New Year's Snowfall#1433
The king of a small but proud African nation decided that there must be snow in his country for the New Year. To accomplish this, he ordered the purchase of special weather control devices. These devices were purchased, installed, and activated—and indeed, it began to snow.
The king was pleased that his plan had succeeded. However, it turned out that the snow fell with varying intensity in different parts of the country. Naturally, the king would like to celebrate the New Year in the location where the snow intensity is greatest. Your task is to help him identify this place.
The country's map is modeled as a plane with a Cartesian coordinate system. Each device is installed at a point with integer coordinates and increases the snow intensity by exactly at all integer-coordinate points that lie on the boundaries of squares with the following properties:
The side lengths of the squares are of the form 4k+2, where is a non-negative integer.
The sides of the squares are parallel to the coordinate axes.
The center of each square coincides with the point where the device is installed.
The device does not affect the snow intensity at any other points on the plane.
The following illustration demonstrates how the device operates:
In the illustration, the yellow point at the center represents the device. The points where the snow intensity is increased by due to the device are shown in red.
The first line contains the integer (1 \leq N \leq 1000).
The next lines contain the coordinates of the weather control devices. Each line contains the coordinates for one device in the format "", where is the -coordinate and is the -coordinate (-1000000 \leq x, y \leq 1000000). No two devices are installed at the same point.
Output a single integer equal to the maximum snow intensity at any point on the plane.
Example 1