Let’s call the sequence of positive integers

*N-perfect*, if the following conditions are satisfied:

- the sequence contains all the numbers 1, 2, …,
*N*;
- its length does not exceed 2
*N*;
- all the numbers in the sequence are different;
- the sum of any of its first
*k* members is divisible by *k*.

For example, the sequence 1, 3, 2, 6, 8 is 3-perfect.

### Input

The only line contains integer *N* (1 ≤ *N* ≤ 250000).

### Output

Output *N*-perfect sequence in a single line. Its members must not exceed 10^{13}. Separate numbers with spaces. At least one such sequence always exists. If several answers are possible, output any one of them.

### Sample

**Problem Author: **Aleksandr Bacherikov