Given a set of points, calculate the sum of all Manhattan distances between two point pairs.

Input

The first line has an integer n: the number of points.

The following n lines describe the points. Each line has two integers x and y. You can assume that each point is distinct.

Output

Print the sum of all Manhattan distances.

Constraints

• 1 \le n \le 2 \cdot 10^5
• -10^9 \le x, y \le 10^9

Example

Input:

5
1 1
3 2
2 4
2 1
4 5

Output:

36