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

Output

• Print ~n~ integers: the removal order.

Constraints

• ~1 \le n \le 2 \cdot 10^5~

Example Input

7

Example Output

2 4 6 1 5 3 7