Visible Lattice Points

A lattice point (x, y) in the first quadrant (x and y are integers greater than or equal to 0), other than the origin, is visible from the origin if the line from (0, 0) to (x, y) does not pass through any other lattice point. For example, the point (4, 2) is not visible since the line from the origin passes through (2, 1). The figure below shows the points (x, y) with 0 <= x, y <= 5 with lines from the origin to the visible points.

Write a program which, given a value for the size, N, computes the number of visible points (x,y) with 0 <= x, y <= N.

Input

The first line of input contains a single integer C, (1 <= C <= 1000) which is the number of datasets that follow.

Each dataset consists of a single line of input containing a single integer N, (1 <= N <= 1000), which is the size.

Output

For each dataset, there is to be one line of output consisting of: the dataset number starting at 1, a single space, the size, a single space and the number of visible points for that size.

Sample Input

4
2
4
5
231
Sample Output

1 2 5
2 4 13
3 5 21
4 231 32549

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抄袭、复制答案,以达到刷声望分或其他目的的行为,在CSDN问答是严格禁止的,一经发现立刻封号。是时候展现真正的技术了!
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Horizontally Visible Segments
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