CF2160C Reverse XOR

Given a positive integer $ x $ , let $ f(x) $ be the positive integer formed by reversing the binary representation of $ x $ without leading zeroes. For example, if $ x=12=1100_2 $ , then $ f(x)=0011_2=3 $ . You are given an integer $ n $ . Please determine if there exists a positive integer $ x $ such that $ x \oplus f(x) = n $ $ ^{\text{∗}} $ . $ ^{\text{∗}} $ Here, $ \oplus $ denotes the [bitwise XOR operation](https://en.wikipedia.org/wiki/Bitwise_operation#XOR).

Each test contains multiple test cases. The first line contains the number of test cases $ t $ ( $ 1 \le t \le 10^4 $ ). The description of the test cases follows. The first line of each test case contains an integer $ n $ ( $ 0 \leq n

For each test case, output YES if there exists a positive integer $ x $ such that $ x \oplus f(x) = n $ , and NO otherwise. You can output the answer in any case. For example, the strings "yEs", "yes", and "Yes" are also recognized as positive responses.

In the first case, when $ x=1 $ , $ f(x)=1 $ , and $ x \oplus f(x)=0 $ . Thus, the answer is YES. In the second case, when $ x=2 $ , $ f(x)=1 $ , and $ x \oplus f(x)=3 $ . Thus, the answer is YES. In the fourth test case, we can show there is no $ x $ that satisfies $ x \oplus f(x)=8 $ , so the answer is NO.