A singer is recently working on their global tour plan. They represent all the cities they are interested in as points on a plane and intend to select 4 cities from them as the locations for this tour. To show that they are unique, they require that there exists a rectangle such that the 4 selected points are exactly the 4 vertices of this rectangle, and they hope to maximize the area of this rectangle. This has made their agent anxious, so they are soliciting solutions from fans worldwide. As a fan, you certainly won't want to miss this opportunity.

Input

The first line of the input contains a positive integer $N$, representing the number of points on the plane (the number of cities the singer is interested in). The following $N$ lines each contain two space-separated integers $X_i$ and $Y_i$, representing the coordinates of the corresponding point.

Output

The output contains only a single non-negative integer, representing the maximum area of the rectangle.

Constraints

• $20\%$ of the data satisfies $N \le 500$.
• $100\%$ of the data satisfies $N \le 1500$, $-10^8 \le X_i, Y_i \le 10^8$.
• The input data guarantees that a solution exists.

Examples

Input 1

8
-2 3
-2 -1
0 3
0 -1
1 -1
2 1
-3 1
-2 1

Output 1

10