Optimal Number Permutation

You have array a that contains all integers from 1 to n twice. You can arbitrary permute any numbers in a.

Let number i be in positions xi, yi (xi < yi) in the permuted array a. Let's define the value di = yi - xi — the distance between the positions of the number i. Permute the numbers in array a to minimize the value of the sum .

Input

The only line contains integer n (1 ≤ n ≤ 5·105).

Output

Print 2n integers — the permuted array a that minimizes the value of the sum s.

Examples

Input

2

Output

1 1 2 2

Input

1

Output

1 1

inputFormat

Input

The only line contains integer n (1 ≤ n ≤ 5·105).

outputFormat

Output

Print 2n integers — the permuted array a that minimizes the value of the sum s.

Examples

Input

2

Output

1 1 2 2

Input

1

Output

1 1

样例

1

1 1