CF617C.Watering Flowers

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_12 + _r_22 is minimum possible. Find this minimum value.

一个花坛中有很多花朵和两个喷泉。

你可以调节水压，为第一个和第二个喷泉分别设定任意非负值 $r_1$（$r_1 \geq 0$）和 $r_2$（$r_2 \geq 0$），表示水从对应喷泉喷洒出的最大距离。你需要选定这样的 $r_1$ 和 $r_2$，使得所有花朵都被浇灌到，即：对每一朵花，它到第一个喷泉的距离不超过 $r_1$，或者它到第二个喷泉的距离不超过 $r_2$。允许某些花朵同时被两个喷泉浇灌。

你需要最小化用水量，即选定满足上述条件的 $r_1$ 和 $r_2$，使得 $r_1^2 + r_2^2$ 尽可能小。求该最小值。

The first line of the input contains integers n, _x_1, _y_1, _x_2, _y_2 (1 ≤ n ≤ 2000,  - 107 ≤ _x_1, _y_1, _x_2, _y_2 ≤ 107) — 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 ( - 107 ≤ x__i, y__i ≤ 107) — the coordinates of the i-th flower.

It is guaranteed that all n + 2 points in the input are distinct.

输入的第一行包含整数 $n$、$x_1$、$y_1$、$x_2$、$y_2$（$1 ≤ n ≤ 2000$，$-10^7 ≤ x_1, y_1, x_2, y_2 ≤ 10^7$）——分别表示花的数量，以及第一座和第二座喷泉的坐标。

接下来是 $n$ 行。其中第 $i$ 行包含整数 $x_i$ 和 $y_i$（$-10^7 ≤ x_i, y_i ≤ 10^7$）——表示第 $i$ 朵花的坐标。

保证输入中的全部 $n+2$ 个点互不相同。

Print the minimum possible value _r_12 + _r_22. Note, that in this problem optimal answer is always integer.

输出最小可能的值 $r_1^2 + r_2^2$。注意，在本题中，最优解始终为整数。

The first sample is (_r_12 = 5, _r_22 = 1): The second sample is (_r_12 = 1, _r_22 = 32):

第一个样例是（$r_{12} = 5$，$r_{22} = 1$）：
第二个样例是（$r_{12} = 1$，$r_{22} = 32$）：