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.io.BufferedReader
import java.io.BufferedWriter
import kotlin.math.abs

fun main() = Case().exec(::solve)
//fun main() = TestExecutor.assert(testCase) { Case(it.r, it.w).exec(::solve) }

/** https://atcoder.jp/contests/abc178/tasks/abc178_e **/
fun solve(c: Case) {
    val n = c.long().toInt()
    val points = (0 until n).map { c.longList().let { it[0] to it[1] } }

    val rightTop = points.sortedByDescending { it.first + it.second }.take(1000)
    val rightBottom = points.sortedByDescending { it.first - it.second }.take(1000)
    val leftTop = points.sortedByDescending { -it.first + it.second }.take(1000)
    val leftBottom = points.sortedByDescending { -it.first - it.second }.take(1000)

    var score = Long.MIN_VALUE
    rightTop.forEach { a ->
        leftBottom.forEach { b ->
            score = Math.max(score, abs(a.first - b.first) + abs(a.second - b.second))
        }
    }
    rightBottom.forEach { a ->
        leftTop.forEach { b ->
            score = Math.max(score, abs(a.first - b.first) + abs(a.second - b.second))
        }
    }
    c.println(score.toString())
}

class Case(
    private val input: BufferedReader = System.`in`.bufferedReader(),
    private val out: BufferedWriter = System.out.bufferedWriter()
) {
    fun exec(fn: (Case) -> Unit) = input.use { out.use { execInThread(fn) } }
    private fun execInThread(fn: (Case) -> Unit) =
        Thread(null, { fn(this) }, "solve", 64 * 1024 * 1024)
            .apply { setUncaughtExceptionHandler { _, e -> e.printStackTrace(); kotlin.system.exitProcess(1) } }
            .apply { start() }.join()

    fun println(c: CharSequence?) = out.appendln(c)
    fun string(): String = input.readLine().trimEnd()
    fun long(): Long = input.readLine().toLong()
    fun intList(): List<Int> = input.readLine().split(" ").map { it.toInt() }
    fun longList(): List<Long> = input.readLine().split(" ").map { it.toLong() }
}