How many numbers can you create?

The majestic Calvin Set is denoted as CC where

C={0,1,2,4,8,16,32,64,128,256,512,1024}C = \{0, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024\}

Lin takes at least two elements of CC and adds them.

How many numbers can Lin create?

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