Problem Statement

ABC 250 is a commemorable quarter milestone for Takahashi, who aims to hold ABC 1000,
so he is going to celebrate this contest by eating as close to 1/4 of a pizza he bought as possible.
The pizza that Takahashi bought has a planar shape of convex N-gon. When the pizza is placed on an xy-plane, the i-th vertex has coordinates (X_i, Y_i).
Takahashi has decided to cut and eat the pizza as follows.

• First, Takahashi chooses two non-adjacent vertices from the vertices of the pizza and makes a cut with a knife along the line passing through those two points, dividing the pizza into two pieces.
• Then, he chooses one of the pieces at his choice and eats it.

Let a be the quarter (=1/4) of the area of the pizza that Takahashi bought, and b be the area of the piece of pizza that Takahashi eats. Find the minimum possible value of $8 \times |a-b|$. We can prove that this value is always an integer.

Input

Input is given from Standard Input in the following format:
N
X_1 Y_1
X_2 Y_2
$\dots$
X_N Y_N

Output

Print the answer as an integer.

Constraints

• All values in input are integers.
• $4 \le N \le 10^5$
• $|X_i|, |Y_i| \le 4 \times 10^8$
• The given points are the vertices of a convex N-gon in the counterclockwise order.

Sample Input 1

5
3 0
2 3
-1 3
-3 1
-1 -1

Sample Output 1

1

Suppose that he makes a cut along the line passing through the 3-rd and the 5-th vertex and eats the piece containing the 4-th vertex.
Then, $a=\frac{33}{2} \times \frac{1}{4} = \frac{33}{8}, b=4$, and $8 \times |a-b|=1,$ which is minimum possible.

Sample Input 2

4
400000000 400000000
-400000000 400000000
-400000000 -400000000
400000000 -400000000

Sample Output 2

1280000000000000000

Sample Input 3

6
-816 222
-801 -757
-165 -411
733 131
835 711
-374 979

Sample Output 3

157889

见题面 Input 部分

见题面 Output 部分