## Problem A: An antiarithmetic permutation

A permutation of *n+1* is a bijective function of the initial
*n+1* natural numbers: 0, 1, ... *n*. A permutation
*p* is called antiarithmetic if there is no subsequence of it
forming an arithmetic progression of length bigger than 2, i.e. there
are no three indices
0 ≤ *i* < *j* < *k* < *n*
such that
(*p*_{i}, *p*_{j}, *p*_{k})
forms an arithmetic progression.

For example, the sequence (2, 0, 1, 4, 3) is an antiarithmetic
permutation of 5. The sequence (0, 5, 4, 3, 1, 2) is not an
antiarithmetic permutation of 6 as its first, fifth and sixth term (0, 1,
2) form an arithmetic progression; and so do its second, fourth and
fifth term (5, 3, 1).

Your task is to generate an antiarithmetic permutation of *n*.

Each line of the input file contains a natural number
3 ≤ *n* ≤ 10000. The last line of input
contains 0 marking the end of input. For each *n* from input,
produce one line of output containing an (any will do)
antiarithmetic permutation of *n* in the format shown below.

### Sample input

3
5
6
0

### Output for sample input

3: 0 2 1
5: 2 0 1 4 3
6: 2 4 3 5 0 1

*W. Guzicki, adapted by P. Rudnicki
*