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 java.util.*
import kotlin.math.*

fun str() = readLine()!!
fun int() = str().toInt()
fun long() = str().toLong()

fun read(d: String = " ") = str().split(d)
fun <T> list(d: String = " ", f: String.() -> T) = read(d).map { f(it) }
fun list() = list { toInt() }

fun <T> MutableList<T>.removeLast() = this.removeAt(this.lastIndex)

const val mod = 1000000007L

fun main() {
    abc000X()
}

fun abc000X() {
    val n = int()
    val a = Array(n) {
        val (t, u) = list()
        t + u to t - u
    }

    val t = a.map { it.first }.sorted()
    val u = a.map { it.second }.sorted()

    println(max(t.last() - t.first(), u.last() - u.first()))
}