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?

#### Constraints

##### Subtask 1 [30%]

##### Subtask 2 [70%]

#### Input Specification

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 .

#### 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 to , and then to 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 to .

## Comments