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.

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.

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.

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