<p>Given an array of integers <code>nums</code>, sort the array in ascending order and return it.</p>

<p>You must solve the problem <strong>without using any built-in</strong> functions in <code>O(nlog(n))</code> time complexity and with the smallest space complexity possible.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> nums = [5,2,3,1]
<strong>Output:</strong> [1,2,3,5]
<strong>Explanation:</strong> After sorting the array, the positions of some numbers are not changed (for example, 2 and 3), while the positions of other numbers are changed (for example, 1 and 5).
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> nums = [5,1,1,2,0,0]
<strong>Output:</strong> [0,0,1,1,2,5]
<strong>Explanation:</strong> Note that the values of nums are not necessairly unique.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= nums.length &lt;= 5 * 10<sup>4</sup></code></li>
	<li><code>-5 * 10<sup>4</sup> &lt;= nums[i] &lt;= 5 * 10<sup>4</sup></code></li>
</ul>

class Solution:
    def merge(self, array, left, mid, right):
        ls = mid - left + 1
        la = [0] * ls
        rs = right - mid
        ra = [0] * rs

        for x in range(ls):
            la[x] = array[left + x]
        for y in range(rs):
            ra[y] = array[mid + 1 + y]
        
        li = 0
        ri = 0
        i = left

        while li < ls and ri < rs:
            if la[li] <= ra[ri]:
                array[i] = la[li]
                li += 1
            else:
                array[i] = ra[ri]
                ri += 1
            i += 1

        while li < ls:
            array[i] = la[li]
            li += 1
            i += 1
        
        while ri < rs:
            array[i] = ra[ri]
            ri += 1
            i += 1


    
    def sortArrayRecursive(self, array, left, right):
        if left >= right:
            return
        
        mid = left + (right - left) // 2
        self.sortArrayRecursive(array, left, mid)
        self.sortArrayRecursive(array, mid+1, right)
        self.merge(array, left, mid, right)

    def sortArray(self, nums: List[int]) -> List[int]:
        self.sortArrayRecursive(nums, 0, len(nums) - 1)
        return nums
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