ECOO '18 R2 P4 - Three Squares

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Points: 15 (partial)
Time limit: 30.0s
Memory limit: 128M

Problem type

Given N distinct points on a 2D plane, you would like to place three identical, axis-aligned squares on the plane such that every point is either inside or on the border on one of the squares.

Let L be the side length of the squares. What is the minimum possible value of L such that all the points can be covered?

Input Specifications

The standard input will contain 10 datasets. Each dataset begins with an integer N\,(4\leq N\leq100\text{,}000). The next N lines each contain two integers X, Y (-10^9\leq X,Y\leq10^9), the points in the plane.

For the first 4 cases, N\leq30.

Output Specifications

For each dataset, output the value of L.

Sample Input (Two Datasets Shown)

4
1 1
2 2
3 3
4 4
5
1 1
2 1
-2 -1
4 4
-4 -2

Sample Output

1
2

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