In a game, a stupid prize is up for grabs, which X is very fond of. This is a two-player game. X is playing against Y.
The game consists of $$$n$$$ balls arranged in a circular manner, that is each ball has almost $$$2$$$ neighbors. For example, if there are $$$4$$$ balls, then ball $$$1$$$ is neighbor of balls $$$2$$$ and $$$4$$$, similarly ball $$$2$$$ is neighbor of balls $$$1$$$ and $$$3$$$ and so on.
Initially, each ball yields $$$1$$$ point. In a move, a player chooses a ball and removes it, and its point is added to the player's score. Additionally, if there are at least two balls remaining after the removal, the balls on either side of the removed ball will merge, and their points will be added together. For example, if the balls initially has points $$$[1,1,1,1,1]$$$ and a player removes the third ball, the new arrangement will be $$$[1,2,1]$$$. See examples below for visuals.
The game ends when the last ball is removed. Players move alternately, X goes first. The player with a higher score wins.
If X loses, being a sore loser, he will get frustrated and send an email to the organizers complaining about how stupid and unfair the game is. Your task is to help him determine who wins if both players play optimally, or report if it will be a draw.
"playing optimally" means making the best possible moves at each turn to first, maximize one's chances of winning the game, then, minimize opponent's chances of winning the game.
The first line contains an integer $$$t$$$ ($$$1 \leq t \leq 10^5$$$) – denoting the number of test cases.
Each of the following lines contains an integer $$$n$$$ ($$$1 \leq n \leq 2\cdot10^5$$$) – denoting the number of balls in the game.
For each test case, in a single line, print:
- "Beautiful game" if X wins,
- "Never playing this again" if Y wins,
- "No words" if it is a draw.
3174
Beautiful game Never playing this again No words
For the second case, a way Y can win is:
Sample 2: It can be shown that Y can win no matter how X plays. For the third case, the game goes as follows:
