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

    def _merge_sort(
        self, names: List[str], heights: List[int], start: int, end: int
    ):
        if start < end:
            mid = start + (end - start) // 2
            self._merge_sort(names, heights, start, mid)
            self._merge_sort(names, heights, mid + 1, end)
            self._merge(names, heights, start, mid, end)

    def _merge(
        self,
        names: List[str],
        heights: List[int],
        start: int,
        mid: int,
        end: int,
    ):
        left_size = mid - start + 1
        right_size = end - mid

        left_heights = heights[start : start + left_size]
        right_heights = heights[mid + 1 : mid + 1 + right_size]
        left_names = names[start : start + left_size]
        right_names = names[mid + 1 : mid + 1 + right_size]

        left_index, right_index = 0, 0
        merge_index = start
        while left_index < left_size and right_index < right_size:
            if (
                left_heights[left_index] >= right_heights[right_index]
            ):  
                heights[merge_index] = left_heights[left_index]
                names[merge_index] = left_names[left_index]
                left_index += 1
            else:
                heights[merge_index] = right_heights[right_index]
                names[merge_index] = right_names[right_index]
                right_index += 1
            merge_index += 1

        while left_index < left_size:
            heights[merge_index] = left_heights[left_index]
            names[merge_index] = left_names[left_index]
            left_index += 1
            merge_index += 1

    
        while right_index < right_size:
            heights[merge_index] = right_heights[right_index]
            names[merge_index] = right_names[right_index]
            right_index += 1
            merge_index += 1
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