How to customize wp_list_categories output to menu?

Hi Everyone,

I have built a static html website and now building it in to WordPress. I need to customize the wp_list_categories output to this:

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Anybody have any idea of how i can go about doing this, i have spent roughly about 5 hours searching for a way of customizing the output but i just can’t seem to find anything!! 🙁

If one of you awesome people could please shine some light on how this can be done i would be extremely grateful! 🙂