Is it safer late at night or early in the morning?

So I want to start running, but I am only free when it is dark outside, so my options are either later at night or early in the morning. I should probably mention that I live in the downtown part of a city and there are some rough characters sometimes. I have only felt unsafe one time, and that was in the middle of the day and several months ago. What is the safer option?
Is it safer late at night or early in the morning?
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