Problem Statement

You are given $a permutation P=(P_1,P_2,\ldots,P_N)$ of $(1,2,\ldots,N)$.
You can repeat the following two kinds of operations in any order to make P sorted in increasing order.

• Operation A: Choose an integer i such that $1 \leq i \leq N-1$, and swap P_i and P_{i+1}.

• Operation B: Choose an integer i such that $1 \leq i \leq N-2$, and swap P_i and P_{i+2}.

Find a sequence of operations with the following property:

• The number of Operations A is the minimum possible.

• The total number of operations is not larger than 10^5.

Under the Constraints of this problem, we can prove that a solution always exists.

Input

Input is given from Standard Input in the following format:
N
$P_1 P_2 \ldots P_N$

Output

Let S be the number of operations in your answer.
Print S+1 lines.
The first line should contain S.
The $(s+1)-th (1 \leq s \leq S)$ line should contain the following:

• A i if the s-th operation is Operation A, and the integer chosen in this operation is i.

• B i if the s-th operation is Operation B, and the integer chosen in this operation is i.

If there are multiple solutions satisfying the condition, printing any of them will be accepted.

Constraints

• $2 \leq N \leq 400$
• $1 \leq P_i \leq N$ $,(1 \leq i \leq N)$
• $P_i \neq P_j$ $,(1 \leq i < j \leq N)$
• All values in input are integers.

Sample Input 1

4
3 2 4 1

Sample Output 1

4
A 3
B 1
B 2
B 2

In this Sample Output, P changes like this: $(3,2,4,1) \rightarrow (3,2,1,4) \rightarrow (1,2,3,4) \rightarrow (1,4,3,2) \rightarrow (1,2,3,4)$.
Note that you don't have to minimize the total number of operations.

Sample Input 2

3
1 2 3

Sample Output 2

0

Sample Input 3

6
2 1 4 3 6 5

Sample Output 3

3
A 1
A 3
A 5

见题面 Input 部分

见题面 Output 部分