# 「POJ2187」Beauty Contest

2015年1月25日6,0011

Description

Bessie, Farmer John’s prize cow, has just won first place in a bovine beauty contest, earning the title ‘Miss Cow World’. As a result, Bessie will make a tour of N (2 <= N <= 50,000) farms around the world in order to spread goodwill between farmers and their cows. For simplicity, the world will be represented as a two-dimensional plane, where each farm is located at a pair of integer coordinates (x,y), each having a value in the range -10,000 … 10,000. No two farms share the same pair of coordinates.Even though Bessie travels directly in a straight line between pairs of farms, the distance between some farms can be quite large, so she wants to bring a suitcase full of hay with her so she has enough food to eat on each leg of her journey. Since Bessie refills her suitcase at every farm she visits, she wants to determine the maximum possible distance she might need to travel so she knows the size of suitcase she must bring.Help Bessie by computing the maximum distance among all pairs of farms.

Input

* Line 1: A single integer, N* Lines 2..N+1: Two space-separated integers x and y specifying coordinate of each farm

Output

* Line 1: A single integer that is the squared distance between the pair of farms that are farthest apart from each other.

Sample Input

Sample Output

Hint

Farm 1 (0, 0) and farm 3 (1, 1) have the longest distance (square root of 2)

1. Compute the polygon’s extreme points in the y direction. Call them ymin and ymax.
2. Construct two horizontal lines of support through ymin and ymax. Since this is already an anti-podal pair, compute the distance, and keep as maximum.
3. Rotate the lines until one is flush with an edge of the polygon.
4. A new anti-podal pair is determined. Compute the new distance, compare to old maximum, and update if necessary.
5. Repeat steps 3 and 4 until the anti-podal pair considered is (ymin,ymax) again.
6. Output the pair(s) determining the maximum as the diameter pair(s).