Description

A Grand Prix on Planet X offers $M$ levels of prizes. The prize money at each level is a positive integer.

Moreover, the ratio between two adjacent levels is a fixed value.

That is, the prize amounts for all levels form a geometric sequence. For example:

Its common ratio is $3/2$.

Now, we randomly surveyed the prize amounts of some winners.

Based on this, please infer the maximum possible common ratio.

Input Format

The first line contains an integer $N(0<N<100)$, indicating that the next line contains $N$ positive integers.

The second line contains $N$ positive integers $X_i(X_i<10^{12})$, separated by spaces. Each integer represents the prize amount received by a surveyed person.

Output Format

Output a fraction in the form $A/B$, where $A$ and $B$ are coprime, representing the maximum possible ratio coefficient.

The testdata guarantees that the input format is correct, and that the maximum ratio exists.

3
1250 200 32

25/4

4
3125 32 32 200

5/2

3
549755813888 524288 2

4/1

Hint

Time limit: 3 seconds, 256M. The 7th Lanqiao Cup provincial contest in 2016.

Lanqiao Cup 2016 provincial contest Group A Problem J (Group B Problem J).

Translated by ChatGPT 5