In the rail fence cipher (also called zigzag cipher), the letters of the plaintext are initially written downwards and diagonally on successive "rails" of an imaginary fence, and then moving up after the bottom rail has been reached. When the top rail is reached, the message is again written downwards until the whole plaintext is written out.

If the text

And now for something completely different.

is written as such across four rails, we get the following result

A#####w#####s#####i#####m#####l#####f#####.
#n###o# ### #o###h#n###o#p###e#y###f#e###t#
##d#n###f#r###m#t###g#c###l#t### #i###r#n##
### #####o#####e##### #####e#####d#####e###

The encoded message is then formed by reading the letters on each rail from left to right, and going through the rails top to bottom. The encoded message for the above example thus reads as

Awsimlf.no  ohnopeyfetdnfrmtgclt irn oe ede

Assignment

• Write a function encode that takes two arguments: i) a paintext $$p$$ (str) and ii) a number of rails $$n$$. The function must return the ciphertext (str) that results from applying to the rail fence cipher to plaintext $$p$$ with $$n$$ rails.

• Write a function decode that takes two arguments: i) a ciphertext resulting from applying the rail fence cipher and ii) the number of rails $$n$$ (int) used. The function must return the plaintext (str).

Example

>>> encode('And now for something completely different.', 1)
'And now for something completely different.'
>>> encode('And now for something completely different.', 2)
'Adnwfrsmtigcmltl ifrn.n o o oehn opeeydfeet'
>>> encode('And now for something completely different.', 3)
'Anfstgmt fnn o o oehn opeeydfeetdwrmicllir.'
>>> encode('And now for something completely different.', 4)
'Awsimlf.no  ohnopeyfetdnfrmtgclt irn oe ede'
>>> encode('And now for something completely different.', 5)
'Aftm nn oehopydetdwrmicllir. o on eefensgtf'

>>> decode('And now for something completely different.', 1)
'And now for something completely different.'
>>> decode('Adnwfrsmtigcmltl ifrn.n o o oehn opeeydfeet', 2)
'And now for something completely different.'
>>> decode('Anfstgmt fnn o o oehn opeeydfeetdwrmicllir.', 3)
'And now for something completely different.'
>>> decode('Awsimlf.no  ohnopeyfetdnfrmtgclt irn oe ede', 4)
'And now for something completely different.'
>>> decode('Aftm nn oehopydetdwrmicllir. o on eefensgtf', 5)
'And now for something completely different.'