Adrian, Bruno and Goran wanted to join the bird lovers' club. However, they did not know that all applicants must pass an entrance exam. The exam consists of ~N~ questions, each with three possible answers: ~A, B~ and ~C~.
Unfortunately, they couldn't tell a bird from a whale so they are trying to guess the correct answers. Each of the three boys has a theory of what set of answers will work best:
Adrian claims that the best sequence is: ~A, B, C, A, B, C, A, B, C, A, B, C \cdots~
Bruno is convinced that this is better: ~B, A, B, C, B, A, B, C, B, A, B, C \cdots~
Goran laughs at them and will use this sequence: ~C, C, A, A, B, B, C, C, A, A, B, B \cdots~
Write a program that, given the correct answers to the exam, determines who of the three was right – whose sequence contains the most correct answers.
The first line contains an integer ~N~ ~(1 \le N \le 100)~, the number of questions on the exam.
The second line contains a string of ~N~ letters
C. These are, in order, the correct answers to
the questions in the exam.
On the first line, output ~M~, the largest number of correct answers one of the three boys gets. After that, output the names of the boys (in alphabetical order) whose sequences result in ~M~ correct answers.
Sample Input 1
Sample Output 1
Sample Input 2
Sample Output 2
4 Adrian Bruno Goran