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Matcom Online Grader
Faculty of Mathematics and Computer Science of University of Havana
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Consider an infinite 2-dimensional grid with some marked cells. We are interested in finding the minimum sum of Manhattan distances from all marked cells to some not marked cell .
We define Manhattan distance between two cells with coordinates $a_1, b_1$ and $a_2, b_2$ as $|a_1 - a_2| + |b_1 - b_2|$.
Input
The first line of input contains a single integer $n (1 \leq n \leq 100000)$, the number of marked cells in the grid.
Next $n$ lines contains the coordinates $a_i$ and $b_i$ of marked cells in the grid $(-2^{30} \leq a_i,b_i \leq 2^{30})$.
Output
You should output a single line with the minimum sum of Manhattan distances.
Sample test(s)
Input
4
1 -3
0 1
-2 1
1 -1
Output
10
Input
5
2 2
0 2
4 2
2 0
4 0
Output
11
Input
9
0 0
0 1
0 2
1 0
1 1
1 2
2 0
2 1
2 2
Output
24