Problem Statement

Construct $1$ simple undirected graph with $N$ vertices numbered from $1$ to $N$ such that the number of distinct values among the elements of its degree sequence is maximized.

Notes

• An undirected graph $G$ is simple if $G$ has no self-loops or multiple edges.
• The degree sequence of an undirected graph $G$ is the sequence of the degrees of the vertices of $G$ arranged in descending order.

Input

$N$

• $N$ is an integer satisfying $2 \leq N \leq 500$

Output

Output the constructed graph in the following format. All output values must be integers.

$M$
$u_1\ v_1$
$u_2\ v_2$
$\vdots$
$u_M\ v_M$

Line $i+1\ (1 \leq i \leq M)$ of the output indicates that the $i$-th edge connects vertices $u_i$ and $v_i$ bidirectionally. It must satisfy $1 \leq u_i,v_i \leq N$.

The edges may be output in any order.

Print a newline at the end.

Sample

3

2
1 3
2 3