Given $n$ points on a 2D coordinate system, each represented by the coordinates $(x_i, y_i)$, the task is to find a point $A$ with integer coordinates such that the sum of distances from $A$ to the given $n$ points is minimized.
The distance between point $u$ and point $v$ is $|u_x-v_x|+|u_y-v_y|$.
### Input
- The first line contains an integer $n$.
- The next $n$ lines, each line contains two integers $x_i,y_i$, a point on the coordinate system.
### Output
- An integer representing the minimum sum of distances from $A$ to the given $n$ points.
### Constraints
- $1 \le n \le 10^5$.
- $|x_i|,|y_i| \le 10^9$.
### Example
Input:
```
4
-1 3
6 -5
4 5
3 4
```
Output:
```
19
```