Kingdom Subdivision

Once upon a time there was a kingdom ruled by a wise king. After forty years of his reign, through successful military campaigns and skillful diplomacy, the kingdom became a simple polygon with $n$ vertices — with no self-intersections, self-touches, or holes. This tidy shape made tax collection and land division easy, so everyone was content.

But nothing lasts forever. One autumn evening the king suddenly died. By the laws of the kingdom the eldest son should inherit the realm, yet the king had left twin sons whom he had always loved equally, so no one dared crown just one of them.

After ten days of deliberation the council resolved to split the kingdom into two parts, one for each son. To keep tax accounting simple, the two parts must have exactly equal area. Before the mapmakers start drawing borders, the treasury needs to know the single number that every valid split must satisfy: the area that each of the two equal parts will have.

The first line contains a single integer $n$ — the number of vertices of the kingdom ($3 \le n \le 5000$).

Each of the next $n$ lines contains two integers $x_i$ and $y_i$ — the coordinates of the $i$-th vertex ($0 \le |x_i|, |y_i| \le 10^6$).

The vertices are given in counterclockwise order. No three consecutive vertices are collinear, and the polygon has no self-intersections, self-touches, or holes.

The kingdom is to be divided into two parts of exactly equal area. Output the area of each part as a reduced fraction p/q, where $q > 0$ and $\gcd(|p|, q) = 1$. Because every vertex has integer coordinates, this area is always a rational number; print it in the form p/q even when it is an integer (for example, an area of $4$ is printed as 4/1).