# Problem E

Guillaume

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Guillaume has a unique ability to forget events before a certain point in time, only to look better in his memory. Guillaume and Arnar play pool quite often and you have a log of results from their matches. Guillaume only counts the last $k$ matches such that his win percentage is maximized, and ignores all matches before those. Guillaume cannot ignore the entire match history since Arnar will always remember the result of their last match. Win percentage is defined as the ratio between number of victories and number of valid matches. If multiple values of $k$ are possible then $k$ should be chosen such that it is minimized, because that is easier for Guillaume to remember.

A draw occurs in pool if both players decide the match is invalid and want to restart the match. If a match ends in a draw, then the match has no winner.

What’s the score according to Guillaume?

## Input

Input consists of two lines. The former line has one integer
$n$, the number of matches
logged. The latter line has a sequence of characters which
represent the results of the matches that Arnar and Guillaume
have played. The $i$-th
symbol represents the result of the $i$-th match and is `A` if Arnar won, `G` if
Guillaume won or `D` in case of a
draw.

## Output

Output a single line in the format `g-a` where $g$ is an integer representing the
number of matches won by Guillaume and $a$ is the number of matches won by
Arnar, according to Guillaume.

## Scoring

Group |
Score |
Constraints |

1 |
10 |
$n = 1$ |

2 |
30 |
$1 \leq n \leq 100$ |

3 |
20 |
$1 \leq n \leq 3 \cdot
10^5$, total amount of the symbols |

4 |
40 |
$1 \leq n \leq 3 \cdot 10^5$ |

Sample Input 1 | Sample Output 1 |
---|---|

1 G |
1-0 |

Sample Input 2 | Sample Output 2 |
---|---|

29 AAAGAGAGAAGAAAGADGAAAGGGGGGGA |
7-1 |

Sample Input 3 | Sample Output 3 |
---|---|

12 AGAGDDDDGAGA |
3-2 |

Sample Input 4 | Sample Output 4 |
---|---|

55 GGAAAAAGAAGGAAGGGGAAGGGDDAGGGGGGGGAAGAAAGGGGGGGGGAGGGAA |
12-3 |