Closest Pair (Uniform)

Input contains several test cases. Each test case begins
with an integer $n$
($2 \le n \le 100\, 000$).
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 $100\, 000$.
You may assume that the points have been generated by picking
$x$ and $y$ independently uniformly at random
in the interval $[-100\, 000,
100\, 000]$. The input is terminated by a case beginning
with $0$.

**Warning!** This problem has a largish
input file.

For each test case, output any closest pair of the input
points, on the form `$x_{1}$ $y_{1}$ $x_{2}$ $y_{2}$`.

Sample Input 1 | Sample Output 1 |
---|---|

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 |