Consider a game where there are \(n\) children (numbered \(1,2,\ldots,n\)) 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 \(n\).

Output

• Print \(n\) integers: the removal order.

Constraints

• \(1 \leq n \leq 2 \cdot 10^5\)

Example

Sample input

7 

2 4 6 1 5 3 7