I spent time doing a literature research and then elaborating the whole written proposal. If the literature research can not count as invested time, I spent almost two months in writing, elaborating and reviewing the proposal, and this is the time that I specified in the period below. Two lasts things. First, I wrote it, but I did not get accepted for the second phase. Second, since I did not pass, I am not sure I am allowed to add the pdf of the whole written proposal as document, but, to prove that I submitted it, I attached the pdf of some emails that I received after the submission as proof of it.