Problem Description

You are required to put n straight lines on a plane, guaranteeing no three lines share a common point and no lines are coincident. They will form some intersections, please output all possible numbers of intersections.

Input

The first line, an integer T(1 ≤ T ≤ 5) - the number of test cases.

Following T lines, an positive integer n(1 ≤ n ≤ 700) - the number of lines.

Output

Several lines, each line several numbers separated by a blank space - all possible numbers of intersections.

2
3
5

0 2 3
0 4 6 7 8 9 10