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)

N=int(input())
A=list(map(int,input().split()))
import heapq
B=A[:N]
C=[]
for i in range(N):
  C.append(-1*A[-1*(i+1)])
BP=[]
CP=[]
heapq.heapify(B)
heapq.heapify(C)
Bnow=sum(B)
Cnow=sum(C)*(-1)
BP.append(Bnow)
CP.append(Cnow)
for i in range(N):
  heapq.heappush(B,A[N+i])
  heapq.heappush(C,A[2*N-i-1]*(-1))
  b=heapq.heappop(B)
  c=heapq.heappop(C)
  Bnow+=A[N+i]-b
  Cnow+=c-A[2*N-i-1]*(-1)
  BP.append(Bnow)
  CP.append(Cnow)
D=CP[::-1]
ans=BP[0]-D[0]
for i in range(1,N+1):
  d=BP[i]-D[i]
  ans=max(ans,d)
print(ans)