Once upon a time there was a greedy King who ordered his chief Architect to
build a field for royal cricket inside his park. The King was so greedy, that he
would not listen to his Architect's proposals to build a field right in the
park center with pleasant patterns of trees specially planted around and beautiful walks
inside tree alleys for spectators. Instead, he ordered neither to cut nor to plant
even a single tree in his park, but demanded to build the largest possible cricket
field for his pleasure. If the Kind finds that the Architect has dared to touch even
a single tree in his park or designed a smaller field that it was possible, then
the Architect will loose his head. Moreover, he demanded his Architect to introduce
at once a plan of the field with its exact location and size.
Your task is to help poor Architect to save his head, by writing a program that
will find the maximum possible size of the cricket field and its location inside
the park to satisfy King's requirements.
The task is somewhat simplified by the fact, that King's park has a rectangular shape
and is situated on a flat ground. Moreover, park's borders are perfectly aligned with
NorthSouth and EastWest lines. At the same time, royal cricket is always played on a
square field that is also aligned with NorthSouth and EastWest lines. Architect has
already established a Cartesian coordinate system and has precisely measured the
coordinates of every tree. This coordinate system is, of course, aligned with
NorthSouth and EastWest lines. Southwestern corner of the park has coordinates
(0, 0) and Northeastern corner of the part has coordinates (W, H), where W and H
are the park width and height in feet respectively.
For this task, you may neglect the diameter of the trees. Trees cannot be
inside the cricket field, but may be situated on its side. The cricket field may
also touch park's border, but shall not lie outside the park.
Input
The first line contains three integer numbers N, W, and H,
separated by spaces. N (0 ≤ N ≤ 100) is the number of
trees in the park. W and H (1 ≤ W, H ≤ 10000)
are the park width and height in feet respectively.
Next N lines describe coordinates of trees in the park. Each line contains
two integer numbers X_{i} and Y_{i} separated by a space
(0 ≤ X_{i} ≤ W,
0 ≤ Y_{i} ≤ H) that represent
coordinates of i^{th} tree. All trees are located at different
coordinates.
Output
Write a single line with three integer numbers P, Q, and L
separated by spaces, where (P, Q) are coordinates of the cricket field Southwestern
corner, and L is a length of its sides. If there are multiple possible field
locations with a maximum size, then output any one.
Sample
input  output 

7 10 7
3 2
4 2
7 0
7 3
4 5
2 4
1 7
 4 3 4

Problem Author: Andrey Demidov
Problem Source: 20022003 ACM Northeastern European Regional Programming Contest