Hyperia
Hyperons, inhabitants of a distant universe, have decided to colonize a new planet. In their universe, planets are shaped like n-dimensional cubes.
The Hyperons want to determine the optimal way to place cities to maximize their number on the planet. According to their traditions, cities must be built at the centers of k-dimensional faces of the cube (where vertices are 0-dimensional faces, edges are 1-dimensional, flat squares are 2-dimensional, and so on). Furthermore, all cities must be constructed on faces of the same dimensionality. However, the Hyperons are unsure which dimensionality of faces allows for the most cities.
Input
The dimensionality of the cube n (1 ≤ n ≤ 10^9).
Output
Output a single line listing the permissible dimensionalities of faces that allow for the maximum number of cities, in ascending order, separated by spaces.