HUSGAME - Huseyn and his game


Once our hero Huseyn invited Ziya the ProGrammer ProGamer to play his new game with him. Ziya has a great prestige in the gamers area, so he must win the game or ignore the invitation to save his reputation. The rules of the game are not difficult:

  • Initially, there are N stones on the table. Huseyn will start the game and they will play alternatively.
  • Each turn consisting of replacing the number of stones n on the table with n-1 or [(n+1)/2]. Here [] is floor function.
  • The player who makes 1 stone remain wins.

As Ziya is busy with playing games (you know, he can't pause online games :P) you need to make an honest decision for him.

Input

There will be multiple test cases. The first line of the input consisting of the number of the test cases - T (1 ≤ T ≤ 10000). For each test case, there will be only one line donating single integer - N (1 ≤ N ≤ 1018).

Output

For each test case, print "ZiYES" if Ziya can win the game without matter of the Huseyn's moves, "HuseyNO" otherwise.

Example

Input:
3
1
2
3
Output: HuseyNO
HuseyNO
ZiYES

hide comments
hackerbhaiya: 2021-11-01 19:07:29

Hint : See how many consecutive n-1 move you should do and then apply recursion.

magare: 2018-08-28 06:46:48

Beautiful problem!!

julkas: 2018-04-29 16:03:25

@barishnamazov Good problem.

Re: Thank you :)

Last edit: 2018-07-03 22:22:50
hacker_sk: 2018-03-22 21:05:52

Thumbs UP for the problem. (Y)

Re: Thanks :)

Last edit: 2018-03-23 12:21:38
nadstratosfer: 2018-03-22 03:26:42

Wanted my 666th classical to be devil-themed but couldn't refuse to take this on. Very nice problem.

Re: Thanks much! It is really inspirational to see people like my problems :)

Last edit: 2018-03-22 10:10:04
hwb_worwa: 2018-03-21 21:11:52

another nice problem @barishnamazov

Re: Thanks! I will try to add more problems :)

Last edit: 2018-03-22 00:09:31

Added by:Barish
Date:2018-03-21
Time limit:1s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All
Resource:Deep places of my brain