<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>

def trypop(l, default=None):
    if l:
        return l.pop(0)
    return default
    
def yieldlistpairs(l):
    """
    Given list of lists: [1,2,3,4,5]
    Yield (1,2), (3,4), (5, [])
    """
    while l:
        yield (trypop(l, default=[]), 
               trypop(l, default=[]))

def mergepair(left, right):
    """
    Given a pair of lists like 
    a=[1,4],  b=[3,6]
    return a merged list like
    [1,3,4,6]
    """
    merged = []
    lv = trypop(left)
    rv = trypop(right)
    while lv is not None or rv is not None:
        if lv is None:
            merged.append(rv) 
            rv = trypop(right)
        elif rv is None:
            merged.append(lv)
            lv = trypop(left)
        elif lv < rv:
            merged.append(lv)
            lv = trypop(left)
        elif rv <= lv:
            merged.append(rv)
            rv = trypop(right)
    return merged
    
    
def mergestep(previous):
    """
    Given a list of sorted lists e.g..
    
     [[1,4], [3,6], [2,5], [7,8]]
     
     work through pairs and output the merge e.g.
     
     [[1,3,4,6], [2,5,7,8]]
    """
    new = []
    for a,b in yieldlistpairs(previous):
        new.append(mergepair(a, b))
    return new
    
    
class Solution:
    def sortArray(self, nums: List[int]) -> List[int]:
        working = [[n] for n in nums]
        while len(working) > 1:
            working = mergestep(working)
        return working[0]
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