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)

import heapq
import sys
input=sys.stdin.readline
n=int(input())
a=list(map(int,input().split()))
f=a[:n]
heapq.heapify(f)
b=[-i for i in a[2*n:]]
heapq.heapify(b)
maxi=sum(f)
mini=-sum(b)
fmax=[0]*(n+1)
fmax[0]=maxi
bmin=[0]*(n+1)
bmin[n]=mini
for i in range(n):
  heapq.heappush(f,a[n+i])
  fa=heapq.heappop(f)
  maxi+=a[n+i]-fa
  fmax[i+1]=maxi
  heapq.heappush(b,-a[2*n-1-i])
  ba=-heapq.heappop(b)
  mini+=a[2*n-1-i]-ba
  bmin[n-i-1]=mini
ans=-float('inf')
for i in range(n+1):
  ans=max(ans,fmax[i]-bmin[i])
print(ans)