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Contest: Task: Related: TaskB TaskD

Score : $300$ points

Problem Statement

There are $N$ people in an $xy$-plane. Person $i$ is at $(X_i, Y_i)$. The positions of all people are different.

We have a string $S$ of length $N$ consisting of L and R.
If $S_i =$ R, Person $i$ is facing right; if $S_i =$ L, Person $i$ is facing left. All people simultaneously start walking in the direction they are facing. Here, right and left correspond to the positive and negative $x$-direction, respectively.

For example, the figure below shows the movement of people when $(X_1, Y_1) = (2, 3), (X_2, Y_2) = (1, 1), (X_3, Y_3) =(4, 1), S =$ RRL.

We say that there is a collision when two people walking in opposite directions come to the same position. Will there be a collision if all people continue walking indefinitely?

Constraints

$2 \leq N \leq 2 \times 10^5$
$0 \leq X_i \leq 10^9$
$0 \leq Y_i \leq 10^9$
$(X_i, Y_i) \neq (X_j, Y_j)$ if $i \neq j$.
All $X_i$ and $Y_i$ are integers.
$S$ is a string of length $N$ consisting of L and R.

Input

Input is given from Standard Input in the following format:

$N$
$X_1$ $Y_1$
$X_2$ $Y_2$
$\vdots$
$X_N$ $Y_N$
$S$

Output

If there will be a collision, print Yes; otherwise, print No.

Sample Input 1

Sample Output 1

Yes

This input corresponds to the example in the Problem Statement.
If all people continue walking, Person $2$ and Person $3$ will collide. Thus, Yes should be printed.

Sample Input 2

Sample Output 2

No

Since Person $1$ and Person $2$ walk in the same direction, they never collide.

Sample Input 3

Sample Output 3

Yes