Anti-arithmetic Permutations

Memory limit: 32 MB

We call a permutation of integers anti-arithmetic, when there are no three-term arithmetic series in this permutation, i.e. there are no such three indices , that integers (in this order) make an arithmetic series. For example the series of integers is an anti-arithmetic permutation of integers . The series is not an anti-arithmetic permutation, because its first, fifth and sixth term: form an arithmetic series (as well as its second, forth and fifth term: and second third and forth term: form arithmetic series).

Task

Write a program that:

• reads one positive integer from the standard input,
• computes any anti-arithmetic permutation of numbers and writes it to the standard output.

Input

There is one positive integer , , written in the standard input.

Output

The standard output should be composed of lines. These lines should contain different integers from the set , one in each line. The numbers in the consecutive lines should form an anti-arithmetic permutation of numbers .

Example

For the input data:

5

the correct result is:

3
1
0
4
2

Task author: Wojciech Guzicki.