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.

Input

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.

Output

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

Note

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