URI Online Judge | 1636
# Cyclic Antimonotonic Permutations

**Timelimit: 4**

Local Contest, University of Ulm Germany

A permutation is a sequence of integers which contains each integer from 1 to n exactly once. In this problem we are looking for permutations with special properties:

- Antimonotonic: for each consecutive 3 values p
_{i-1}, p_{i}, p_{i+1}(1 < i < n), pi should either be the smallest or the biggest of the three values. - Cyclic: The permutation should consist of only one cycle, that is, when we use p
_{i}as a pointer from i to p_{i}, it should be possible to start at position 1 and follow the pointers and reach all n positions before returning to position 1.

The input file contains several test cases. Each test case consists of a line containing an integer **n**, (3 ≤ **n** ≤ 10^{6}), the number of integers in the permutation. Input is terminated by **n** = 0.

For each test case print a permutation of the integers 1 to **n** which is both antimonotonic and cyclic. In case there are multiple solutions, you may print any one. Separate all integers by whitespace characters.

Sample Input | Sample Output |

3 |
3 1 2 |