How to correct my extremely crooked and crowded teeth? (Photo)

I want to know if it is possible to reasonably 'fix' my teeth. I am 23 and have lived all my life so far without paying much attention to my teeth. Now I wish to do something about them. I don't want to pull any of them out but I am prepared to wear braces for as long as required. The question is whether braces will be enough for my teeth. As you can see they look terrible.

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