Given an integer N, your task is to judge whether there exist N points in the plane such that satisfy the following conditions:
1. The distance between any two points is no greater than 1.0.
2. The distance between any point and the origin (0,0) is no greater than 1.0.
3. There are exactly N pairs of the points that their distance is exactly 1.0.
4. The area of the convex hull constituted by these N points is no less than 0.5.
5. The area of the convex hull constituted by these N points is no greater than 0.75.
The first line of the date is an integer T, which is the number of the text cases.
Then T cases follow, each contains an integer N described above.
1 <= T <= 100, 1 <= N <= 100
For each case, output “Yes” if this kind of set of points exists, then output N lines described these N points with its coordinate. Make true that each coordinate of your output should be a real number with AT MOST 6 digits after decimal point.
Your answer will be accepted if your absolute error for each number is no more than 10-4.
Otherwise just output “No”.
See the sample input and output for more details.
3 2 3 5
No No Yes 0.000000 0.525731 -0.500000 0.162460 -0.309017 -0.425325 0.309017 -0.425325 0.500000 0.162460