Soldiers in a Line

Problem Description

On a playground divided into a grid, $n$ soldiers stand scattered on grid points, represented by integer coordinates $(x, y)$.

A soldier can move one step up, down, left, or right along the grid edges, but at any moment at most one soldier may occupy a given grid point.

By the officer's command, they must form a neat horizontal line, that is, stand at $(x,y), (x+1,y), \ldots, (x+n-1,y)$. Find the values of $x$ and $y$ that minimize the total number of steps the soldiers must move to line up.

Input Format

The first line of input is an integer, the number of soldiers $n$.

Lines $2$ through $n+1$ each contain two integers; the $(i+1)$-th line's $x_i, y_i$ are the coordinates of the $i$-th soldier.

Output Format

Output one integer on a line: the answer (the minimum total number of moves).

Sample Input

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

Sample Output

8

Hint

For $100\%$ of the data: $1 \le n \le 10000$, $-10000 \le x, y \le 10000$.