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Description

Consider a game where there are n children (numbered 1,2,…,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 Format

The only input line has an integer n.

Output Format

Print n integers: the removal order.

7

2 4 6 1 5 3 7

Hint

1≤n≤2⋅10⁵

Source

CSES