Much thanks but I still think I did not get the meaning exactly. If you explain all the steps maybe I can understand. Why don't we group all the U s together than say the number of elements are 5 then continue our work. It does not matter if it is the U number one getting the first place or U number two getting the first place there is no difference. So IMO we should eliminate these opinions but how I just can not figure it out and trial method is way too long even for attempting. Is there any place where I can find the proof on the net?