Switch and Flip

1000ms

262144K

Description:

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.

Input:

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 $$$i\neq j$$$).

Output:

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.

Sample Input:

3
2 1 3

Sample Output:

Sample Input:

5
1 2 3 4 5

Sample Output:

Note:

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.

Informação

Provedor Codeforces

Código CF1491G