#934 Pepero Tasting

Statement

Statement language

There is one Pepero stick of each length $1,2,\ldots,N$ . Arrange them in a row, and let $P_i$ be the length at position $i$ . Define $S_i=P_i+P_{i+1}$ for $1\leq i<N$ . Find an arrangement minimizing $\max(S_1,\ldots,S_{N-1})-\min(S_1,\ldots,S_{N-1})$ .

Input

The input is given in the following format:

$N$

Output

Print $P_1,P_2,\ldots,P_N$ of an optimal arrangement, separated by spaces. Each integer from to must appear exactly once. If there are multiple optimal arrangements, print any of them. Do not print the minimum value itself.

Constraints

$2 \leq N \leq 200\ 000$ .

Subtasks

#	Score	Constraints
1	20	$N \leq 9$ .
2	80	No additional constraints.

Samples

Sample 1

Input

2

Output

1 2

Sample 2

Input

5

Output

3 4 2 5 1