Problem Statement

Have you noticed this part of AtCoder website?

Here the numbers are carefully chosen so that we can jump from any page to any page in small number of steps, while each page doesn't contain too many links.
In this task you are asked to do a similar thing with only two links on each page!
Snuke made a website with N pages numbered 1 through N.
For each $i (1 \leq i \leq N), choose two integers a_i$ and $b_i (1 \leq a_i, b_i \leq N)$, and add two links on Page i: a link to Page a_i and a link to Page b_i.
The website must satisfy the following constraint:

• You must be able to jump from any page to any other page by clicking at most 10 links.

Under the constraints of the problem, we can prove that this is always possible.

Input

Input is given from Standard Input in the following format:
N

Output

Print the answer in the following format:
a_1 \ b_1
:
a_N \ b_N

In case there are multiple possible answers, print any.

Constraints

• $1 \leq N \leq 1000$

Sample Input 1

1

Sample Output 1

1 1

Snuke made an excellent website with only one page.
It even contains two links to itself!

Sample Input 2

3

Sample Output 2

2 3
1 3
1 2

Here we can jump from any page to any other page by a direct link.

见题面 Input 部分

见题面 Output 部分