Map

While sorting through old archives of an abandoned library at the edge of the world, Captain Zhenya Vodogrey found a pirate map that shows the way to a treasure. The map is drawn on squared paper and is in good condition.

The map is a non-degenerate polygon cut strictly along the grid lines of a very large sheet of squared paper. Every vertical and horizontal line crosses the map in at most one continuous segment.

Zhenya wants to fold the map once along a vertical line $x = c$ that lies on a grid line of the paper. He wants the area of the polygon formed after folding to be as small as possible. Choose $c$ to minimize it.

The left part of the picture shows the map from the statement. The right part shows folding along $x = 2$.

The first line contains $n$ ($1 \le n \le 3 \cdot 10^5$), the number of vertices of the map. Each of the next $n$ lines contains two integers, the coordinates of a vertex, in clockwise order. The coordinates are integers, non-negative, and do not exceed $10^9$.

Print a single integer, the minimum area after folding.