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 2N;
• 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.

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

Output N-perfect sequence in a single line. Its members must not exceed 10¹³. Separate numbers with spaces. At least one such sequence always exists. If several answers are possible, output any one of them.