You are a composer who just wrote an awesome piece of music. Now it's time to present it to a band that will perform your piece, but there's a problem! The singers vocal range doesn't stretch as your piece requires, and you have to transpose the whole piece.

Your task

Given a list of notes (represented as strings) and an interval, output a list of transposed notes in sharp notation.

• Input notes may be represented both in flat and sharp notations (more on that below).

• For this kata, assume that input is always valid and the song is at least 1 note long.

• Assume that interval is an integer between -12 and 12.

Short intro to musical notation

Transposing a single note means shifting its value by a certain interval.

The notes are as following:

A, A#, B, C, C#, D, D#, E, F, F#, G, G#.

This is using sharp notation, where '#' after a note means that it is one step higher than the note. So A# is one step higher than A.

An alternative to sharp notation is the flat notation:

A, Bb, B, C, Db, D, Eb, E, F, Gb, G, Ab.

The 'b' after a note means that it is one step lower than the note.

Examples

['G'] -> 5 steps -> ['C']
['Db'] -> -4 steps -> ['A']
['E', 'F'] -> 1 step -> ['F', 'F#']