Given a positive integer n, create a maximum-size subset X \subseteq \{1,2,\dots,n\} such that for all distinct integers a,b,c,d \in X, a+b \neq c+d.

Input

The only input line has an integer n.

Output

First print an integer k: the number of elements in X. Then, print an example how to construct X. You can print any valid solution.

Constraints

• 1 \le n \le 80

Example

Input:

11

Output:

5
2 4 6 9 10