Help me with pythonBessie is a robovine, also known as a cowborg. She is on a number line trying to shoot a series of $)T({10}^5$ targets located at distinct positions. Bessie starts at position $0$ and follows a string of $)C({10}^5$ 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?

INPUT FORMAT $($pipe 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 $($pipe stdout$)$:

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

SAMPLE INPUT:

$37$

$0-11$

LFFRFRR

SAMPLE OUTPUT:

$3$

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

$\backslash$table$[[$Command$,$Position,Total Targets Hit$],[$Start$,0,0],[$L$,-1,0],[$F$,-1,1],[$F$,-1,1],[$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:

$\backslash$table$[[$Command$,$Position,Total Targets Hit$],[$Start$,0,0],[$L$,-1,0],[$F$,-1,1],[$F$,-1,1],[$R$,0,1],[$F$,0,2]]$

R

F

$12$

SAMPLE INPUT:

$15$

$0$

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:

$56$

$12345$

FFRFRF

SAMPLE OUTPUT:

$3$

SCORING:

Inputs $4-6$: $T,C1000$

Inputs $7-15$: No additional constraints.

Problem credits: Suhas Nagar