Extraordinary 4-digit number.

There is a 4-digit number such as: abcd. When you raise each number to the power of itself and add up their products, thus: a^a + b^b + c^c + d^d, you get the original number that you started with, namely: abcd!. What is this unique 4-digit number? Thanks and have a good day.

$\begin{array}{rcll} a^a + b^b + c^c + d^d &=& abcd \\ 3^3+4^4+3^3+5^5 &=& 3435 \end{array}$