<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]:
        hashMap = {}
        for name, height in zip(names, heights):
            hashMap[height] = name

        def merge(arr, L, M, R):
            left, right = arr[L : M + 1], arr[M + 1 : R + 1]
            i, j, k = L, 0, 0
            while (j < len(left)) and (k < len(right)):
                if left[j] <= right[k]:
                    arr[i] = left[j]
                    j += 1
                else:
                    arr[i] = right[k]
                    k += 1
                i += 1
            while j < len(left):
                arr[i] = left[j]
                j += 1
                i += 1
            while k < len(right):
                arr[i] = right[k]
                k += 1
                i += 1
            return arr

        def mergeSort(arr, l, r):
            if l == r:
                return arr
            m = (l + r) // 2
            mergeSort(arr, l, m)
            mergeSort(arr, m + 1, r)
            merge(arr, l, m, r)
            return arr

        res = []
        for height in reversed(mergeSort(heights, 0, len(heights) - 1)):
            res.append(hashMap[height])
        return res

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