Given an array of integers, determine for each number whether it is a Fibonacci number.

For every element in the array:

• If the number belongs to the Fibonacci sequence, return Yes.
• Otherwise, return No.

The Fibonacci sequence is:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ...

Input

• An integer n representing the size of the array.
• An array arr of n integers.

Output

For each element of the array, print:

Yes

if it is a Fibonacci number, otherwise:

No

Example 1

Input:
arr = [2, 4, 8, 10, 13]

Checking each number:

2  → Yes
4  → No
8  → Yes
10 → No
13 → Yes

Output:
Yes No Yes No Yes

Example 2

Input:
arr = [0, 1, 7, 21]

Output:
Yes Yes No Yes

Constraints

1 ≤ n ≤ 10^5
0 ≤ arr[i] ≤ 10^18

Goal: Efficiently determine whether each number is a Fibonacci number without generating the entire Fibonacci sequence for every element.