**Time limit:**1.00 s**Memory limit:**512 MB

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

Output:

2 4 6 1 5 3 7