<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 sortArray(self, nums: List[int]) -> List[int]:
        n = len(nums)
        def merge(left, right, mid, num):
            nums = num
            temp_left, temp_right = left, right
            temp_list = [0] * n
            k = left
            mid_dup = mid+1
            while left <= mid and mid_dup <= right:
                if nums[left] <= nums[mid_dup]:
                    temp_list[k] = nums[left]
                    left += 1
                else:
                    temp_list[k] = nums[mid_dup]
                    mid_dup += 1
                k += 1
            while left <= mid:
                temp_list[k] = nums[left]
                left += 1
                k += 1
            while mid_dup <= right:
                temp_list[k] = nums[mid_dup]
                mid_dup += 1
                k += 1
            while temp_left <= temp_right:
                nums[temp_left] = temp_list[temp_left]
                temp_left += 1
            num = nums
            

        def sort(l, r, num):
            if l >= r:
                return
            mid = (l + r) // 2
            sort(l, mid, num)
            sort(mid+1, r, num)
            merge(l, r, mid, num)

        # sort(0, n-1)
        # return nums

        unique_elements_dict = {}
        for i in nums:
            count = unique_elements_dict.get(i, 0) + 1
            unique_elements_dict[i] = count
        unique_elements_list = list(unique_elements_dict.keys())
        len_unique_elements_list = len(unique_elements_list)
        sort(0, len_unique_elements_list - 1, unique_elements_list)
        sol = []
        for sorted_element in unique_elements_list:
            count = unique_elements_dict.get(sorted_element)
            sol.extend([sorted_element]*count)
        return sol


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