Algosia and Bajtek love participating in the Algorithmic Engagements. During the remote rounds, there are 18 tasks to solve, and for each of them, one can score between 0 and 10 points. Participants in the ranking are sorted by the total number of points scored. In the event of a tie, the participant who received 10 points in a greater number of tasks is ranked higher. In the event of a further tie, the participant who scored 9 points in a greater number of tasks is ranked higher, and so on. If it is impossible to distinguish between the participants in this way, a draw is declared between them.

Algosia and Bajtek remember their results on all tasks from the last edition, but they do not remember... who won. Will you help them and write a program that reads their results and says which of them took a higher place?

Input

The first line of input contains 18 integers in the range $[0, 10]$ – Algosia's results on the consecutive tasks.

Similarly, the second line of input contains 18 integers in the range $[0, 10]$ – Bajtek's results on the consecutive tasks.

Output

The only line of output should contain one word – "Algosia" or "Bajtek", indicating the name of the winner. If there was a draw, the word "remis" should be placed there instead of a name.

Examples

Input 1

10 10 7 10 10 10 10 10 10 10 10 10 0 10 4 10 10 10
10 10 10 10 10 10 10 10 10 10 10 10 4 3 4 10 10 10

Output 1

Algosia

Note 1

Although both Algosia and Bajtek scored exactly 161 points, according to the rules of the Algorithmic Engagements, Algosia achieved a better result.