SPOJ.com - Problem SHAKTI

SHAKTI - SHAKTIMAN AND KILWISH

Since very long time shaktiman and kilwish have been fighting with each other but the fight never came to end . So finally I came to rescue . I decided that the result of the fight will be decided by a mathematical game, in which I will write a number (N) . Kilwish and shaktiman will play the game alternatively and each of them would subtract a number(n) [n is less than N] such that N modulo n gives zero. The game is repeted turn by turn until the one, who now cannot make a further move looses the game

Shaktiman being weak at mathematics asks you for help, whether or not he can win in that particular case. If Shaktimaan wins that game then print "Thankyou Shaktiman" otherwise print "Sorry Shaktiman".The game begins with shaktimaan playing first move.It is well understood that both of them will make moves in optimal way.

Input

Input contains test cases t (< 10^5) and followed by t numbers (1 ≤ N ≤ 10⁶).

Output

If Shaktimaan wins that game then print "Thankyou Shaktiman" otherwise print "Sorry Shaktiman".

Example

Input:
2
212
424

Output:
Thankyou Shaktiman
Thankyou Shaktiman

Submit solution!

Added by:	aqfaridi
Date:	2014-01-24
Time limit:	1s
Source limit:	50000B
Memory limit:	1536MB
Cluster:	Cube (Intel G860)
Languages:	All except: ASM64

hide comments

2014-12-29 06:39:01 Mitch Schwartz
It's possible that some people misunderstood the question, as it is not written very precisely. To clarify: At the start of the game, Shaktiman chooses some positive integer n<N such that N modulo n gives zero (if such an n exists), then he replaces N with N' = N-n, and in the following turn Kilwish will choose an n'<N' such that N' modulo n' gives zero (if such an n' exists), etc.

Last edit: 2014-12-29 06:49:21

2014-07-01 19:00:57 chin
beautiful concept..(y)

2014-03-23 19:56:15 Anubhav Balodhi
@Mitch thank U, yes this is an easy one...

2014-03-01 01:42:15 a b
it intresting to solve it by understanding the proof... nt jst observation

2014-01-27 23:47:42 Mitch Schwartz
I've observed that game theory is a weak point for many SPOJ users, based on number of solvers for other problems. If you found this easy, you could try e.g. DCEPC807, MYQ8, OVOXO, DCEPC12B. In my view this is ok for an easy classical problem, and might help increase interest in the field. (Also, if you've "solved" this problem without proving your solution is correct, you could learn something by proving it.)

Last edit: 2014-02-04 01:11:03