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