CSES - Josephus Problem I
  • Time limit: 1.00 s
  • Memory limit: 512 MB

Consider a game where there are nn children (numbered 1,2,,n1,2,\dots,n) in a circle. During the game, every other 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 nn.

Output

Print nn integers: the removal order.

Constraints

  • 1n21051 \le n \le 2 \cdot 10^5

Example

Input:

7

Output:

2 4 6 1 5 3 7