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 Python (3.4.3) (judge verdict: Accepted)

# -*- coding: utf-8 -*-
from heapq import heappush,heappushpop,heapify

n = int(input())
a = [int(x) for x in input().split()]

q = []
s = 0
for i in range(n):
    heappush(q, a[i])
    s += a[i]
left = [s]
for k in range(n):
    x = heappushpop(q, a[n+k])
    s = s - x + a[n+k]
    left.append(s)

q = []
s = 0
for i in range(n):
    heappush(q, -1*a[3*n-1-i])
    s += a[3*n-1-i]
right = [0 for _ in range(n+1)]
right[n] = s
for k in range(n):
    x = heappushpop(q, -1*a[2*n-1-k])
    s = s - (-1*x) + a[2*n-1-k]
    right[n-1-k] = s

m = None
for k in range(n+1):
    if m is None:
        m = left[k] - right[k]
    else:
        m = max(m, left[k]-right[k])

print(m)