Watering Flowers

题意翻译

花园中存在花若干和喷泉 $2$ 个。 每个喷泉都有一个圆形的覆盖范围。 给出花的数量，每朵花的坐标，以及每个喷泉的坐标，在每朵花都可以被喷泉覆盖的情况下，算出**最小**的 $r_1^2$(第一个喷泉的半径平方)与 $r_2^2$(第二个喷泉半径平方)的和。 （最优答案应为整数） 输入格式: 第一行 $4$ 个数字：花的数量，两个喷泉的坐标 后面每一行为每个花的坐标。 输出一个整数，最小的半径平方和。

题目描述

A flowerbed has many flowers and two fountains. You can adjust the water pressure and set any values $ r_{1}(r_{1}>=0) $ and $ r_{2}(r_{2}>=0) $ , giving the distances at which the water is spread from the first and second fountain respectively. You have to set such $ r_{1} $ and $ r_{2} $ that all the flowers are watered, that is, for each flower, the distance between the flower and the first fountain doesn't exceed $ r_{1} $ , or the distance to the second fountain doesn't exceed $ r_{2} $ . It's OK if some flowers are watered by both fountains. You need to decrease the amount of water you need, that is set such $ r_{1} $ and $ r_{2} $ that all the flowers are watered and the $ r_{1}^{2}+r_{2}^{2} $ is minimum possible. Find this minimum value.

输入输出格式

输入格式

The first line of the input contains integers $ n $ , $ x_{1} $ , $ y_{1} $ , $ x_{2} $ , $ y_{2} $ ( $ 1<=n<=2000 $ , $ -10^{7}<=x_{1},y_{1},x_{2},y_{2}<=10^{7} $ ) — the number of flowers, the coordinates of the first and the second fountain. Next follow $ n $ lines. The $ i $ -th of these lines contains integers $ x_{i} $ and $ y_{i} $ ( $ -10^{7}<=x_{i},y_{i}<=10^{7} $ ) — the coordinates of the $ i $ -th flower. It is guaranteed that all $ n+2 $ points in the input are distinct.

输出格式

Print the minimum possible value $ r_{1}^{2}+r_{2}^{2} $ . Note, that in this problem optimal answer is always integer.

输入输出样例

输入样例 #1

2 -1 0 5 3
0 2
5 2

输出样例 #1

6

输入样例 #2

4 0 0 5 0
9 4
8 3
-1 0
1 4

输出样例 #2

33

说明

The first sample is ( $ r_{1}^{2}=5 $ , $ r_{2}^{2}=1 $ ):  The second sample is ( $ r_{1}^{2}=1 $ , $ r_{2}^{2}=32 $ ):