silver_Target_Practice (USACO December_Contest)
Time limit: 2 seconds | Memory limit: 256 MB | Task type: batch
Algorithms: case analysis, simulation, prefix sum, implementation

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

Starter code:

Grader code:

Setup script:

Evaluation script: