Prime Cut 5

Kirby has to set up a space station to survey a set of $n$ stars, each of which has a distinct position $(x_i, y_i)$. To set up a space station, Kirby must choose a position on a cut in spacetime. This cut is a line segment that begins at position $(s, 0)$ and ends at $(e,0)$, meaning that kirby can choose any position on the x axis between $s$ and $e$ for his space station.

The space station will send out a light beam to each star sequentially, starting with star $1$, then $2$, ... until it sends a signal to star $n$. When the station sends out a signal to a star $i$, it takes $d_i$ seconds to reach the star, where $d_i$ is the distance to the star from the space station. the signal then takes $d_i$ seconds to travel back to the space station. Only then can the station send a signal to star $i+1$.

The amount of time taken to send and receive a signal from every star is a period, and can be expressed as $2d_1 + 2d_2 + 2d_3 ... + 2d_n$. Kirby wants to maximise the number of signals sent to stars, so he wants to choose a position for his station such that the period is small as possible. What is the smallest period that can be achieved?

hint: functions of the form $f(x) = (x-a)/ sqrt((x-a)^2 + b^2)$ are monotonically increasing.

Input

The first line has 3 integers $n, s, e, (1 \le n \le 1e5) (-1e5 \le s, e \le 1e5)$, the number of stars, and the start and end points of the cut in spacetime.

$n$ lines follow, each with $x_i y_i$, the coordinates of a star $-1e5 \le x_i, y_i \le 1e5$.

All points are distinct and guaranteed to not be all collinear.

Output

Write the smallest possible period that occurs when kirby chooses the optimal location for a space station

Sample Input

2 -1000 1000
1 1
2 2

6.32455532

1 -2000 1000
5 5

10

7 -10 0
8 3
10 1
0 2
0 8
7 2
0 0
5 10

94.10865829