In an array of integers, a "peak" is an element which is greater than or equal to the adjacent integers in the array, and a "valley" is an element which is less than or equal to the adjacent integers. For example, in the array [5, 8, 6, 2, 3, 4, 6], the elements 8 and the final 6 are peaks, the elements 5 and 2 are valleys, and the elements 6, 3 and 4 are neither peaks nor valleys.

Given a Python list of integers, return the list sorted into an alternating sequence of peaks and valleys. Note that there can be more than one possible valid output for a given input.

Example:

Input: [5, 3, 1, 2, 3]

Output: [5, 1, 3, 2, 3]