Dodecaphony

In the past century, a new style of music composition has
emerged. Unlike more traditional methods based on keys and
chords, the technique known as *dodecaphony* focuses on using all twelve notes
equally. As a quick reminder, the twelve notes, in ascending
order are,

The sequence then wraps around so that the next note after $B$ is $C$ and so on. For this problem, we’ll ignore equivalent notations that use flats, double sharps, or double flats.

Each successive note above is considered one *semitone* away from the next. Now in our
simplified version of dodecaphony, a melody is a permutation of
the previous melody by one of three relations.

First, we have *transposition*, where
each note has been shifted up by $n$ semitones. A *retrograde* is when the notes have their order
reversed. Finally we have *inversion*
about the first note of the melody. With inversions, the first
note doesn’t change, but the rest of the notes are inverted
such that the the interval (number of semitones) between that
note and the first note is negated.

For example, if $F$ is our first note, and we want to invert an $A\sharp $, which is $5$ semitones higher, the inverted note would be a $C$, which is $5$ semitones lower. Note that the first note in an inverted melody is always just the first note of the original melody.

Given two melodies, can you tell what relation the second has to the first?

The first line contains a single integer $2 \leq l \leq 50$, the number of notes in each melody.

The next two lines each contain $l$ space separated notes. It is guaranteed that each note will be one of the twelve listed above.

Output on a single line “Transposition” if the second melody is a transposition of the first, “Retrograde” if the second melody is the first melody reversed, “Inversion” if the second melody is an inversion of the first melody, else “Nonsense” if it is none of the other cases.

If the second melody satisfies more than one relation, output the first valid relation in the order of “Transposition”, then “Retrograde”, then “Inversion”.

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

3 C E G D F# A |
Transposition |

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

7 C C G G A A G C C F F D# D# F |
Inversion |

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

7 A B C D E F G G F E D C B A |
Retrograde |

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

5 C D E F G C C C C C |
Nonsense |