Competitions

# Dilemma

Askar and Damir love teaching students and kids. Recently, they found the birthplace of many genius kids, so they've decided to teach them. They were given the map of the city with 4n schools, 2n girls only schools and 2n boys only schools. The map of the city represented as a Cartesian plane and coincidentally no two schools were on the same line on the map (this is part of the city’s geniusity magic). Now elders want to split the city by the line, so that there is an equal number of boys only schools and girls only schools from both sides of this line. Since n could be very large, they instructing this task to you.

#### Input

The first line contains one number n (14n106).

Following 4n lines are coordinates of schools, each in separate line. First half is 2n boys only schools, then 2n girls only schools, where i-th line contain two space separated integers xi, yi (-109xi, yi109) for i = 1, ..., 4n.

#### Output

If there is no such line output "No".

If there is such line, print "Yes" without quotes and in the next 3 lines output 3 real numbers A, B, C that determine line by equation Ax + By + C = 0. This line must splits 4n schools equally for both type of schools.

Checker splits points into two groups with respect to this line: {(x, y) : Ax + By + C > 10-6} and its complement.

Time limit 1 second
Memory limit 128 MiB
Input example #1
2
1 4
4 5
5 1
6 3
3 1
3 4
6 2
7 4

Output example #1
Yes
0.000000000
-1.000000000
3.500000000

Source 2021 KBTU Open, Spring Kazakhstan, Alma-Ata, May 30, Problem J