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?

The only input line has an integer $n$ .

• $1 \le n \le 2 \cdot 10^5$

Print $n$ integers: the removal order.