A Munchausen number is a natural number n the sum of whose digits (in base 10), each raised to the power of itself, equals n.

(Munchausen is also spelled: Münchhausen.)

For instance:    3435 = 33 + 44 + 33 + 55 



Task
Find all Munchausen numbers between   1   and   5000.



Also see

 The OEIS entry:  A046253
 The Wikipedia entry:  Perfect digit-to-digit invariant, redirected from Munchausen Number


# sum power of digits
val .spod = f(.n) fold f{+}, map(f (.x-'0') ^ (.x-'0'), s2cp toString .n)
 
# Munchausen
writeln "Answers: ", where f(.n) .n == .spod(.n), series 0..5000