Target Practice

문제

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

입력

The first line contains $TT$ and $CC$.

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

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

출력

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

3 7
0 -1 1
LFFRFRR

3

1 5
0
FFFFF

1

5 6
1 2 3 4 5
FFRFRF

3