Self-Descriptive Numbers

The number 10213223 is self-descriptive. Count the number of zeros, ones, twos, and threes that are contained in this number and you have 1 zero, 2 ones, 3 twos, 2 threes, but that is a replica of the number itself 10|21|32|23.

Write a function that returns true if its argument is a self-descriptive number, false if not.

Examples

selfDescriptive(22) ➞ true

selfDescriptive(3999) ➞ false

selfDescriptive(31331419) ➞ true

selfDescriptive(21321316) ➞ false

selfDescriptive(4132232416171) ➞ false

selfDescriptive(31331819) ➞ true

Notes

• Since the number's descriptors are always in pairs, any self-descriptive number must have an even number of digits.
• The largest self-descriptive number possible is reportedly 71322723161814151019.