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.

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.

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.

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