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 wi, outputs HAPPY if it is possible to make a friend list for each dog i of length wi, 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 ≤ 105 followed by an ordered list of N wishes 0 ≤ wi ≤ 105.

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
Sivakumaran M: 2014-02-18 16:20:38

@thomas: can you provide a test case where my soln fails? id: 11087727
Thanks

Kevin Sebastian: 2014-02-18 16:20:38

@author any tricky test cases

|RAMSDEN|: 2014-02-18 16:20:38

@author can u pls check my soln id 11082248
thanks

Last edit: 2014-02-17 18:48:11
anurag garg: 2014-02-18 16:20:38

@thomas thank you for your response

Last edit: 2014-02-17 19:47:04
Thomas Dybdahl Ahle: 2014-02-18 16:20:38

@anurag garg: You are right about symetric. I've fixed the statement. You are wrong on "0 1 3 3 3 4 4 5 5 8"

Last edit: 2014-02-17 17:47:03
anurag garg: 2014-02-18 16:20:38

@thomas
I think friendship should be a symmetric relation i.e a~b then b~a
if yes then can you provide a test case where my algo fails:
submission id:11081783
thanks

Thomas Dybdahl Ahle: 2014-02-18 16:20:38

RAM┬žDEN: Yes
Bhavik: 1 1 1
And no, you can't have yourself on your friend list.

Last edit: 2014-02-17 17:14:43
|RAMSDEN|: 2014-02-18 16:20:38

@author is the wishlist sorted in a non decreasing order??

Last edit: 2014-02-17 16:20:45
Bhavik: 2014-02-18 16:20:38

@thomas: can you kindly chk id:11081408...i am unable to find test case where my algo fails...
kindly clarify my doubts:
by reflexive do u mean 1 1 should print "HAPPY"
similarly 4 1 2 0 0 should also print "HAPPY" since 2nd dog can be friends with himself and 1st dog...
am i right??

thank you..

EDIT:AC finally:)

Last edit: 2014-02-17 18:45:33
Thomas Dybdahl Ahle: 2014-02-18 16:20:38

If n=0 no doges will be sad.


Added by:Thomas Dybdahl Ahle
Date:2014-02-17
Time limit:1s-2s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ASM64 GOSU