Cube Sum Pairs Problem Statement

Given a positive integer N, find the number of ways to express N as a sum of cubes of two integers, A and B, such that:

N = A^3 + B^3

Ensure you adhere to the following conditions:

• A must be greater than or equal to 1 (A≥1).
• B must be greater than or equal to 0 (B≥0).
• Pairs (A, B) and (B, A) are distinct unless A = B.

Input:

The first line contains an integer T, representing the number of test cases.

Each test case consists of a single positive integer N.

Output:

For each test case, return an integer denoting the count of ways to represent N as a sum of cubes of two integers, A and B.

Example:

Input:

2
N = 9
N = 16

Output:

2
0

Constraints:

• 1 ≤ T ≤ 10³
• 1 ≤ N ≤ 10⁸
• Time Limit: 1 sec