Linux Foundation Mentorship Program - How do you get accepted?

I'm wondering how one gets accepted as a mentee to one of the projects supported by the Linux Foundation.

Do you have to/should you contribute to open source projects run by one of the participating organizations, and then when you apply they are more likely to accept you?

Or do you contribute to the projects first and then ask if they would be your mentee, and then you apply formally through the Linux Foundation?

I'm looking at this and Google Summer of Code. Would doing one exclude me from the other? It seems like doing the Linux Foundation program might exclude me from Google Summer of Code?

Thanks!!