## PITPAIR - Pythagorean Legacy

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It is necessary to find a minimal integer value R which is equal to the length of the hypotenuse (the side opposite the right angle) of N non-identical rectangular triangles with integer lengths of sides.

### Input

t - number of test cases [t <= 100], than t lines follow, each line contains one integer - N, equal to the required number of different rectangular triangles. [1 <= N <= 2000]

### Output

For each test case your program should output a number R in a separate line (R fits in a 64-bit integer), equal to the minimal integer value of a hypotenuse for which exactly N different rectangular triangles can be constructed; then in separate lines follow exactly N numbers equal to the shorter cathetus (side adjacent to the right angle) of each of the rectangular triangles, in ascending order.

### Example

```Input:
2
1
2

Output:
5
3
25
7
15
```

hide comments Tanmay: 2012-09-16 14:08:15 Should the hypotenuse be in exactly N distinct triangles or the value of hypotenuse should be such that it is least and it appears in at least N distinct triangles? i.e. for N = 3, should we output 65 or 125? Because 125 is first hypotenuse to appear in exactly 3 triangles, but 65 is the least with at least 3 triangles (even though it appears in 4 distinct triangles, actually). Last edit: 2012-09-16 14:09:04

 Added by: Roman Sol Date: 2005-03-01 Time limit: 2.25s Source limit: 8192B Memory limit: 1536MB Cluster: Cube (Intel G860) Languages: All except: ERL JS-RHINO NODEJS PERL6 VB.NET Resource: ZCon 2005