Maximizing Absolute Differences in a Sequence

Given a sequence of n integers, rearrange the sequence so that the sum of absolute differences between consecutive elements is maximized. The sum is calculated as

\( S = \sum_{i=1}^{n-1} |a_i - a_{i-1}| \).

Your task is to output one valid rearrangement of the given sequence that achieves this goal. If there are multiple valid solutions, any one of them will be accepted.

inputFormat

The first line contains an integer n, representing the number of integers in the sequence.

The second line contains n space-separated integers.

outputFormat

Output a single line with the rearranged sequence of integers separated by spaces, such that the sum of the absolute differences between adjacent elements is maximized.

4
1 2 3 4

1 4 2 3