If you don't have a Indonesian visa yet, you can go early in the morning to the embassy, hand everything in, and you will be able to pick up the visa and cross the border to W Papua on the same day! (it is a good idea to have a driver waiting for you to take you from the embassy to the border).
If you hand in the forms later, you will need to wait one day for your visa, so go to the beach, and walk the long way to the "big rock", it's worth it :)
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