Astronomy

Time limit2sMemory limit128 MB

Summary

Given orbital periods of n planets moving on circular orbits, compute the exact fractional time interval between consecutive moments all planets and the star are collinear.

Level: Medium6 of 10
Topics: Math, Number theory, Geometry
Solved: No attempts yet

Problem

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.

Input

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

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

Hint

Examples2

Example 1
Input
```
3
6 2 3
```
Expected output
```
3 1
```
Example 2
Input
```
2
3 9
```
Expected output
```
9 4
```