 UCalgary Competitive Programming Week 12

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2021-11-26 13:21 AKST

UCalgary Competitive Programming Week 12

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2021-12-03 13:00 AKST
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Problem LMusical Scales

The following are musical notes in “increasing order”:

$A$, $A\sharp$, $B$, $C$, $C\sharp$, $D$, $D\sharp$, $E$, $F$, $F\sharp$, $G$, $G\sharp$

The difference between consecutive notes is a semitone, and the sequence wraps around so the note that is one semitone above $G\sharp$ is $A$. The difference between a tone is the same as two semitones. So the note that is one tone above $B$ is $C\sharp$. The note that is one tone above $G$ is $A$.

We do not worry about flats such as $C\flat$ nor do we worry about adding a $\sharp$ sign to $B$ and $E$ in this problem (they are aliases for notes that are already listed).

A major scale is defined by a note (such as $A$ or $C\sharp$) and all other notes following that one in an arithmetic progression:

tone, tone, semitone, tone, tone, tone, semitone

The starting note appears in the name of the scale.

For example, the scale $A\sharp$-major consists of the following notes:

$A\sharp$, $C$, $D$, $D\sharp$, $F$, $G$, $A$, $A\sharp$

(by convention, the first note is repeated at the end of the sequence).

Note that $A\sharp$-major is typically not considered a standard musical scale. It is identical in sound to $B\flat$, and proper notation of $A\sharp$-major would require the use of double-sharps. We ignore such issues in this problem and just use the $12$ notes given at the top of this problem.

Finally, in this problem a song is just a sequence of notes. Your job is to identify all major scales such that the song uses only notes in that scale.

Input

The first line of input is an integer $1\leq n \leq 100$ denoting the number of notes played in a song. The second line consists of a sequence of notes, separated by spaces.

Output

Output consists of a single line that lists all scales the song may be played in. Consecutive scales should be separated by a single space and the scales must appear in lexicographic order. If the song may not fit in any one of these scales, simply output a line containing the text none.

Sample Input 1 Sample Output 1
10
C D F D C D F F F C
A# C D# F
Sample Input 2 Sample Output 2
6
A B A F# G# C
none