Score : $700$ points

Problem Statement

You are given an integer $N$. Build an undirected graph with $N$ vertices with indices $1$ to $N$ that satisfies the following two conditions:

• The graph is simple and connected.
• There exists an integer $S$ such that, for every vertex, the sum of the indices of the vertices adjacent to that vertex is $S$.

It can be proved that at least one such graph exists under the constraints of this problem.

Constraints

• All values in input are integers.
• $3 \leq N \leq 100$

Input

Input is given from Standard Input in the following format:

$N$

Output

In the first line, print the number of edges, $M$, in the graph you made. In the $i$-th of the following $M$ lines, print two integers $a_i$ and $b_i$, representing the endpoints of the $i$-th edge.

The output will be judged correct if the graph satisfies the conditions.

3

2
1 3
2 3

• For every vertex, the sum of the indices of the vertices adjacent to that vertex is $3$.