Hanbunko

Twin siblings, Yae and Joe, received a rice cracker as a snack from their mother. The rice cracker is shaped like a convex polygon and has slits on all the diagonals to make it easier to break.

They want to split the rice cracker into two pieces, but since they are not strong enough, they can only do so by clamping their hands on both sides of one of the diagonals. They started to think about which diagonal line they should divide the rice cracker into two so that it would be closest to Hanbunko and the difference between their shares would be the smallest.

Wreate a program which reads the information about the shape of the rice cracker represented by the convex polygon and finds the smallest difference between the two people's shares. The difference between two people's shares is expressed as the absolute value of the difference in their areas when the rice cracker is divided into two along one diagonal line.

Input

The input is given in the following form.

$N$
$x_1$ $y_1$
$x_2$ $y_2$
:
$x_N$ $y_N$

The first line gives the number of vertices of the convex polygon $N$ ($4 \leq N \leq 60,000$). In the following $N$ lines, the coordinates $x_i$, $y_i$ ($0 \leq x_i,y_i \leq 100,000,000$) of the vertices of the convex polygon are given as integers. The vertices of the convex polygon are given in such an order that the adjacent vertices are visited in a counterclockwise direction.

Output

Output the minimum difference between the two shares as a real number in a line. The error must not exceed plus or minus 0.0001.  

Sample Input and Output

Sample Input 1

4
0 0
1 0
1 1
0 1

Sample Output 1

0.0

Sample Input 2

4
0 0
1 0
1 2
0 1

Sample Output 2

0.5000

 

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