Problem Description

Bessie is a bionic cow. On a number line, she is trying to hit $T$ ($1 \leq T \leq 10^5$) targets located at different positions. Bessie starts at position $0$ and follows a sequence of $C$ ($1 \leq C \leq 10^5$) commands consisting of L, F, and R:

• L: Bessie moves one unit to the left.
• R: Bessie moves one unit to the right.
• F: Bessie fires. If there is a target at Bessie's current position, it is hit and destroyed. It cannot be hit again.

Before Bessie starts, you are allowed to modify at most one command in the sequence. What is the maximum number of targets Bessie can hit?

Input Format

The first line contains $T$ and $C$.

The next line contains $T$ positions of the targets, all different integers within the range $[-C, C]$.

The next line contains a sequence of $C$ commands, consisting only of the characters F, L, and R.

Output Format

Output the maximum number of targets Bessie can hit after modifying at most one command.

Sample Input and Output

Sample Input #1

3 7
0 -1 1
LFFRFRR

Sample Output #1

3

Sample Input #2

1 5
0
FFFFF

Sample Output #2

1

Sample Input #3

5 6
1 2 3 4 5
FFRFRF

Sample Output #3

3

Notes

Sample Explanation 1

If you do not modify the command sequence, Bessie will hit two targets.

If you change the last command from R to F, Bessie will hit three targets:

Sample Explanation 2

If the command sequence is not modified, the only target at position $0$ will be hit.

Since a target cannot be destroyed multiple times, the answer is $1$.

Test Case Properties

• Test cases $4-6$ satisfy $T, C \le 1000$.
• Test cases $7-15$ have no additional restrictions.

见题面 Input 部分

见题面 Output 部分