<p>You are given an array of strings <code>names</code>, and an array <code>heights</code> that consists of <strong>distinct</strong> positive integers. Both arrays are of length <code>n</code>.</p>

<p>For each index <code>i</code>, <code>names[i]</code> and <code>heights[i]</code> denote the name and height of the <code>i<sup>th</sup></code> person.</p>

<p>Return <code>names</code><em> sorted in <strong>descending</strong> order by the people&#39;s heights</em>.</p>

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

<pre>
<strong>Input:</strong> names = [&quot;Mary&quot;,&quot;John&quot;,&quot;Emma&quot;], heights = [180,165,170]
<strong>Output:</strong> [&quot;Mary&quot;,&quot;Emma&quot;,&quot;John&quot;]
<strong>Explanation:</strong> Mary is the tallest, followed by Emma and John.
</pre>

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

<pre>
<strong>Input:</strong> names = [&quot;Alice&quot;,&quot;Bob&quot;,&quot;Bob&quot;], heights = [155,185,150]
<strong>Output:</strong> [&quot;Bob&quot;,&quot;Alice&quot;,&quot;Bob&quot;]
<strong>Explanation:</strong> The first Bob is the tallest, followed by Alice and the second Bob.
</pre>

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

<ul>
	<li><code>n == names.length == heights.length</code></li>
	<li><code>1 &lt;= n &lt;= 10<sup>3</sup></code></li>
	<li><code>1 &lt;= names[i].length &lt;= 20</code></li>
	<li><code>1 &lt;= heights[i] &lt;= 10<sup>5</sup></code></li>
	<li><code>names[i]</code> consists of lower and upper case English letters.</li>
	<li>All the values of <code>heights</code> are distinct.</li>
</ul>

class Solution:
    def merge_sort(self, names, nums: List[int], left: int, right: int): 
        if (right - left) + 1 <= 1:
            return nums 
        mid = (left + right) // 2
        self.merge_sort(names, nums, left, mid)
        self.merge_sort(names, nums, mid+1, right)
        self.merge(names, nums, left , mid, right)
        return nums

    def merge(self, names, nums: List[int], left: int, mid: int, right: int):
        
        L = nums[left:mid+1]
        R = nums[mid+1:right+1]

        namesL = names[left:mid+1]
        namesR = names[mid+1:right+1]

        i, j, k = left, 0, 0
        while j < len(L) and k < len(R):
            if L[j] > R[k]:
                nums[i] = L[j]
                names[i] = namesL[j]
                j += 1
            else:
                nums[i] = R[k]  
                names[i] = namesR[k] 
                k += 1
            i += 1   
        
        while j < len(L):
            nums[i] = L[j]
            names[i] = namesL[j]
            i += 1
            j += 1

        while k < len(R):
            nums[i] = R[k]
            names[i] = namesR[k]
            i += 1
            k += 1 

    def sortPeople(self, names: List[str], heights: List[int]) -> List[str]:
        self.merge_sort(names, heights, 0, len(heights)-1)
        return names




        
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