Enumeration of Subsets I
Print all subsets of a set SS, which contains 0,1,...n−10,1,...n−1 as elements. Note that we represent 0,1,...n−10,1,...n−1 as 00...0001, 00...0010, 00...0100, ..., 10...0000 in binary respectively and the integer representation of a subset is calculated by bitwise OR of existing elements.
Input
The input is given in the following format.
nn
Output
Print subsets ordered by their decimal integers. Print a subset in a line in the following format.
dd: e0e0 e1e1 ...
Print ':' after the integer value dd, then print elements eiei in the subset in ascending order. Seprate two adjacency elements by a space character.