Migrated from Lutece 930 Lucky Boy

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Description

Recently, Lur have a good luck. He is also the cleverest boy in his school as he create the most popular computer game – Lucky Boy. The game is played by two players, $a$ and $b$, in $2$d planar .In the game Lucky Boy, there are $n$ different points on plane, each time one can remove one or multiple co-line points from the plane. The one who can firstly remove more than two points from the plane wins. The one who removes the last point on the plane can also win the game. You may assume that two players are both clever enough that they can always make the best choice. The winner is called Lucky Boy.

Given the n points, can you tell me who will be the Lucky Boy ? Note that player a will always the first one to remove points from the plane.

Input

The first line of each case is an integer $n(0<n \leq 10^3)$, following $n$ lines each contains two integers $x$ and $y(0 \leq x, y \leq 10^8)$, describing the coordinates of each point. Ended by EOF.

Output

Output a is the lucky boy. in a single line if a win the game, otherwise you should output b is the lucky boy. in a single line.

Samples

3
0 0
1 1
2 2
3
0 0
1 1
2 3

a is the lucky boy.
b is the lucky boy.

Resources

2011 Heilongjiang collegiate programming contest