Three-Step Tunnels

A far away city has $n$ buildings located along a straight line going from left to right. Because the city is laid out in a straight line, traffic is always a nightmare.

A company has decided to connect the buildings with bidirectional underground tunnels to provide an alternative form of transportation. Each tunnel connects two buildings. To make navigation easy, the company requires that for any two different buildings $a$ and $b$, it must be possible to get from $a$ to $b$ using only tunnels:

• always going in the same direction: left to right if $b$ is to the right of $a$, and right to left if $b$ is to the left of $a$; and
• using at most 3 tunnels.

Design a set of tunnels that satisfies these requirements and contains at most $5n$ tunnels. You do not need to find the smallest possible set.

The only line of input contains a single integer $n$ ($2 \le n \le 500$).

On the first line, print the number $m$ of tunnels you propose to build. On each of the next $m$ lines, print two distinct integers, the numbers of the buildings connected by that tunnel. The buildings are numbered from 1 to $n$ from left to right.

$m$ must be less than or equal to $5n$. You may print the tunnels in any order. All tunnels must be distinct. For example, you may not include both "1 2" and "2 1".