P. Josephus Problem I
time limit per test
2 s
memory limit per test
256 megabytes
input
standard input
output
standard output

Consider a game where there are $$$n$$$ children (numbered $$$1,2,\dots,n$$$) in a circle. During the game, every second child is removed from the circle, until there are no children left. In which order will the children be removed?

Input

The only input line has an integer n.

Constraints:

  • $$$1 \le n \le 2\cdot 10^5$$$
Output

Print $$$n$$$ integers: the removal order.

Example
Input
7
Output
2 4 6 1 5 3 7