$N$ chocolate frogs are trying to move from Coco Land to Hanbyeol Land. There is a river between Coco Land and Hanbyeol Land, and since chocolate melts when it touches water, they must cross the river using $N$ stepping stones to get from Coco Land to Hanbyeol Land. The stepping stones are numbered $1$ to $N$ in order. For convenience, let the riverbank on the Coco Land side be $0$ and the riverbank on the Hanbyeol Land side be $N+1$.

The chocolate frogs are also numbered $1$ to $N$, and they are stacked at position $0$ in order from $N$ at the bottom to $1$ at the top. Only one frog can move at a time, and if multiple frogs are stacked vertically, only the top frog can move. Furthermore, a frog at position $i$ can only move to position $i+1$ or $i+2$ in a single move, cannot move backward, and a frog with a larger number cannot be placed on top of a frog with a smaller number.

Hanbyeol Land is protected by a barrier, so if the frogs do not enter in descending order of their numbers (from frog $N$ to frog $1$), the magic on the chocolate frogs will be broken. Can all the chocolate frogs safely reach Hanbyeol Land?

Input

The first line contains an integer $N$. $(1 \le N \le 1\,000)$

Output

If all chocolate frogs can safely cross the river, output the number of moves $M$ on the first line. This value does not need to be the minimum.

From the second line onwards, output the $M$ moves of the frogs in order, one per line. When the top frog at position $i$ moves to position $j$, output $i$ and $j$ separated by a space.

If they cannot cross the river, output -1 on the first line.

Examples

Input 1

2

Output 1

4
0 2
0 1
1 3
2 3