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 (see Resources tab).