WUSTOJ 1336: Lucky Boy（Java）博弈

题目链接：1336: Lucky Boy

参考博客：LUCKY BOY 博弈——HandsomeHow

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 2d 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.

在一个二维平面，有 n 个不同的点，每次可以从平面上拿走一个点或者在一条直线上的多个点。先拿走两个以上的点或者拿走最后一个点的人获胜。问谁获胜？

Input

The first line of each case is an integer n(0<n<=103), following n lines each contains two integers x and y(0<=x, y<=108), 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.

Sample Input

3
0 0
1 1
2 2
3
0 0
1 1
2 3
4
0 0
1 1
2 2
3 5
4
0 0
0 1
1 1
1 0

Sample Output

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

分析