Dice

Feadagor wants to play a tabletop role-playing game that needs a very unusual set of dice. There must be $n$ dice, and the $i$-th die must have $a_i$ faces. Every die is fair, so each of its faces comes up with equal probability.

You must write the integers from $1$ to $m$, where $m = a_1 + a_2 + \cdots + a_n$, on the faces, using each integer exactly once across all faces. Choose the arrangement so that, when all $n$ dice are thrown at once, the mathematical expectation $E$ of the sum of the shown values is as large as possible.

Report this maximal expectation $E$.

The first line contains a single integer $n$ ($1 \le n \le 1000$).

The second line contains $n$ integers $a_1, a_2, \ldots, a_n$ ($1 \le a_i \le 100$), separated by spaces.

Print the maximal expectation $E$ on one line as an irreducible fraction $p/q$, where $q \ge 1$ and $\gcd(p, q) = 1$. If $E$ is an integer $k$, print it as k/1.