Problem Statement

An integer $N$ is given as input.

Find the limit

$\displaystyle \lim_{m \to \infty} \frac{1}{m!} \sum_{k = 0}^{m! - 1} \frac{e^{2 kN \pi i / (m!)}}{e^{4 k \pi i / (m!)} + e^{2 k \pi i / (m!)} + 10} $

Here, $e$ is the base of the natural logarithm, $\pi$ is the ratio of a circle's circumference to its diameter, and $i$ is the imaginary unit.

Background

This limit is a translation into complex analysis of an integral called the Schnirelmann integral^{[1] p. 488, [2] p. 2522} used in $p$-adic analysis, but no knowledge of $p$-adic analysis is needed for the computation.

In the original context of $p$-adic analysis, one fixes a prime $p$, considers the field of $p$-adic complex numbers $\mathbb{C}_p$ instead of the complex number field $\mathbb{C}$, considers roots of $1$ in $\mathbb{C}_p$ instead of powers of $e$, considers $m$ instead of $m!$, and, instead of $m \to \infty$, considers what is called a directed limit with respect to the divisibility relation, with $m$ ranging over all positive integers coprime to $p$.

Understanding directed limits requires knowledge of topology, so we do not explain them in detail, but this is equivalent to the limit obtained by fixing a prime $p$, considering the field of $p$-adic complex numbers $\mathbb{C}_p$ instead of the complex number field $\mathbb{C}$, considering roots of $1$ in $\mathbb{C}_p$ instead of powers of $e$, considering the product of all positive integers at most $m$ that are coprime to $p$ instead of $m!$, and letting $m \to \infty$.

Input

$N$

Constraints

The input satisfies the following constraints:

• $N$ is an integer satisfying $-20 \leq N \leq 20$

Output

It can be proved that the answer can be expressed as a fraction whose denominator is a power of $10$.

That is, it can be written as $n/d$ using an integer $n$ and an integer $d$ expressible as a power of $10$, so print such a pair $n,d$ separated by / on $1$ line.

$n$/$d$

Print a newline at the end.

This problem uses a special judge. The correct pair is not unique, and you may print any of them.

However, strictly follow the format described above. For example, the behavior of the judge is not guaranteed if there is extra whitespace.

Also, due to judge limitations, your output must be at most $100$ characters.

Sample

0

1/10

1

0/1

-20

-9939764889/1000000000000000000000

References

1. Л. Г. Шнирельман (L. G. Schnirelmann), О функциях в нормированных алгебраически замкнутых телах (French official title: Sur les fonctions dans les corps normés et algébriquement fermés, English title referered to from [2]: On functions in normed, algebraically closed fields), Izvestiya Rossiiskoi Akademii Nauk SSSR Seriya Matematicheskaya, 2:5-6, pp. 487--498 (1938). (French summary)
2. M. M. Vishik, Nonarchimedean Spectral Theory, Journal of Soviet Mathematics volume 30, pp. 2513--2555 (1985).