Lines

On the plane you are given a set $A$ of $n$ points. The distance from a line $p$ to the set $A$ is the largest of the distances from the points of $A$ to the line $p$.

Among all lines that pass through a fixed point $P$, choose the one whose distance to $A$ is as small as possible, and report that smallest distance.

Write a program that:

• reads the set $A$ and the point $P$ from standard input,
• computes the minimum possible distance from a line through $P$ to the set $A$,
• writes that value to standard output.

The first line contains one integer $n$ ($1 \le n \le 100000$).

The second line contains two integers: the coordinates of the point $P$.

Each of the next $n$ lines contains two integers: the coordinates of one point of the set $A$.

All coordinates are integers whose absolute value does not exceed $10^6$.

Print exactly one real number: the required distance, written with exactly three digits after the decimal point and rounded down (truncated).

The tests are chosen so that any answer within $10^{-6}$ of the exact value gives the correct result after this rounding, so computing the distance to about six decimal places of accuracy is enough.