Degrees of freedom in a water molecule

Let's consider all of them. I know a few.

3 translational kinetic ones due to movement in the x y z space
3 rotational, as it is non linear it can rotate about any axis

These are the easy ones

I think it gets interesting when we get to the vibrational ones

We have two hydrogen atoms, both of which are capable of vibrating away/towards from the oxygen molecule. Would that constitute as 2 different pieces of vibrational freedom? With total of four degrees of vibrational freedom? Or, because they're the same vibrational freedom, is it counted as one vibrational freedom?

Now, what about the angular vibration possible due to the bent shape of the molecule? Does this ever get counted? My guess is yes it does, and thus, two more degrees. However, would this mode of vibrational be quadratic in nature?

That's a total of 12 degrees of freedom, can anyone confirm if i am correct? If i am wrong, please point out the flaw in my reasoning.

Let's see, the three spatial, three rotational is six... there's the length of the bond for each O-H bond, making 8, the angle between each bond making nine, and a binormal for each, making eleven, but I'm not sure if the binormals would be counted seperately from each other, or even from the angle of the bonds, making 9, 10, or 11, but definitely not 12. I'm thinking 9.