An inexperienced slalomer

Today is Hubert's first slalom race, and he is nervous. It is also his first day on skis, so he has not learned how to turn yet and can only slide along a straight line. The race is not lost, though. If the designer of this course was careless, it may be possible to pass every gate without turning once.

You are given a slalom course with $n$ gates. The course runs from left to right. Each gate is a vertical segment between two poles. Seen from above, Hubert is a disk of diameter $d$ ($d \ge 0$) and the center of the disk moves along a straight line. He may start anywhere to the left of the leftmost gate and finish anywhere to the right of the rightmost gate. To complete the course, his whole body must pass between the two poles of every gate. Touching a pole is allowed.

Find the largest diameter $d$ for which such a straight trajectory exists.

The first line contains the number of gates $n$ ($1 \le n \le 100000$).

Each of the next $n$ lines contains three space separated integers $x$, $y_1$, $y_2$ ($0 \le x \le 10^9$, $0 \le y_1 \le y_2 \le 10^9$) that describe one gate, the vertical segment with endpoints $(x, y_1)$ and $(x, y_2)$. No two gates have the same $x$ coordinate.

If Hubert cannot complete the course with any diameter $d \ge 0$, print Impossible.

Otherwise let $d$ be the largest diameter. Print $d^2$ as a reduced fraction. Every coordinate is an integer, so $d^2$ is always rational. Print it in the form p/q with $q \ge 1$ and $\gcd(p, q) = 1$, and print 0/1 when $d = 0$. The numerator can exceed the range of a 64-bit integer.