How many numbers can be expressed as the sum of two or more distinct elements of the set $\{ 0, 1, 2, 4, 8, 16 \}$?
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
How many numbers can be expressed as the sum of two or more distinct elements of the set $\{ 0, 1, 2, 4, 8, 16 \}$?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
31
How many numbers can be expressed as the sum of two or more distinct elements of the set $\{ 0, 1, 2, 4, 8, 16 \}$?
train