A14110. Switch and Flip

There are $n$ coins labeled from $1$ to $n$ . Initially, coin $c_i$ is on position $i$ and is facing upwards (( $c_1, c_2, \dots, c_n)$ is a permutation of numbers from $1$ to $n$ ). You can do some operations on these coins.

In one operation, you can do the following:

- Choose $2$ distinct indices $i$ and $j$ .
- Then, swap the coins on positions $i$ and $j$ .
- Then, flip both coins on positions $i$ and $j$ . (If they are initially faced up, they will be faced down after the operation and vice versa)

Construct a sequence of at most $n+1$ operations such that after performing all these operations the coin $i$ will be on position $i$ at the end, facing up.

Note that you do not need to minimize the number of operations.

The first line contains an integer $n$ ( $3 \leq n \leq 2 \cdot 10^5$ ) — the number of coins.

The second line contains $n$ integers $c_1,c_2,\dots,c_n$ ( $1 \le c_i \le n$ , $c_i \neq c_j$ for $i\neq j$ ).

In the first line, output an integer $q$ $(0 \leq q \leq n+1)$ — the number of operations you used.

In the following $q$ lines, output two integers $i$ and $j$ $(1 \leq i, j \leq n, i \ne j)$ — the positions you chose for the current operation.

Let coin $i$ facing upwards be denoted as $i$ and coin $i$ facing downwards be denoted as $-i$ .

The series of moves performed in the first sample changes the coins as such:

- $[~~~2,~~~1,~~~3]$
- $[-3,~~~1,-2]$
- $[-3,~~~2,-1]$
- $[~~~1,~~~2,~~~3]$

In the second sample, the coins are already in their correct positions so there is no need to swap.