Score : 800 points
Niwango-kun, an employee of Dwango Co., Ltd., likes Niconico TV-chan, so he collected a lot of soft toys of her and spread them on the floor.
Niwango-kun has N black rare soft toys of Niconico TV-chan and they are spread together with ordinary ones. He wanted these black rare soft toys to be close together, so he decided to rearrange them.
In an infinitely large two-dimensional plane, every lattice point has a soft toy on it. The coordinates (x_i,y_i) of N black rare soft toys are given. All soft toys are considered to be points (without a length, area, or volume).
He may perform the following operation arbitrarily many times:
Let's define the scatteredness of an arrangement by the minimum side length of an axis-aligned square enclosing all black rare soft toys. Black rare soft toys on the edges or the vertices of a square are considered to be enclosed by the square.
Find the minimum scatteredness after he performs arbitrarily many operations.
Input is given from Standard Input in the following format:
N D x_1 y_1 : x_N y_N
Print the answer.
3 1 0 0 1 0 2 0
1
19 2 1 3 2 3 0 1 1 1 2 1 3 1 4 4 5 4 6 4 7 4 8 4 8 3 8 2 8 1 8 0 7 0 6 0 5 0 4 0
4
8 3 0 0 0 3 3 0 3 3 2 2 2 5 5 2 5 5
4