Score : 800 points
Takahashi is doing a research on sets of points in a plane. Takahashi thinks a set S of points in a coordinate plane is a good set when S satisfies both of the following conditions:
Here, D_1 and D_2 are positive integer constants that Takahashi specified.
Let X be a set of points (i,j) on a coordinate plane where i and j are integers and satisfy 0 ≤ i,j < 2N.
Takahashi has proved that, for any choice of D_1 and D_2, there exists a way to choose N^2 points from X so that the chosen points form a good set. However, he does not know the specific way to choose such points to form a good set. Find a subset of X whose size is N^2 that forms a good set.
Input is given from Standard Input in the following format:
N D_1 D_2
Print N^2 distinct points that satisfy the condition in the following format:
x_1 y_1 x_2 y_2 : x_{N^2} y_{N^2}
Here, (x_i,y_i) represents the i-th chosen point. 0 ≤ x_i,y_i < 2N must hold, and they must be integers. The chosen points may be printed in any order. In case there are multiple possible solutions, you can output any.
2 1 2
0 0 0 2 2 0 2 2
Among these points, the distance between 2 points is either 2 or 2\sqrt{2}, thus it satisfies the condition.
3 1 5
0 0 0 2 0 4 1 1 1 3 1 5 2 0 2 2 2 4