Description

Wintokk likes playing games on convex-hull. One day, Dragon wants to test him.

Dragon has drawn N points on a plane with no points in the same place. Dragon wants to know the smallest of the N convex-hulls formed by removing exactly one point from the N points.

But Wintokk is so stupid. Can you help him find the smallest area after removing a single point?

Input

The input contains several test cases.

Each test starts with an integer N(4 ≤ N < 10⁵+1), the total number of points on the plane.

The next N lines, each contains two integers x and y, indicating the position of the point.

The input ends up with N=0.

Output

Output the smallest area with two digits after the decimal point.

4
1 0
0 0
0 1
1 1
0

0.50

Source

, Wang, Dong