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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