i or y >= m+1:
                if y == m or x >= i and enum[x][1] > enum[y][1]:
                    counts[enum[x][0]] += y-m
                    merged.append(enum[x])
                    x -= 1
                else:
                    merged.append(enum[y])
                    y -= 1
            for k in range(i, j+1):
                enum[k] = merged[len(merged)-1-k+i]
        
        counts = [0] * n
        merge_sort(list(enumerate(nums)), 0, n-1)

        return counts
2194