Doubt about Lagrange Multiplier Statistics for q exclusions restrictions

For obtaining the Lagrange Multiplier Statistics I follow this steps (Wooldridge 2019, Introductory Econometrics):

1. Regress 𝑦 on the restricted set of independent variables and consider the residuals 𝑢̃;
2. Regress 𝑢̃ on all of the independent variables and obtain the R-squared 𝑅^2_𝑢
3. Compute 𝐿𝑀=𝑛⋅𝑅^2_𝑢
4. Compare 𝐿𝑀 to the appropriate critical value, 𝑐, in a 𝜒^2_𝑞 distribution: if 𝐿𝑀>𝑐 the null hypothesis is rejected and all the coefficients.

My doubt is about point 2., I don't understand if I should include an intercept in regressing the 𝑢̃ on the independent variables or not. If I do include the intercept the resulting 𝑅^2_𝑢 is the same as the one from the unrestricted regression.