Problem Statement

You are given an integer $N$. Determine whether there exists a simple connected undirected graph with $N$ vertices numbered $1$ to $N$ that satisfies the following condition, and if it exists, show one such graph.

• There exists an integer $X$ such that for any vertex $v$, the sum of the numbers of all vertices other than $v$ that can be reached from $v$ by traversing an edge once or twice is $X$.

Constraints

• $2 \le N \le 200$
• All input values are integers.

Input

The input is given from Standard Input in the following format:

N

Output

If there does not exist a simple connected undirected graph with $N$ vertices satisfying the condition in the problem statement, print -1. If it exists, print the number of edges $M$ on the first line. On the $i$-th of the following $M$ lines, print two integers. These represent the vertex numbers of the endpoints of the $i$-th edge.

Any constructed graph that satisfies the condition will be accepted.