Icecream

Time Limit: 1 Second    Memory Limit: 32768 KB

Summer is hot, and everyone is inactive in programming. But cyjj has ideas.

Thers is n-2 QSes, so cyjj take out a big icecream which looks like a convex n-edge-polygon.

cyjj: We can divide this ice cream into n-2 triangles by cutting through its diagonals and these diagonals can't be intersected. But I want the areas of n-2 triangles to be as equilibrated as possible. In other words, I want the standard deviation S of these areas is minimum. The QS who solve it earlier will get a bigger one:))

QS: What a big icecream

In a moment, the icecream disppears.

cyjj: 8-), I will give you another big icecream next week.

Input

The first line of the input is an integer n (n <= 100).

Next n lines denote the coordinate of each vertex.

Output

For each test case, output a float number which is the minimum standard deviation and the decimal digits is 2.

Sample Input

4
0 0
1 0
1 1
0 1

Sample Output

0.00

Submit

Source: ZOJ Monthly, February 2004