翻译题意：

在一个平面直角坐标系的以（0,0）为左下角、(N,N）为右上角的矩形中，除了（0,0）之外，每个坐标上都插着一个钉子，如图所示。 求在原点向四周看去，能够看到多少个钉子。一个钉子能被看到，当且仅当连接它和原点的线段上没有其他钉子。图也画出了所有能看到的钉子以及 视线。 1≤N≤1000。

Description

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