911.K. Drone Racing
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

$$$n$$$ participants have already been invited to a new drone race. According to the organizers' plan, as soon as the race starts, each participant's drone will start moving from its starting position to its finishing position along a straight trajectory. The organizers have already determined the starting position for each participant.

Initially, it was also planned to select a separate finishing position for each participant individually. However, now, for the sake of a spectacular finale, the race organizers want to move the finishing positions of all participants to a single point. Of course, the distance between the starting and finishing positions for all participants must be the same. It is not possible to change the starting positions of the participants, but it is possible to change the race distance.

Help the organizers find such a distance and the common finishing position, or report that they do not exist.

Input

The first line contains a single integer $$$n$$$ $$$(1 \le n \le 10^5)$$$ - the number of race participants.

Then follows $$$n$$$ lines, each containing two integers $$$x_i, y_i$$$ $$$(-1000 \le x_i, y_i \le 1000)$$$ - the starting position of the $$$i$$$-th race participant. Participants can start from the same points.

Output

If there is no suitable finishing position for all participants, print «NO».

Otherwise, print «YES». Then, on the second line, print three numbers $$$x_e, y_e, d$$$ - the coordinates of the finishing position and the distance from the start to the finish.

If there are multiple possible answers, you can print any of them.

Your answer will be considered correct if the race distance for all participants is equal with an accuracy of $$$10^{-6}$$$.

Example
Input
2
2 -1
4 -3
Output
YES
2.000000 -3.000000 2.000000