The Enigma Machine

The Enigma machine encrypted messages with rotors: wired wheels that scramble the alphabet and turn after every key press, so the same letter comes out differently each time. Write enigma(text, rotors, start, plugs) that returns text encrypted by the simplified Enigma described here.

The parts. Letters are numbered A = 0, B = 1, up to Z = 25. Each rotor has a wiring, a string of 26 letters, and a notch letter; the reflector is one more wiring. Your starter code has them all, as the dictionary ROTORS (name: (wiring, notch)) and the string REFLECTOR:

Rotor      Wiring                      Notch
I          EKMFLGDQVZNTOWYHXUSPAIBRCJ  Q
II         AJDKSIRUXBLHWTMCQGZNPYFVOE  E
III        BDFHJLCPRTXVZNYEIWGAKMUSQO  V
IV         ESOVPZJAYQUIRHXLNFTGKDCMWB  J
V          VZBRGITYUPSDNHLXAWMJQOFEKC  Z
Reflector  YRUHQSLDPXNGOKMIEBFZCWVJAT

• rotors names three different rotors from left to right, for example ['I', 'II', 'III'].
• start is three capital letters: the starting positions of the left, middle and right rotor (a position is a letter, A = 0 to Z = 25).
• plugs is a list of two-letter strings such as 'AQ': the plugboard swaps the two letters of each pair. No letter is in more than one pair, and the list may be empty.

Stepping. Before each letter is encrypted, the rotors turn, depending on where they were before this key press:

• if the middle rotor is at its notch letter, the middle rotor and the left rotor both move one place;
• otherwise, if the right rotor is at its notch letter, the middle rotor moves one place;
• the right rotor always moves one place.

Moving one place means the position goes up by 1, wrapping from Z back to A. Because of the first rule, the middle rotor moves on two key presses in a row when it reaches its own notch, exactly as the real machine did.

The path of a letter. After the stepping, the letter's number c travels:

• through the plugboard (if c is in a pair, it becomes the other letter of the pair);
• into the right rotor, then the middle rotor, then the left rotor: a rotor at position p with wiring w turns c into (w[(c + p) % 26] - p) % 26, where w[i] means the number of the i-th letter of the wiring;
• through the reflector: c becomes the number of REFLECTOR[c];
• back out through the left rotor, then the middle rotor, then the right rotor: a rotor at position p turns c into (j - p) % 26, where j is the place in its wiring that holds the letter numbered (c + p) % 26;
• through the plugboard again.

Letters of text, upper or lower case, are encrypted and written in upper case. Every other character is copied unchanged and does not turn the rotors.

Examples

enigma("AAAAA", ["I", "II", "III"], "AAA", [])          # returns 'BDZGO'
enigma("BDZGO", ["I", "II", "III"], "AAA", [])          # returns 'AAAAA'
enigma("Hi there!", ["III", "I", "V"], "KEY", ["AB", "QZ"])  # returns 'QP WZPQF!'

In the first example the right rotor moves from A to B before the first letter, and the first A comes out as B. The second example shows the machine's best-known property: with the same settings, encrypting the encrypted text gives the message back.

Constraints

• text has 0 to 30,000 characters.
• plugs has 0 to 13 pairs.