## Pythagorean TriplesProblem #54 |

*This task is inspired by the discussion in the Blog on algorithms by Faisal Rahman on similar task from
ProjectEuler*

As we know, the Pythagorean Theorem tells us about the simple equation:

```
a^2 + b^2 = c^2
```

There really exist such triples `a, b, c`

of **integer** numbers, which satisfy this equation. This is not self-evident
fact, moreover there are no such triples for any other powers except `2`

- this is the famous
Fermat Theorem which could not be solved for more than `350`

years.

However, for the power of `2`

there are countless amount of such triples. One of them `3, 4, 5`

, for example.

Nevertheless, it is not always easy to find a triple satisfying some specific conditions:

**In this problem you need to write a program which for given value of s = a + b + c
will find the only triple which satisfies the equation.**

For example, given sum of `12`

the only `3, 4, 5`

triple fits, for sum `30`

the only `5, 12, 13`

etc.

**Input data** will contain the number of test-cases in the first line.

Other lines will contain a single value each - the sum for which triple should be found.

**Answer** should contain the values of `c^2`

for each triple found (it is equal to `a^2 + b^2`

of course),
separated with spaces.

**Note:** the real values of `s`

would be large enough, about `10e+7`

- so the simplest solutions could be inefficient.

Example:

```
input data:
2
12
30
answer:
25 169
```

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