Bessie is a robovine, also known as a cowborg. She is on a number line trying to shoot a series of $T\ (1≤T≤10^5)$ targets located at distinct positions. Bessie starts at position 00 and follows a string of $C\ (1≤C≤10^5)$ 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?

The first line contains $T,C$.

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.

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

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

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.