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- Project Euler #126: Cuboid layers

# Project Euler #126: Cuboid layers

# Project Euler #126: Cuboid layers

_{This problem is a programming version of Problem 126 from projecteuler.net}

The minimum number of cubes to cover every visible face on a cuboid measuring is twenty-two.

If we then add a second layer to this solid it would require forty-six cubes to cover every visible face, the third layer would require seventy-eight cubes, and the fourth layer would require one-hundred and eighteen cubes to cover every visible face.

However, the first layer on a cuboid measuring also requires twenty-two cubes; similarly the first layer on cuboids measuring , , and all contain forty-six cubes.

We shall define to represent the number of cuboids that contain cubes in one of its layers. So , , , and .

Given , compute .

**Input Format**

The first line of input contains , the number of test cases. Each test case consists of a single line containing a single integer, .

**Constraints**

*For the first few test files worth 25% of the total points:*

*For the next few test files worth 25% of the total points:*

*For the last few test files worth 50% of the total points:*

**Output Format**

For each test case, output a single line containing a single integer, the value .

**Sample Input**

```
5
22
46
78
118
154
```

**Sample Output**

```
2
4
5
8
10
```

**Explanation**

The sample I/O are mentioned in the problem statement.