+ Time limit: 1 second + Memory limit: 256 megabytes ---------- Pegah introduced herself as Minoo's travel companion. Now they want to start the marvelous tour by train. Their train has $n$ wagons, and for every $1 \leq i \leq n$, exactly one of the wagons has $i$ compartments. The compartments of the train are numbered sequentially from left to right, from $1$ to $\frac{n \times (n+1)}{2}$. The "number" of a wagon is equal to the number of its leftmost compartment. We know the wagons are connected in an order such that the number of wagons whose number is odd is maximized. What is the arrangement of the wagons in this train? # Input The only input is the number $n$, the total number of wagons. $$ 1 \leq n \leq 100\ 000 $$ # Output Output $n$ numbers, representing the number of compartments in each wagon from left to right. If several optimal arrangements exist, output any one of them. # Example ## Sample Input ``` 5 ``` ## Sample Output ``` 2 1 3 4 5 ``` **Sample Explanation:** The wagon numbers (leftmost compartment indices) for the arrangement 5 4 3 1 2 are 11, 7, 4, 3, 1 respectively, and among all different arrangements of $n$ wagons, the maximum number of wagons whose number is odd is 4.