Problem Statement

$10^6$ squares are arranged in a horizontal row. The squares are numbered $1, 2, \ldots , 10^6$ from left to right.

$N$ coins are placed on the squares. Initially, there is $1$ coin on each of the squares $A_1, A_2, \ldots , A_N$. Rusk can perform the following operation any number of times: choose $1$ coin and move it to the square adjacent on its left or right. However, he cannot perform an operation that would result in $2$ or more coins being on the same square, or an operation that would move a coin outside the squares.

Rusk's goal is to reach a state in which there is $1$ coin on each of the squares $B_1, B_2, \ldots , B_N$. Find the minimum number of operations required for this, and find $1$ sequence of operations that achieves this minimum.

Input

$N$
$A_1\ A_2\ \ldots \ A_N$
$B_1\ B_2\ \ldots \ B_N$

• $1\leq N\leq 2\times 10^5$
• $1\leq A_1 < A_2 < \ldots < A_N\leq 10^6$
• $1\leq B_1 < B_2 < \ldots < B_N\leq 10^6$
• The goal can be achieved in at most $2\times 10^5$ operations.
• All input values are integers.

Output

Output in the following format.

$M$
$k_1\ c_1$
$k_2\ c_2$
$:$
$k_M\ c_M$

On the following $M$ lines, output a sequence of operations that achieves the minimum number of operations. On line $i+1$ ($1\leq i\leq M$), output the integer $k_i$ ($1\leq k_i\leq N$) and the character $c_i$ (L or R) representing the $i$-th operation, separated by a space. This means moving the $k_i$-th coin from the left to the square adjacent on its left if $c_i$ is L, and moving the $k_i$-th coin from the left to the square adjacent on its right if it is R.

If there are multiple sequences of operations satisfying the conditions, you may output any of them.

Sample

2
1 2
2 4

3
2 R
1 R
2 R

3
1 R
2 R
2 R

3
999998 999999 1000000
999998 999999 1000000

0

4
2 4 7 8
3 4 5 6

5
3 L
1 R
4 L
3 L
4 L