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 2 integers, the smallest possible period that occurs when kirby chooses the optimal location for a space station and the x-value of the position for which this occurs. Answers with a relative or absolute error less than 1e-6 will be accepted.

Sample Input

Input 1

2 -1000 1000
1 1
2 2

Output 1

6.32455532

Input 2

1 -2000 1000
5 5

Output 2

10

Input 3

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

Output 3

94.10865829