What dimension is the gradient vector output of tSNE

Question

My question is this: Suppose we have -dimensional vectors. We want to reduce the dimension to 2 using tSNE, naturally. When we compute tSNE using gradient descent, the gradient vector computed at each iteration contains exactly this many real numbers:

3. 2
4. 2

This question relies on how many dimensions tSNE's gradient vector is.

I'm between nd and 2n. If the gradient vector output is in d dimension, meaning the original dimension of all the input points, then the answer is nd, as there would be d real numbers for each n. However, if the gradient vector gets outputted in the 2nd dimension, then the answer is 2n, as there would be 2 real numbers for each n.