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 Kotlin (1.3.71) (judge verdict: Accepted)

import kotlin.math.abs
import kotlin.math.max

fun main() {
    val n = readInt()
    val xy = List(n) {
        val (x, y) = readInts()
        Pair(x, y)
    }

    fun manhattan(x: Pair<Int, Int>, y: Pair<Int, Int>): Int {
        return abs(x.first - y.first) + abs(x.second - y.second)
    }

    val maxPlus = xy.maxBy { it.first + it.second }!!
    val minPlus = xy.minBy { it.first + it.second }!!

    val maxMinus = xy.maxBy { it.first - it.second }!!
    val minMinus = xy.minBy { it.first - it.second }!!

    println(max(manhattan(maxPlus, minPlus), manhattan(maxMinus, minMinus)))
}

// Input Reader
private fun readLn() = readLine()!!

private fun readStrings() = readLn().trim().split(" ")
private fun readInt() = readLn().toInt()
private fun readInts() = readStrings().map { it.toInt() }