Problem:
Score : 500 points

Problem Statement

There are N points on the 2D plane, i-th of which is located on (x_i, y_i).
There can be multiple points that share the same coordinate.
What is the maximum possible Manhattan distance between two distinct points?

Here, the Manhattan distance between two points (x_i, y_i) and (x_j, y_j) is defined by |x_i-x_j| + |y_i-y_j|.

Constraints

2 \leq N \leq 2 \times 10^5

1 \leq x_i,y_i \leq 10^9

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
x_1 y_1
x_2 y_2
:
x_N y_N

Output

Print the answer.

Sample Input 1

3
1 1
2 4
3 2

Sample Output 1

4

The Manhattan distance between the first point and the second point is |1-2|+|1-4|=4, which is maximum possible.

Sample Input 2

2
1 1
1 1

Sample Output 2

0

Solution in OCaml (4.10.0) (judge verdict: Wrong Answer)

Scanf.scanf "%d" (fun n ->
    let xy = Array.init n (fun _ -> Scanf.scanf " %d %d" (fun x y -> x, y)) in

    let calc f =
        Array.sort f xy;
        let x0, y0 = xy.(0) in
        let rec loop i acc =
            if i = n then acc else
                let x1, y1 = xy.(i) in
                let dist = abs (x1 - x0) + abs (y1 - y0) in
                loop (i + 1) (max acc dist)
        in
        let d1 = loop 0 0 in

        let x0, y0 = xy.(n - 1) in
        let rec loop i acc =
            if i = n then acc else
                let x1, y1 = xy.(i) in
                let dist = abs (x1 - x0) + abs (y1 - y0) in
                loop (i + 1) (max acc dist)
        in
        let d2 = loop 0 0 in
        max d1 d2
     in

    let m1 = calc (fun (x0, y0) (x1, y1) -> compare ( x0,  y0) ( x1,  y1)) in
    let m2 = calc (fun (x0, y0) (x1, y1) -> compare ( x0, -y0) ( x1, -y1)) in
    let m3 = calc (fun (x0, y0) (x1, y1) -> compare ( y0,  x0) ( y1,  x1)) in
    let m4 = calc (fun (x0, y0) (x1, y1) -> compare ( y0, -x0) ( y1, -x1)) in

    Printf.printf "%d\n" @@ max (max m1 m2) (max m3 m4)
)