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).
Write a program that, given the number of vases, determines a linear arrangement of the vases that satisfies the condition of the exhibition organizers.
|1 ≤ N ≤ 2,000||The number of vases|
The first and only line contains a singer integer N
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
Sample Input 1
Sample Output 1
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.