Snip! Snip!

You're planting a tree, which sprouts 2 leaves on day 1. Each day, the tree branches out, doubling the number of leaves, but from day 2 on, you will trim one of the branches out, ceasing the leaves to grow on that branch. The number of leaves consequently runs as the day passes by as shown above.

On day 17, how many leaves will this tree have?

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