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How to find the number of parameters in the result of solve function?

I would like to find a way to obtain the number of parameters in the result of solve function. For example, in the following result of solve:

[{c0: -r77, c1: r77, c2: -r75 - r76, c3: 0, c4: -r77, c5: r76, c6: r75}]

the parameters are r75, r76, r77. So the number is 3. How to obtain this number automatically?

I think we can check each c[i] to see if it is a non-zero monomial. Then the number is the number of these non-zero monomials. But I don't know which function could check if a result in solve is a monomial.

Thank you very much.