Watering Flowers

A flowerbed has many flowers and two fountains.

You can adjust the water pressure and set any values r₁(r₁ ≥ 0) and r₂(r₂ ≥ 0), giving the distances at which the water is spread from the first and second fountain respectively. You have to set such r₁ and r₂ that all the flowers are watered, that is, for each flower, the distance between the flower and the first fountain doesn't exceed r₁, or the distance to the second fountain doesn't exceed r₂. 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 r₁ and r₂ that all the flowers are watered and the r₁² + r₂² is minimum possible. Find this minimum value.

The first line of the input contains integers n, x₁, y₁, x₂, y₂ (1 ≤ n ≤ 2000,  - 10⁷ ≤ x₁, y₁, x₂, y₂ ≤ 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 r₁² + r₂². Note, that in this problem optimal answer is always integer.

2 -1 0 5 3
0 2
5 2

6

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

33

 Note

The first sample is (r12 = 5, r22 = 1):  The second sample is (r12 = 1, r22 = 32):