The car registering system of a city assigns two types of numbers:

The Customer ID - it's a natural number between 0 and 17558423 inclusively, which is assigned to the car buyers in the following order: the first customer receives ID 0, the second customer receives ID 1, the third customer receives ID 2, and so on.

Number Plate - assigned to the car and contains the series ( three Latin letters from ‘a’ to ‘z’) and the serial number (three digits from 0 to 9).
Example: aaa001. Each Number Plate is related to the given Customer ID. For example: Number Plate aaa000 is related to Customer ID 0; Number Plate aaa001 is related to Customer ID 1, and so on.

Write a function findPlate which takes the Customer ID as an argument, calculates the Number Plate corresponding to this ID and returns it as a string, considering the following:

The serial numbers start at 001, end at 999.

The series change once the serial number hits 999. The left letter changes first, alphabetically:

aaa001...aaa999, 
baa001...baa999,
...... , 
zaa001...zaa999

As soon as the left letter reaches z and the series z** has moved through all the serial numbers the middle letter changes alphabetically as follows:

aba001...aba999, 
bba001... bba999, 
cba001...cba999, 
......, 
zba001...zba999, 
aca001...aca999, 
bca001...bca999,

As soon as the middle letter and the left letter both reaches z and the series zz* has moved through all its serial numbers, the right letter changes alphabetically as follows:

aab001...aab999, 
bab001...bab999, 
cab001...cab999, 
......, 
zab001...zab999, 
abb001...abb999, 
bbb001...bbb999, 
cbb001...cbb999, 
......,
zbb001...zbb999, 
acb001...acb999, 
......, 
zzz001...zzz999

When all the possible series and their serial numbers are exhausted the last Number Plate will be zzz999.

Notes:

• No spaces are allowed between the characters in the returned string. So 'abc123' is valid, but 'a b c 1 2 3' is not.
• If the serial number has less than 3 digits, the missing places should be filled with zeroes. Example: serial number '12' should equal '012'; serial number '4' should equal '004'. Customer IDs starts with 0.

Tests

findPlate(3)
findPlate(1487)
findplate(17558423)
findPlate(234567)

Good luck!

This challenge comes from William_2004 on CodeWars. Thank you to CodeWars, who has licensed redistribution of this challenge under the 2-Clause BSD License!

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