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A. Difference Row

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYou want to arrange *n* integers *a* _{1}, *a* _{2}, ..., *a* _{ n} in some order in a row. Let's define the value of an arrangement as the sum of differences between all pairs of adjacent integers.

More formally, let's denote some arrangement as a sequence of integers *x* _{1}, *x* _{2}, ..., *x* _{ n}, where sequence *x* is a permutation of sequence *a*. The value of such an arrangement is (*x* _{1} - *x* _{2}) + (*x* _{2} - *x* _{3}) + ... + (*x* _{ n - 1} - *x* _{ n}).

Find the largest possible value of an arrangement. Then, output the lexicographically smallest sequence *x* that corresponds to an arrangement of the largest possible value.

Input

The first line of the input contains integer *n* (2 ≤ *n* ≤ 100). The second line contains *n* space-separated integers *a* _{1}, *a* _{2}, ..., *a* _{ n} (|*a* _{ i}| ≤ 1000).

Output

Print the required sequence *x* _{1}, *x* _{2}, ..., *x* _{ n}. Sequence *x* should be the lexicographically smallest permutation of *a* that corresponds to an arrangement of the largest possible value.

Examples

Input

5

100 -100 50 0 -50

Output

100 -50 0 50 -100

Note

In the sample test case, the value of the output arrangement is (100 - ( - 50)) + (( - 50) - 0) + (0 - 50) + (50 - ( - 100)) = 200. No other arrangement has a larger value, and among all arrangements with the value of 200, the output arrangement is the lexicographically smallest one.

Sequence *x* _{1}, *x* _{2}, ... , *x* _{ p} is lexicographically smaller than sequence *y* _{1}, *y* _{2}, ... , *y* _{ p} if there exists an integer *r* (0 ≤ *r* < *p*) such that *x* _{1} = *y* _{1}, *x* _{2} = *y* _{2}, ... , *x* _{ r} = *y* _{ r} and *x* _{ r + 1} < *y* _{ r + 1}.

Codeforces (c) Copyright 2010-2020 Mike Mirzayanov

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