G. Soccer League
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

The soccer league started and our friend, B.B.C. wants to show the entire world he's the best soccer statistician in the world. Soccer is played as a game between two teams and the team who scores more goals wins. In case of equality, we will consider the game to end in a draw.

For this reason, he gave you the results of $$$T$$$ teams playing in different leagues and he wants you to tell him if for a given tuple $$$(W, D, L, G_f, G_a)$$$, where $$$W$$$ is the number of wins, $$$D$$$ is the number of draws, $$$L$$$ is the number of losses, $$$G_f$$$ is the numbers of goals scored and $$$G_a$$$ is the number of goals conceded, there is a unique set of results that corresponds to the tuple given in the input.

For example, if we have the tuple $$$(1, 1, 1, 1, 1)$$$, we have a unique set of results that lead us here $$$(1-0, 0-1, 0-0)$$$, the order these results show isn't important, however if we have $$$(1, 1, 1, 2, 2)$$$, we can have $$$(2-0, 0-2, 0-0)$$$ or $$$(1-0, 0-1, 1-1)$$$, so the set of results is not unique.

Now you need to show B.B.C. what you're made of and conquer this challenge!

Take note that if there is no valid way of assigning scores, you should also print "Better luck next time".

Input

On the first line you are given $$$T$$$, the number of test cases $$$(1 \le T \le 10^5$$$).

On the next $$$T$$$ lines you are given $$$W$$$, $$$D$$$, $$$L$$$, $$$G_f$$$, $$$G_a$$$, with the meaning from the statement. ($$$0 \le W, D, L, G_f, G_a \le 10^9$$$).

Output

You will need to print on each line either the message "Amazing" if the set of valid results is unique, or "Better luck next time" otherwise.

Example
Input
5
3 1 1 4 1
4 0 0 6 0
0 5 0 1 2
0 3 0 1 1
1 1 0 2 1
Output
Amazing
Better luck next time
Better luck next time
Amazing
Better luck next time