<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 f(self,a,b):
        c = [None for _ in range(len(a)+len(b))]
        count = len(c)-1
        i = len(a)-1
        j = len(b)-1
        while(i >=0 or j >=0):
            if i == -1:
                c[count] = b[j]
                j-=1
            elif j == -1:
                c[count] = a[i]
                i-=1
            else:
                if a[i] <= b[j]:
                    c[count] = b[j]
                    j-=1
                else:
                    c[count] = a[i]
                    i-=1
            count -=1
        return c
    def merge(self, nums, counts):
        if len(nums) <= 1:
            return nums
        a = self.merge(nums[:len(nums)>>1],counts)
        b = self.merge(nums[len(nums)>>1:],counts)

        j  = 0
        for i in range(len(a)):
            while(j < len(b) and b[j][0] < a[i][0]):
                j+=1
            counts[a[i][1]] += j
        return self.f(a,b)

        
    def countSmaller(self, nums: List[int]) -> List[int]:
        
        counts = [0 for i in range(len(nums))]

        self.merge([(num,i) for i,num in enumerate(nums)], counts)

        return counts
43738