E. Lunar Phases
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

Horse is sitting on the Earth staring in the sky at the moon. However, he doesn't have great vision, so he needs your help to figure out the lunar phase! He is quite perceptive though and knows the location of the moon as well as where the sun's rays are coming from. More specifically, the Earth is located at the origin $$$(0, 0)$$$, and the sun's rays are parallel to the vector $$$(s_x, s_y)$$$. Furthermore, the moon is located at $$$(m_x, m_y)$$$. The sun illuminates half of the moon, and a (potentially different) half of the moon is visible from the Earth. There are four events that Horse really cares about: the new moon, first quarter, full moon, and third quarter. Horse wants to know what is the next event that will occur. Horse has a lot of questions, so please answer them all.

Note that the moon moves counterclockwise around the origin. For more info on the moon phases, please check Wikipedia.

Input

The first line contains a single number $$$q$$$ ($$$1 \leq q \leq 10^5$$$) — the number of queries.

The following $$$q$$$ lines contain 4 integers $$$s_x, s_y, m_x, m_y$$$ ($$$-10^5 \leq s_x, s_y, m_x, m_y \leq 10^5$$$) — where $$$(s_x, s_y)$$$ is the vector the sun's rays are parallel to, and $$$(m_x, m_y)$$$ is the point the moon is located at.

It is guaranteed that $$$(m_x, m_y)$$$ is not the origin and that $$$(s_x, s_y) \neq (0, 0)$$$. Furthermore, the moon's state is more than $$$\frac{1}{360}$$$th of the lunar cycle away from an event.

Example
Input
4
1 1 1 0
1 1 0 -1
1 1 -1 0
1 1 0 1
Output
Full moon
First quarter
New moon
Third quarter