VFRIENDS  Very Friends
NOTICE: The test cases for this problem are not as hard as intended. If you've solved this problem, and think your solution is up for it, try VFRIEND2!
You are creating a new soical network for dogs. Wow. The dogs don't have many possibilities for interacting with your website, but they can bark how many friends they want. E.g. if a dog wants to have much 8 friends it will bark 8 times, and if it doesn't want any friends, it'll just stay quiet.
After spending a good year of your life collecting these barks, you are finally ready to assign a friend list for each dog. The only problem is: You are not sure whether it is actually possible. Thus before you proceed you would like to write a program, that given a list of N wishes w_{i}, outputs HAPPY if it is possible to make a friend list for each dog i of length w_{i}, or SAD if some dog will have to get more or fewer friends than it wished for.
Notice: Being friends is considered an irreflexive, symetric relation.
Update: If you manage to solve this problem much efficiently, have a look at VFRIEND2, which is a so harder version of this problem.
Input
The first line will contain a single integer T  the number of test cases to process.
Each following lines will start with an integer 0 ≤ N ≤ 10^{5} followed by an ordered list of N wishes 0 ≤ w_{i} ≤ 10^{5}.
Output
Write the answer  HAPPY or SAD  for each test case on a separate line.
Example
Input: 3
3 0 1 1
5 0 1 2 3 4
6 1 1 2 2 3 3 Output: HAPPY
SAD
HAPPY
Explanation
In the first case we can make dog 2 and 3 be friends.
In the second case no assignment that works, since dog 5 would have to be friends with everyone, but dog 1 doesn't want that.
hide comments
Bhavik:
20140218 16:20:38
what if n=0? 

Thomas Dybdahl Ahle:
20140218 16:20:38
Problem levl 2: http://www.spoj.com/problems/VFRIEND2/ So scare! 

Jacob Plachta:
20140218 16:20:38
Such happy solution, many excite. 

newbie:
20140218 16:20:38
@author.can u tell will my approach work 

Thomas Dybdahl Ahle:
20140218 16:20:38
Jacob you have so happy solution! 

Jacob Plachta:
20140218 16:20:38
Wow, much linear solution. 

Thomas Dybdahl Ahle:
20140218 16:20:38
Intended solution is very linear time. I will try to update the problem to reflect this. Last edit: 20140217 08:06:26 
Added by:  Thomas Dybdahl Ahle 
Date:  20140217 
Time limit:  1s2s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: ASM64 GOSU 