The Plovdiv Museum of Modern Art has an exhibition of ancient Thracian vases. There are N vases total. The first one is a miniature of height 1 centimeter. The second one is of height 2 centimeters; the third one is 3 centimeters tall and so on until the Nth vase, which is N centimeters tall.
Since this a modern art museum and the vases are ancient, the organizers of the exhibition would like to add a modern, chaotic twist to the presentation of the vases. They have decided to arrange the vases in a line that satisfies the following condition: For any three vases A, B and C, such that B's height is exactly the average of the heights of A and C, either B must be positioned to the left of both A and C, or B must be positioned to the right of both A and C (in other words, B may not be positioned between A and C on the line).
Task
Write a program that, given the number of vases, determines a linear arrangement of the vases that satisfies the condition of the exhibition organizers.
Constraints
| 1 ≤ N ≤ 2,000 | The number of vases |
Input
The first and only line contains a singer integer
N.
Output
There should be
N lines, each representing the
N positions in the arrangement, in order from left to right. Line
k should contain a single integer
Hk, the height of the vase you decided to place on position
k. All
N heights should be distinct integers between 1 and
N inclusive.
Sample Input 1
5
Sample Output 1
3
1
2
5
4
Explanation for Sample Output 1
In the above arrangement, 3 is neither between 2 and 4, nor is it between 1 and 5. Also, 2 is not between 1 and 3, and 4 is not between 3 and 5. Thus, it satisfies the condition of the exhibition organizers.