quantum mechanics - How many eigenstates for four (non-identical) spin 1/2 particles?

Question

Consider a system of four non-identical spin 1/2 particles. Find the possible values for the total spin and state the number of eigenstates for each of these.

Attempt

So I coupled S1 and S2 to get S12 and I also coupled S3 and S4 to get S34. I will then couple S12 and S34 to get S1234: (states are in the form (S1, S2, S12, m))

Eigenstates for S12: {(1/2, 1/2, 1, 1),(1/2, 1/2, 1, 0),(1/2, 1/2, 1, -1),(1/2, 1/2, 0, 0)}

Eigenstates for S34: {(1/2, 1/2, 1, 1),(1/2, 1/2, 1, 0),(1/2, 1/2, 1, -1),(1/2, 1/2, 0, 0)}

Eigenstates for S1234: {(1,1,2,2),(1,1,2,1),(1,1,2,0),(1,1,2,-1),(1,1,2,-2),(1,1,1,1),(1,1,1,0),(1,1,1,-1),(1,1,0,0),(1,0,1,1),(1,0,1,0),(1,0,1,-1),(0,1,1,1),(0,1,1,0),(0,1,1,-1),(0,0,0,0)}

That would make 16 different states but i'm not sure about the last 7 states (it disagrees with the answers my friends have). Cheers!