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:

1. Antimonotonic: for each consecutive $3$ values $p_{i-1}, p_i, p_{i+1}$ ($1 < i < n$), $p_i$ should either be the smallest or the biggest of the three values.
2. 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 $1$.

Input Specification

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 $n=0$.

Output Specification

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

3
5
10
0

Sample Output

3 1 2
4 5 2 3 1
6 10 2 9 3 5 4 7 1 8