<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]:
        if len(nums) == 0:
            return []
        if len(nums) == 1:
            return [0]

        nums = [(nums[i], i) for i in range(len(nums))]
        def merge(arr, temp, ans, left, mid, right):
            ptr1, ptr2 = left, mid + 1
            wptr = left
            ctr = 0
            while ptr1 <= mid and ptr2 <= right:
                if arr[ptr1][0] <= arr[ptr2][0]:
                    temp[wptr] = arr[ptr1]
                    ans[arr[ptr1][1]] += ctr
                    ptr1 += 1
                else:
                    temp[wptr] = arr[ptr2]
                    ctr += 1
                    ptr2 += 1
                wptr += 1
            
            while ptr1 <= mid:
                temp[wptr] = arr[ptr1]
                ans[arr[ptr1][1]] += ctr
                ptr1 += 1
                wptr += 1
            while ptr2 <= right:
                temp[wptr] = arr[ptr2]
                ptr2 += 1
                wptr += 1
            
            for i in range(left, right+1):
                arr[i] = temp[i]
            # print(arr)

        def merge_sort(arr, temp, ans, left, right):
            mid = (left + right) // 2
            if left < right:
                merge_sort(arr, temp, ans, left, mid)
                merge_sort(arr, temp, ans, mid+1, right)
            merge(arr, temp, ans, left, mid, right)
        
        temp = [0 for _ in range(len(nums))]
        ans = [0 for _ in range(len(nums))]
        merge_sort(nums, temp, ans, 0, len(nums)-1)
        return ans

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