Eccoci.

Surprisingly there are only three numbers that can be written as the sum of fourth powers of their digits: \begin{align} 1634 &= 1^4 + 6^4 + 3^4 + 4^4\\ 8208 &= 8^4 + 2^4 + 0^4 + 8^4\\ 9474 &= 9^4 + 4^4 + 7^4 + 4^4 \end{align}

As $1 = 1^4$ is not a sum it is not included.

The sum of these numbers is $1634 + 8208 + 9474 = 19316$.

Find the sum of all the numbers that can be written as the sum of fifth powers of their digits.