Zigzag Sequence Formation

You are given an integer n and a sequence of n integers. Your task is to reorder the sequence (if possible) into a zigzag sequence such that:

• For every even index i (0-indexed), the element at position i is strictly greater than the element at position i+1.
• For every odd index i, the element at position i is strictly less than the element at position i+1.

If n = 1, the sequence is trivially a zigzag sequence.

If such an arrangement exists, print YES on the first line and a valid zigzag sequence on the second line (all numbers separated by a space). Otherwise, print NO on a single line.

Note: If there are multiple possible answers, outputting any one of them is acceptable.

Example:

Input:
5
4 1 3 2 5
Output:
YES
5 1 4 2 3

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inputFormat

The input is given via standard input (stdin) and has the following format:

• First line: an integer n, representing the number of elements in the sequence.
• Second line: n space-separated integers.

outputFormat

If a zigzag sequence can be formed, output should be:

• First line: YES
• Second line: a rearranged sequence of n integers separated by spaces, satisfying the zigzag conditions.

If it is impossible to form such a sequence, output a single line containing NO.

## sample

1
5

YES
5

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