The story/player select will let you make your own icon. The only thing that will be the same for every version of the custom character is its sprites. I'm not sure if I'll make it fully customizable, with different jump heights, or speed.
Also I've added a nice little sideflip for the main character. if your horizontal speed is more than 2, and you hold right, and jump, you will move backwards, enter a backflip animation, and jump a bit higher than usual.
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