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.
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.
Print the minimum possible value *r*12<=+<=*r*22. Note, that in this problem optimal answer is always integer.
The first sample is (*r*<sub class="lower-index">1</sub><sup class="upper-index">2</sup> = 5, *r*<sub class="lower-index">2</sub><sup class="upper-index">2</sup> = 1): <img class="tex-graphics" src="https://espresso.codeforces.com/15e780f508832a19b14698dd8eb54b4c0dd131bf.png" style="max-width: 100.0%;max-height: 100.0%;"/> The second sample is (*r*<sub class="lower-index">1</sub><sup class="upper-index">2</sup> = 1, *r*<sub class="lower-index">2</sub><sup class="upper-index">2</sup> = 32): <img class="tex-graphics" src="https://espresso.codeforces.com/da4dc31002cc9b37092d64035ab56ad8544c0d7b.png" style="max-width: 100.0%;max-height: 100.0%;"/>