<|im_start|>system
You are a helpful assistant. You first think about the reasoning process in the mind and then provide the user with the answer. You should try to truely solve the question by yourself without cheating.  <|im_end|>
<|im_start|>user
 In the range $0 \leq r \le n \leq 63$, how many pairs of $(n, r)$ are there for which $C_{n}^{r} = \frac{n!}{r!(n-r)!}$ is an even number?

(Note: This problem is from the Japanese Mathematical Olympiad, 1991.) Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>
<|im_start|>assistant
Let me solve this step by step.
<think>
user
1351
In the range $0 \leq r \le n \leq 63$, how many pairs of $(n, r)$ are there for which $C_{n}^{r} = \frac{n!}{r!(n-r)!}$ is an even number?

(Note: This problem is from the Japanese Mathematical Olympiad, 1991.)
test