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 Go (1.6) (judge verdict: Accepted)

package main

import (
    "bufio"
    "os"
    "strconv"
    "fmt"
    "container/heap"

)

/*********** PriorityQueue ***********/
type PriorityQueue struct {
    arr []interface{}
    comps []CompFunc
}

/*
p < q ... -1
p == q ... 0
p > q ... 1
*/
type CompFunc func(p, q interface{}) int

func NewPriorityQueue() *PriorityQueue {
    return new(PriorityQueue)
}

func (pq PriorityQueue) Len() int {
    return len(pq.arr)
}

func (pq PriorityQueue) Swap(i, j int) {
    pq.arr[i], pq.arr[j] = pq.arr[j], pq.arr[i]
}

func (pq PriorityQueue) Less(i, j int) bool{
    for _, comp := range pq.comps {
        result := comp(pq.arr[i], pq.arr[j])
        switch result {
            case -1: return true
            case 1:  return false
            case 0:  continue
        }
    }
    return true
}

func (pq *PriorityQueue) Push(x interface{}) {
    pq.arr = append(pq.arr, x)
}

func (pq *PriorityQueue) Pop() interface{} {
    n := pq.Len()
    item := pq.arr[n - 1]
    pq.arr = pq.arr[:n - 1]
    return item
}

func (pq *PriorityQueue) IsEmpty() bool {
    return pq.Len() == 0
}

/* input */
var sc = bufio.NewScanner(os.Stdin)

func readInt() int {
    sc.Scan()
    n, _ := strconv.Atoi(sc.Text())
    return n
}

func main() {
    sc.Split(bufio.ScanWords)
    comp := func(p, q interface{}) int {
        if p.(int) < q.(int) {
            return -1
        } else if p.(int) == q.(int) {
            return 0
        } else {
            return 1
        }
    }
    n := readInt()
    preQue := new(PriorityQueue)
    preQue.comps = append(preQue.comps, comp)
    sufQue := new(PriorityQueue)
    sufQue.comps = append(sufQue.comps, comp)
    mid := make([]int, n)
    var preScore, sufScore int
    preScores := make([]int, n + 1)
    sufScores := make([]int, n + 1)
    for i := 0; i < n; i++ {
        v := readInt()
        preScore += v
        heap.Push(preQue, v)
    }
    for i := 0; i < n; i++ {
        mid[i] = readInt()
    }
    for i := 0; i < n; i++ {
        v := -readInt()
        sufScore += v
        heap.Push(sufQue, v)
    }
    
    preScores[0] = preScore
    for i, m := range mid {
        v := heap.Pop(preQue).(int)
        if v < m {
            preScore += (m - v)
            heap.Push(preQue, m)
        } else {
            heap.Push(preQue, v)
        }
        preScores[i + 1] = preScore
    }

    sufScores[0] = sufScore
    for i := n - 1; i >= 0; i-- {
        m := mid[i]
        v := heap.Pop(sufQue).(int)
        if -v > m {
            sufScore += -v - m
            heap.Push(sufQue, -m)
        } else {
            heap.Push(sufQue, v)
        }
        sufScores[n - i] = sufScore
    }
    ans := -10000000000000000
    for i := 0; i <= n; i++ {
        score := preScores[i] + sufScores[n - i]
        if ans < score {
            ans = score
        }
    }
    fmt.Println(ans)
}