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, \dots~

Bruno is convinced that this is better: ~B, A, B, C, B, A, B, C, B, A, B, C, \dots~

Goran laughs at them and will use this sequence: ~C, C, A, A, B, B, C, C, A, A, B, B, \dots~

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.

Input Specification

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 A, B and C. These are, in order, the correct answers to the questions in the exam.

Output Specification

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

5
BAACC

Sample Output 1

3
Bruno

Sample Input 2

9
AAAABBBBB

Sample Output 2

4
Adrian
Bruno
Goran