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Problem of the day

You are given a positive integer N, and you have to find the number of ways to represent N as a sum of cubes of two integers(let’s say A and B), such that:

```
N = A^3 + B^3.
```

Note:

```
1. A should be greater than or equal to one (A>=1).
2. B should be greater than or equal to zero (B>=0).
3. (A, B) and (B, A) should be considered different solutions, if A is not equal to B, i.e (A, B) and (B, A) will not be distinct if A=B.
```

Detailed explanation

```
1 <= T <= 10^3
1 <= N <= 10^8
Time Limit: 1 sec.
```

```
1
9
```

```
2
```

```
There are 2 ways to represent N in the (A^3 + B^3) form ie. {(1, 2), (2, 1)}.
Eg. 1^3 + 2^3 = 9 and 2^3 + 1^3 = 9.
```

```
1
27
```

```
1
```

```
There is only 1 way to represent N in the (A^3 + B^3) form ie. {(3, 0)}.
Eg. 3^3 + 0^3 = 27.
```