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A - Make it Zigzag /

Time Limit: 2 sec / Memory Limit: 1024 MB

### 問題文

(1,2,\cdots,2N) の順列 P=(P_1,P_2,\cdots,P_{2N}) が与えられます．

あなたは，以下の操作を 0 回以上 N 回以下行うことができます．

• 整数 x (1 \leq x \leq 2N-1) を選ぶ． P_xP_{x+1} の値を入れ替える．

• i=1,3,5,\cdots,2N-1 について，P_i<P_{i+1} である．
• i=2,4,6,\cdots,2N-2 について，P_i>P_{i+1} である．

なお，条件を満たすような操作列が必ず存在することが証明できます．

### 制約

• 1 \leq N \leq 10^5
• (P_1,P_2,\cdots,P_{2N})(1,2,\cdots,{2N}) の順列
• 入力される値はすべて整数である

### 入力

N
P_1 P_2 \cdots P_{2N}


### 出力

K
x_1 x_2 \cdots x_K


ここで，K は行う操作の回数 (0 \leq K \leq N) であり，x_i (1 \leq x_i \leq 2N-1) は i 回目の操作で選ぶ x の値である． 条件を満たす解が複数存在する場合，どれを出力しても正解とみなされる．

### 入力例 1

2
4 3 2 1


### 出力例 1

2
1 3


### 入力例 2

1
1 2


### 出力例 2

0


Score : 400 points

### 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