Divide into 2 groups

Divide the numbers $1,2,...,n$ into two groups so that the absolute difference between the sums of the elements in these groups is the smallest possible.

Input

One integer $n(2\le n\le 10^5)$.

Output

In the first line, print two integers — the number of elements in the first and second groups.

In the second line, print the elements of the first group, and in the third line — the elements of the second group.

The elements within each group can be printed in any order. Each number from $1$ to $n$ must be included in exactly one of the groups.

Examples