Mary

Memory limit: 32 MB

Mary really enjoys playing with numbers - just like you. From time to time she chooses a function and seeks for a permutation of numbers which minimizes the value of the function. Now she is considering the following function, which she finds quite elegant:

Here denotes the absolute value of the number .

Unfortunately, this example turned out to be difficult to Mary. If you are willing to help her, write a program that finds any permutation of the sequence which minimizes the value of .

Input

The first and only line of input contains an integer ().

Output

Your program should output a single line with space-separated integers: a permutation of for which attains a minimum value. If there are multiple such permutations, your program should output any one of them.

Example

For the input data:

4

a correct result is:

2 4 1 3

whereas for the input data:

5

a correct result is:

3 2 5 1 4

Task author: Szymon Acedanski.