Number of Parameters in Multidimensional rnn

I have the following equation for the hidden unit in a Multidimensional RNN and I need to calculate the total number of trainable parameters:

$$h^{i,j} = sigma (W_{in}x^{i,j} + W_{left}h^{i-1,j} + W_{top}h^{i,j-1})$$
Assume that the input grid is $n times n$, each input $x^{i,j}$ is a
$c$-channel vector, and the hidden state $h^{i,j}$ has dimension $h$.
How many trainable parameters does this architecture have?

So I want to know if I’m correct with the sizes of the W matrices:
begin{aligned}
W_{in} = n times h
W_{left} = h times h
W_{top} = h times h
end{aligned}

If so, where does the $c$-channel vector take place? What am I doing wrong? Thank you