Let
A=[4312]A = \begin{bmatrix} 4 & 3 \\ 1 & 2 \end{bmatrix}A=[4132]
and suppose that
A2004=[abcd]A^{2004} = \begin{bmatrix} a & b \\ c & d \end{bmatrix}A2004=[acbd].
Then, a+b+c+d52004=\dfrac{a+b+c+d}{5^{2004}} = 52004a+b+c+d= ___.