<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, list1, list2):
        res = []
        index1 = 0
        index2 = 0

        while index1 < len(list1) and index2 < len(list2):
            if list1[index1] < list2[index2]:
                res.append(list1[index1])
                index1 += 1
            else:
                res.append(list2[index2])
                index2 += 1
            
        res.extend(list1[index1:])
        res.extend(list2[index2:])

        return res

    def sortArray(self, nums: List[int]) -> List[int]:

        from collections import deque
        queue = deque([[num] for num in nums])

        while len(queue) > 1:
            size = len(queue)
            for i in range(0,size, 2):
                l1 = queue.popleft()
                if i+1 < size:
                    l2 = queue.popleft()
                else:
                    l2 = []
                
                queue.append(self.merge(l1, l2))
                print()
                

        return queue.popleft()
    


    def sortArrayIter(self, nums):
        if len(nums) < 2:
            return nums
        
        mid = len(nums)//2
        left = self.sortArray(nums[:mid])
        right = self.sortArray(nums[mid:])

        def merge(l1, l2):
            l1_index = 0
            l2_index = 0
            res = []
            while l1_index < len(l1) and l2_index < len(l2):
                if l1[l1_index] < l2[l2_index]:
                    res.append(l1[l1_index])
                    l1_index += 1
                else:
                    res.append(l2[l2_index])
                    l2_index += 1
            
            res.extend(l1[l1_index:])
            res.extend(l2[l2_index:])
            return res

        return merge(left, right)
        
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