A10249. 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 $r_{1}^{2}+r_{2}^{2}$ is minimum possible. Find this minimum value.

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.

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

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