Valley Permutation

You are given an integer n and a list of n distinct integers. Your task is to determine whether a valley permutation exists. A valley permutation is defined as a permutation where every element (except the first and last) is either a local minimum or a local maximum. In other words, for every index i (with 1 < i < n), the element at i should either be strictly less than both of its neighbors or strictly greater than both.

If n < 3, it is impossible to form a valid valley permutation, and you should output NO.

Otherwise, find any valley permutation of the array. The output should first print YES on one line, followed by the permutation on the next line as space-separated integers.

inputFormat

The input is read from standard input and consists of two lines:

• The first line contains a single integer n — the number of elements.
• The second line contains n space separated integers.

outputFormat

If a valley permutation is not possible (i.e. when n < 3), output NO.

Otherwise, output two lines: the first line should be YES and the second line should contain the valley permutation as n space-separated integers.

Your answer must be printed to standard output.

## sample

5
1 2 3 4 5

YES
1 4 2 5 3

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