You are given $N$ points in the coordinate system. They need to be covered with one or more rectangles, such that the following conditions are met:

• The sides of each rectangle are parallel with the coordinate axes,
• The center of each rectangle is in the origin, i.e. point $(0,0)$,
• Each given point is located either inside of the rectangle or on its boundaries.

Of course, it is possible to cover all the points using only one rectangle, but this rectangle could have a very large surface area. Our goal is to find a selection of required rectangles such that the sum of their surface areas is minimal.

Input

The first line of input contains the integer $N(1\le N\le 5000)$, the number of points. Each of the following $N$ lines contains two integers $X$ and $Y$ $(-50000000\le X,Y\le 50000000,XY\ne 0)$, the coordinates of each point.

Output

You must output the required minimal sum of surface areas of the rectangles.

Samples

Input 1

2
1 1
-1 -1

Output 1

4

Input 2

3
-7 19
9 -30
25 10

Output 2

2080

Input 3

6
1 20
3 17
5 15
8 12
9 11
10 10

Output 3

760