Problem F
Closest Pair (Uniform)

Input

Input contains several test cases. Each test case begins with an integer $n$ ($2\le n\le 100000$). Then follows a list of $n$ points, one per line, each of the form $x$ $y$. Coordinates are floating point values with at most $2$ decimals and absolute value bounded by $100000$. You may assume that the points have been generated by picking $x$ and $y$ independently uniformly at random in the interval $[-100000,100000]$. The input is terminated by a case beginning with $0$.

Warning! This problem has a largish input file.

Output

For each test case, output any closest pair of the input points, on the form $x_1$ $y_1$ $x_2$ $y_2$.

2
1.12 0
0 0.51
3
158 12
123 15
1859 -1489
3
21.12 -884.2
18.18 43.34
21.12 -884.2
0

0.0 0.51 1.12 0.00
123 15 158 12.00
21.12 -884.20 21.12 -884.20