Problem:
Score : 500 points

Problem Statement

Let N be a positive integer.

There is a numerical sequence of length 3N, a = (a_1, a_2, ..., a_{3N}).
Snuke is constructing a new sequence of length 2N, a', by removing exactly N elements from a without changing the order of the remaining elements.
Here, the score of a' is defined as follows: (the sum of the elements in the first half of a') - (the sum of the elements in the second half of a').

Find the maximum possible score of a'.

Constraints

1 ≤ N ≤ 10^5

a_i is an integer.

1 ≤ a_i ≤ 10^9

Partial Score

In the test set worth 300 points, N ≤ 1000.

Input

Input is given from Standard Input in the following format:

N
a_1 a_2 ... a_{3N}

Output

Print the maximum possible score of a'.

Sample Input 1

2
3 1 4 1 5 9

Sample Output 1

1

When a_2 and a_6 are removed, a' will be (3, 4, 1, 5), which has a score of (3 + 4) - (1 + 5) = 1.

Sample Input 2

1
1 2 3

Sample Output 2

-1

For example, when a_1 are removed, a' will be (2, 3), which has a score of 2 - 3 = -1.

Sample Input 3

3
8 2 2 7 4 6 5 3 8

Sample Output 3

5

For example, when a_2, a_3 and a_9 are removed, a' will be (8, 7, 4, 6, 5, 3), which has a score of (8 + 7 + 4) - (6 + 5 + 3) = 5.

Solution in Kotlin (1.0.0) (judge verdict: Accepted)

import java.util.PriorityQueue
import kotlin.comparisons.compareByDescending
fun main(args: Array<String>) {
    val N = nextInt()
    val A = listOfLong()
    //前半
    val first = LongArray(N + 1)
    val fQ = PriorityQueue<Long>(N)
    fQ.addAll(A.subList(0, N))
    var fS = fQ.toList().sum()
    for (n in 0 .. N) {
        first[n] = fS
        fS += A[n + N]
        fQ.add(A[n + N])
        fS -= fQ.poll()!! //一番小さい引く
    }
    //後半
    val latter = LongArray(N + 1)
    val lQ = PriorityQueue<Long>(N, compareByDescending { it })
    lQ.addAll(A.subList(2 * N, 3 * N))
    var lS = lQ.toList().sum()
    for (n in 0 .. N) {
        latter[N - n] = lS
        lS += A[2 * N - n - 1]
        lQ.add(A[2 * N - n - 1])
        lS -= lQ.poll()!! // 一番大きい引く
    }
    var ans = (0 .. N).map { first[it] - latter[it] }.max()!!
    println(ans)
}

fun List<Long>.SUM() = this.reduce { acc, value -> acc + value }

fun next() = readLine()!!
fun nextInt() = next().toInt()
fun nextLong() = next().toLong()
fun listOfString() = next().split(" ")
fun listOfInt() = listOfString().map(String::toInt)
fun listOfInt(vararg deltas: Int) = listOfString().map { Integer.parseInt(it) }.mapIndexed { index, int -> int + deltas[index % deltas.size] }
fun listOfLong(offset: Long = 0L) = listOfString().map { it.toLong() + offset}