Eric wants to visit all ~N~ of his friends. Each friend lives at house ~i~, labelled from ~1~ to ~N~. Each house is separated by a single kilometre, meaning that the distance between house ~i~ and house ~j~ would be ~\left | i-j \right |~. He decides to be a "cool kid", and not travel a certain distance more than once.

For example, if there are 3 houses, he could start at the third house, proceed to the first house, and visit the second house last, with travel distances of ~[2, 1]~.

Eric must visit all of the ~N~ houses. Can you output a sequence that Eric can follow, such that he visits all ~N~ houses and never travels the same distance twice?

Constraints

Subtask 1 [30%]

~2 \le N \le 10~

Subtask 2 [70%]

~2 \le N \le 10^5~

Input Specification

The first and only line of input will contain an integer ~N~, the number of houses Eric needs to visit. The houses are labelled from ~1~ to ~N~.

Output Specification

You are to output a sequence of houses that matches the constraints stated in the problem description, each house separated by a space.

Sample Input 1

3

Sample Output 1

1 3 2

Sample Explanation 1

For the first sample, he could also travel from house ~3~ to ~1~, and then ~1~ to ~2~ as stated in the problem description

Sample Input 2

2

Sample Output 2

2 1

Sample Explanation 2

In the second sample, he could also travel from ~1~ to ~2~.