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


Func<char, int> toInt = c => c-'0';
 
foreach (var i in Enumerable.Range(1,5000)
	.Where(n => n == n.ToString()
		.Sum(x => Math.Pow(toInt(x), toInt(x)))))
	Console.WriteLine(i);