Eric wants to visit all of his friends. Each friend lives at house , labelled from to . Each house is separated by a single kilometre, meaning that the distance between house and house would be . 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 .
Eric must visit all of the houses. Can you output a sequence that Eric can follow, such that he visits all houses and never travels the same distance twice?
Subtask 1 [30%]
Subtask 2 [70%]
The first and only line of input will contain an integer , the number of houses Eric needs to visit. The houses are labelled from to .
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
Sample Output 1
1 3 2
Sample Explanation 1
For the first sample, he could also travel from house to , and then to as stated in the problem description
Sample Input 2
Sample Output 2
Sample Explanation 2
In the second sample, he could also travel from to .