Swipe is a new mobile game that has recently exploded in popularity. In each level of Swipe, you are given 2 rows of integers that can be represented as arrays $A$ and $B$ of size $N$. The objective of Swipe is to beat each level by turning array $A$ into array $B$.
There are two swipe operations you can perform on array $A$.

• Swipe right: Select the subarray $[l,r]$ and set $A_i=A_l$ for all $l\leq i \leq r$.
• Swipe left: Select the subarray $[l,r]$ and set $A_i=A_r$ for all $l\leq i \leq r$.

For example, starting with array $A=[0,1,2,3,4,5]$, if we swipe right on $[2,4]$, we would obtain the array $[0,1,2,2,2,5]$. If instead, we started with the same array $A$, and swiped left on $[3,5]$, we would obtain the array $[0,1,2,5,5,5]$. Note that these arrays are 0-indexed.
Unfortunately, the game is bugged and contains levels that are impossible to beat. Determine if it is possible to transform array $A$ into array $B$. If it is possible, determine a sequence of swipe operations that transforms array $A$ into array $B$.

The first line of input will consist of one positive integer $N$, representing the length of each of the two arrays of integers.
The second line of input contains $N$ space separated integers contained in array $A$.
The third line of input contains $N$ space separated integers contained in array $B$.

The first line of output will contain YES if there is a sequence of swipes that can transform array $A$ into array $B$; otherwise, the first line of output will contain NO.
If the first line of output is YES, the next line contains a non-negative integer $K\ (K \leq N)$, indicating the number of swipes.
Each of the next $K$ lines contain three space-separated values: $D_j,l_j,r_j$. The value $D_j$ will be either R or L, indicating that the $j^{th}$ swipe is either a right or left swipe, respectively. The values $l_j$ and $r_j$ indicate the left-end and right-end of the swipe where $0 \leq l_j \leq r_j \leq N$.

$1 \leq N \leq 300,000$
$1 \leq A_i, B_i \leq 300,000$
Note that for a subtask worth $M$ marks, you will receive $⌊\frac{M}{2}⌋$ marks for a solution that only correctly outputs the first line of output.