Wow. Flagstaff Mountain is not exactly a remote area, either. It's citified, as far as mountains go. I've always wanted to see a mountain lion in the wild.
I met one in the desert of Utah (I had no weapons with me) and I'll say this. It is a hair raising experience...
Some mule deer had just wandered by and he was tracking them. We met eyeball to eyeball at a distance of about 40 feet. After the hair on my neck stood up, we both turned and went opposite ways. It scared the hell out of me. I now carry a Winchester 12 gauge on my back and a large hunting knife strapped to my leg. I rate the knife as my most important defense as if a cat hits me, I won't know he's coming until I get struck from behind.
Let me add, he was a beautiful animal...