hackercupai/hackercup huggingface dataset:
A double-square number is an integer **X** which can be expressed as the sum
of two perfect squares. For example, 10 is a double-square because 10 = 32 \+
12. Your task in this problem is, given **X**, determine the number of ways in
which it can be written as the sum of two squares. For example, 10 can only be
written as 32 \+ 12 (we don't count 12 \+ 32 as being different). On the other
hand, 25 can be written as 52 \+ 02 or as 42 \+ 32.

### Input

You should first read an integer **N**, the number of test cases. The next
**N** lines will contain **N** values of **X**.

### Constraints

0 ≤ **X** ≤ 2147483647
1 ≤ **N** ≤ 100

### Output

For each value of **X**, you should output the number of ways to write **X**
as the sum of two squares.