Astronomy

There are $n$ planets in the planetary system of star X. They all orbit star X along circular orbits lying in the same plane, and each planet moves with a constant tangential speed. All planets orbit in the same direction.

Occasionally an event called a planet parade occurs: the moment when all $n$ planets and star X lie on a single straight line.

Find the length of the time interval between two consecutive planet parades.

The first line contains an integer $n$ — the number of planets ($2 \le n \le 1000$).

The second line contains $n$ integers $t_i$ — the orbital periods of the planets ($1 \le t_i \le 10000$). Not all $t_i$ are equal.

Output the answer as an irreducible common fraction: the numerator and the denominator separated by a single space.