Many Swaps Sorting

Snuke has a sequence p, which is a permutation of (0,1,2, ...,N-1). The i-th element (0-indexed) in p is p_i.

He can perform N-1 kinds of operations labeled 1,2,...,N-1 any number of times in any order. When the operation labeled k is executed, the procedure represented by the following code will be performed:

for(int i=k;i<N;i++) swap(p[i],p[i-k]);

He would like to sort p in increasing order using between 0 and 10^{5} operations (inclusive). Show one such sequence of operations. It can be proved that there always exists such a sequence of operations under the constraints in this problem.

Constraints

• 2 \leq N \leq 200
• 0 \leq p_i \leq N-1
• p is a permutation of (0,1,2,...,N-1).

Input

Input is given from Standard Input in the following format:

N p_0 p_1 ... p_{N-1}

Output

Let m be the number of operations in your solution. In the first line, print m. In the i-th of the following m lines, print the label of the i-th executed operation. The solution will be accepted if m is at most 10^5 and p is in increasing order after the execution of the m operations.

Examples

Input

5 4 2 0 1 3

Output

4 2 3 1 2

Input

9 1 0 4 3 5 6 2 8 7

Output

11 3 6 1 3 5 2 4 7 8 6 3

inputFormat

Input

Input is given from Standard Input in the following format:

N p_0 p_1 ... p_{N-1}

outputFormat

Output

Let m be the number of operations in your solution. In the first line, print m. In the i-th of the following m lines, print the label of the i-th executed operation. The solution will be accepted if m is at most 10^5 and p is in increasing order after the execution of the m operations.

Examples

Input

5 4 2 0 1 3

Output

4 2 3 1 2

Input

9 1 0 4 3 5 6 2 8 7

Output

11 3 6 1 3 5 2 4 7 8 6 3

样例

9
1 0 4 3 5 6 2 8 7

11
3
6
1
3
5
2
4
7
8
6
3

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