We call a permutation p₀, p₁, ... , p_n-1 of integers 0, 1, ... , n-1 anti-arithmetic, when there are no three-term arithmetic series in this permutation, i.e. there are no such three indices i < j < k, that integers p_i, p_j, p_k make an arithmetic series. For example the series of integers 3, 1, 0, 4, 2 is an anti-arithmetic permutation of integers 0, 1, 2, 3, 4. The series 0, 5, 4, 3, 1, 2 is not an anti-arithmetic permutation, because its first, fifth and sixth term: 0, 1, 2 form an arithmetic series (as well as its second, forth and fifth term: 5, 3, 1 and second third and forth term: 5, 4, 3 form arithmetic series).

Task

Write a program that:

• reads one positive integer n from the text file PER.IN,
• computes any anti-arithmetic permutation of numbers 0, 1, ... , n-1 and writes it into the text file PER.OUT.

Input

There is one positive integer n, 3 <= n <= 1000000, written in the text file PER.IN. 

Output

The output file PER.OUT should be composed of n lines. These lines should contain different integers from the set {0, 1, ... , n-1}, one in each line. The numbers in the consecutive lines should form an anti-arithmetic permutation of numbers 0, 1, ..., n-1.

Example

If there is number 5 written in the input file PER.IN, then one of the correct solutions is the following file PER.OUT :
3
1
0
4
2

Your program should look for the file PER.IN in the current directory and produce the output file PER.OUT in the current directory too. The file containing the source code of your program should have a name PER.???, whereas you should put three-letter abbreviation of the used programming language name instead of ???. The same program in executable form should be written in file PER.EXE