Box Run#6033
Once every year, Jo and his friends want to visit the local fair in Erlangen, called Bergkirchweih. This year, they want to make a Kastenlauf (box run). They start at Jo's home and have one box (Kasten) of water (with bottles). As they are very thirsty, they drink one bottle of water every metres.
As the way from Jo's home to the Bergkirchweih is pretty long, they need more water than they have initially. Fortunately, there are stores selling water on the way. When they visit a store, they can drop their empty bottles and buy new bottles, but their total number of full bottles will not be more than (because they are too lazy to carry more than one full box).
You are given the coordinates of the stores, of Jo's home, and of the location of the Bergkirchweih. Write a program to determine whether Jo and his friends can happily reach the Bergkirchweih, or whether they will run out of water on the way.
The first line contains the number of test cases (t \leq 50). Each test case starts with one line, containing the number (0 \leq n \leq 100) of stores selling water. The next n + 2 lines contain (in this order) the location of Jo's home, of the stores, and of the Bergkirchweih. The location is given with two integer coordinates and (both in meters, -32\,768 \leq x, y \leq 32\,767). As Erlangen is a rectangularly laid out city, the distance between two locations is the sum of the absolute differences of their coordinates (also called Manhattan-Metric).
For each test case, print one line, containing either happy (if Jo and his friends can happily reach the Bergkirchweih), or sad (if they will run out of water on the way).
\begin{example}\exmp{220 01000 02000 10002000 2000}{happysad}\end{example}
Example 1