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.*

fun main() {
    println(solve())
}

val solve: () -> Any = solve@{
    val N = readInt()
    val xy = List(N) { readIntList() }
    val ps = xy.map { it[0] + it[1] }
    val ng = xy.map { it[0] - it[1] }

    listOf(
        ps.max()!! - ps.min()!!,
        ng.max()!! - ng.min()!!,
        -ng.max()!! + ng.min()!!
    ).max()!!
}

val mod: Int = 1_000_000_007


fun readString() = readLine()!!
fun readStringList() = readLine()!!.split(" ")
fun readInt() = readLine()!!.toInt()
fun readLong() = readLine()!!.toLong()
fun readIntList() = readLine()!!.split(" ").map(String::toInt)
fun readLongList() = readLine()!!.split(" ").map(String::toLong)

fun <T> T.alsoPrintln() = also { println(this) }

fun Boolean.toYesOrNo(yes: String = "Yes", no: String = "No") = if (this) yes else no

fun <E> List<E>.toPair() = this[0] to this[1]

fun <T> readPair(t: (String) -> T) = readPair(t, t)
fun <S, T> readPair(s: (String) -> S, t: (String) -> T) =
    readLine()!!.split(" ").let { Pair(s(it[0]), t(it[1])) }

fun Int.pow(n: Int) = this.toDouble().pow(n).toInt()

fun minAndMax(a: Int, b: Int) = if (a < b) a to b else b to a

fun <T> T.ifOrThis(bool: (T) -> Boolean, trans: (T) -> T) = if (bool(this)) trans(this) else this
fun <T> T.ifOrThis(bool: Boolean, trans: (T) -> T) = if (bool) trans(this) else this