Visible Lattice Points
时间限制:C/C++/Rust/Pascal 1秒,其他语言2秒
空间限制:C/C++/Rust/Pascal 32 M,其他语言64 M
64bit IO Format: %lld

题目描述

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.

输入描述:

The first line of input contains a single integer Cwhich is the number of datasets that follow.
Each dataset consists of a single line of input containing a single integer N, which is the size.

输出描述:

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.
示例1

输入

复制
4
2
4
5
231

输出

复制
1 2 5
2 4 13
3 5 21
4 231 32549