LogiQuest

82. Zig-Zag Arrangement

MediumGreedy

Rearrange the array so that a₁ < a₂ > a₃ < a₄ > … using this rule: scan left to right and swap a[i] and a[i+1] whenever the pair breaks the pattern. Print the result. All values are distinct.

Input format

Line 1: n Line 2: n distinct integers

Output format

The rearranged array.

Example 1

Input

7
4 3 7 8 6 2 1

Output

3 7 4 8 2 6 1

Example 2

Input

4
1 4 3 2

Output

1 4 2 3

Constraints

1 ≤ n ≤ 10⁵

Read input from standard input and print the answer to standard output. Your code is judged against 5 test cases, most of them hidden.

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