CF1408F.Two Different

You are given an integer $n$ .

You should find a list of pairs $(x_1, y_1)$ , $(x_2, y_2)$ , ..., $(x_q, y_q)$ ( $1 \leq x_i, y_i \leq n$ ) satisfying the following condition.

Let's consider some function $f: \mathbb{N} \times \mathbb{N} \to \mathbb{N}$ (we define $\mathbb{N}$ as the set of positive integers). In other words, $f$ is a function that returns a positive integer for a pair of positive integers.

Let's make an array $a_1, a_2, \ldots, a_n$ , where $a_i = i$ initially.

You will perform $q$ operations, in $i$ -th of them you will:

1. assign $t = f(a_{x_i}, a_{y_i})$ ( $t$ is a temporary variable, it is used only for the next two assignments);
2. assign $a_{x_i} = t$ ;
3. assign $a_{y_i} = t$ .

In other words, you need to simultaneously change $a_{x_i}$ and $a_{y_i}$ to $f(a_{x_i}, a_{y_i})$ . Note that during this process $f(p, q)$ is always the same for a fixed pair of $p$ and $q$ .

In the end, there should be at most two different numbers in the array $a$ .

It should be true for any function $f$ .

Find any possible list of pairs. The number of pairs should not exceed $5 \cdot 10^5$ .

The single line contains a single integer $n$ ( $1 \leq n \leq 15\,000$ ).

In the first line print $q$ ( $0 \leq q \leq 5 \cdot 10^5$ ) — the number of pairs.

In each of the next $q$ lines print two integers. In the $i$ -th line print $x_i$ , $y_i$ ( $1 \leq x_i, y_i \leq n$ ).

The condition described in the statement should be satisfied.

If there exists multiple answers you can print any of them.

In the first example, after performing the only operation the array $a$ will be $[f(a_1, a_2), f(a_1, a_2), a_3]$ . It will always have at most two different numbers.

In the second example, after performing two operations the array $a$ will be $[f(a_1, a_2), f(a_1, a_2), f(a_3, a_4), f(a_3, a_4)]$ . It will always have at most two different numbers.