Collision 2

Problem Description

In the $xy$ coordinate system there are $N$ people. The $i$-th person is at position $(X_i, Y_i)$, and all positions are distinct.

We have a string $S$ of length $N$ consisting of L and R. $S_i =$ R means the $i$-th person faces right, and $S_i =$ L means the $i$-th person faces left.

Now everyone starts walking in the direction they face: facing right means $x$ increases, facing left means $x$ decreases.

For example, when $(X_1, Y_1) = (2, 3), (X_2, Y_2) = (1, 1), (X_3, Y_3) = (4, 1)$ and $S =$ RRL, the movement of the people is as shown in the figure.

We call it a collision when two people walk toward each other and meet at one position. If the people can walk forever, will anyone collide?

Input Format

The first line contains an integer $N$;

The next $N$ lines each contain two integers $X_i$ and $Y_i$, the position of the $i$-th person;

The last line contains a string $S$ of length $N$ consisting of L and R.

Output Format

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

Sample Input 1

3
2 3
1 1
4 1
RRL

Sample Output 1

Yes

Sample Input 2

2
1 1
2 1
RR

Sample Output 2

No

Sample Input 3

10
1 3
1 4
0 0
0 2
0 4
3 1
2 4
4 2
4 4
3 3
RLRRRLRLRR

Sample Output 3

Yes

Constraints

For all data, $2 \leq N \leq 2\times 10^5$, $0 \leq X_i \leq 10^9$, $0 \leq Y_i \leq 10^9$.