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 JavaScript (Node.js 12.16.1) (judge verdict: Wrong Answer)

"use strict"

function Main(input) {
  let lines = input.split('\n');
  let N = parseInt(lines[0], 10);
  const points = [];
  for ( let i = 0; i < N; i++ ) {
    points.push(lines[i+1].split(' ').map(Number));
  }

  const lengths = [];
  for ( let i = 0; i < N; i++ ) {
    lengths.push(manhattanLength(points[i%N], points[(i+1)%N]));
  }
  console.log(lengths.reduce((a,b)=>a>b?a:b));

  return;
}

function manhattanLength(a1, a2) {
  return Math.abs(a1[0] - a2[0]) + Math.abs(a1[1] - a2[1]);
}

Main(require("fs").readFileSync("/dev/stdin", "utf8"));