Problem Statement

You are given $a permutation P=(P_1,P_2,\cdots,P_{2N})$ of $(1,2,\cdots,2N)$.
The following operation may be performed between 0 and N times (inclusive).

• Choose an integer $x (1 \leq x \leq 2N-1).$ Swap the values of P_x and P_{x+1}.

Present a sequence of operations that make P satisfy the following conditions.

• P_i<P_{i+1} for each $i=1,3,5,\cdots,2N-1$;
• P_i>P_{i+1} for each $i=2,4,6,\cdots,2N-2$.

It can be proved that such a sequence of operations always exists.

Input

Input is given from Standard Input in the following format:
N
$P_1 P_2 \cdots P_{2N}$

Output

Print a desired sequence of operations in the following format:
K
$x_1 x_2 \cdots x_K$

Here, K is the number of operations performed $(0 \leq K \leq N)$, and x_i is the value of x chosen in the $i-th operation (1 \leq x_i \leq 2N-1)$.
If there are multiple solutions satisfying the condition, printing any of them will be accepted.

Constraints

• $1 \leq N \leq 10^5$
• $(P_1,P_2,\cdots,P_{2N})$ is a permutation of $(1,2,\cdots,{2N})$.
• All values in input are integers.

Sample Input 1

2
4 3 2 1

Sample Output 1

2
1 3

These operations make P=(3,4,1,2), which satisfies the conditions.

Sample Input 2

1
1 2

Sample Output 2

0

见题面 Input 部分

见题面 Output 部分