Problem 3. Target Practice

USACO 2023 December Contest, Silver

Bessie is a robovine, also known as a cowborg. She is on a number line trying to shoot a series of $T$ $(1 \leq T \leq 10^5)$ targets located at distinct positions. Bessie starts at position $0$ and follows a string of $C$ $(1 \leq C \leq 10^5)$ commands, each one of L, F, or 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, and cannot be hit again.

If you are allowed to change up to one command in the string to a different command before Bessie starts following it, what is the maximum number of targets that Bessie can hit?

INPUT FORMAT (input arrives from the terminal / stdin):

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

The next line contains the locations of the $T$ targets, distinct integers in the range $[-C,C]$.

The next line contains the command string of length $C$, containing only the characters F, L, and R.

OUTPUT FORMAT (print output to the terminal / stdout):

Print the maximum number of targets that Bessie can hit after changing up to one command in the string.

SAMPLE INPUT:

3 7
0 -1 1
LFFRFRR

SAMPLE OUTPUT:

3

If you make no changes to the string, Bessie will hit two targets:

Command | Position | Total Targets Hit
--------+----------+-------------------
Start   |  0       | 0 
L       | -1       | 0
F       | -1       | 1
F       | -1       | 1 (can't destroy target more than once)
R       |  0       | 1
F       |  0       | 2
R       |  1       | 2
R       |  2       | 2

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

Command | Position | Total Targets Hit
--------+----------+-------------------
Start   |  0       | 0 
L       | -1       | 0
F       | -1       | 1
F       | -1       | 1 (can't destroy target more than once)
R       |  0       | 1
F       |  0       | 2
R       |  1       | 2
F       |  1       | 3

SAMPLE INPUT:

1 5
0
FFFFF

SAMPLE OUTPUT:

1

If the commands are left unchanged, the only target at 0 will be destroyed. Since a target cannot be destroyed multiple times, the answer is 1.

SAMPLE INPUT:

5 6
1 2 3 4 5
FFRFRF

SAMPLE OUTPUT:

3

SCORING: Inputs 4-6: $T,C \le 1000$Inputs 7-15: No additional constraints.

Problem credits: Suhas Nagar