# 4967. A number game

Foxity and Foxitu are good friends. They like to play number games. One day, Foxity played ICPC with his teammates, leaving Foxitu alone at labs. So he played a number game with himself.

There are $n$ numbers from $1$ to $n$ in a set, each time he can choose two distinct number $a$ and $b$($a \ne b$). He firstly remove $a$ and $b$ from this set, then insert $a+b$ and $\lvert a-b \rvert$ to the set. His goal is to leave the set with only two elements, and He can only operate on this set at most $n$ times.

Please provide any of his possible operation sequence.

There will be no identical elements in the set, and identical elements are treated as one element.

### 输入格式

One line contains one integer $n(2 \le n \le 10^5)$ ,which is the size of the set.

### 输出格式

The first line contains an integer $m$, which is the number of operations.
Follow $m$ lines with two integer $a$ and $b$, which represents each operation.

### 样例

Input
10

Output
5
4 5
1 9
3 7
2 8
4 6

Input
6

Output
3
1 6
2 5
3 4


### 提示

We guarantee that the first $9$ test data satisfying that $n$ is less than $11$.

16 人解决，30 人已尝试。

17 份提交通过，共有 79 份提交。

6.1 EMB 奖励。