Problem Description

Given a positive integer $n$, determine whether there exist a palindromic number$^{\bm{\dagger}}$ $a$ and a non-negative integer $b$ such that $a+2^b=n$.

$\bm \dagger$ A non-negative integer is called a palindromic number if and only if it reads the same forwards and backwards.

Input Format

This problem contains multiple test cases.

The first line of the input contains a positive integer $T$, indicating the number of test cases.

Then, the $T$ test cases follow sequentially. For each test case:

• One line containing a single positive integer $n$.

Output Format

For each test case, output a single line:

• If there exist $a,b$ satisfying the condition, output Yes.
• If there do not exist $a,b$ satisfying the condition, output No.

3
15
1022
58187

Yes
No
Yes

Hint

Explanation for Sample #1

For the first test case, we have $a=11$, $b=2$, and $n=11+2^2=15$.

For the second test case, it can be proven that there do not exist $a,b$ satisfying the conditions.

For the third test case, we have $a=57\,675$, $b=9$, and $n=57\,675+2^9=58\,187$.

Data Range

This problem uses bundled subtasks.

For all test cases, it is guaranteed that $1 \le T \le 10^4$ and $1 \le n \le 10^{18}$.

::cute-table{tuack}