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 (2.7.6) (judge verdict: Accepted)

import itertools
import datetime
from heapq import heapify,heappush,heappop



N=input()
a=[]
a=map(int, raw_input().split())
a1=a[:N]
#print a1


heapify(a1)

l1=[]
sum_a1=sum(a1)
l1.append(sum_a1)



# Max
for i in range(N,2*N):
	if a[i]>a1[0]:
		sum_a1=sum_a1+a[i]-a1[0]
		heappop(a1)
		heappush(a1, a[i])

	l1.append(sum_a1)

 

l2=[]
a2=[ -x for x in a[2*N:]]
heapify(a2)
sum_a2=-1*sum(a2)
l2.append(sum_a2)

# Min
for i in reversed(range(N,2*N)):
	if a[i]<-1*a2[0]:
		sum_a2=sum_a2+a[i]-(-1*a2[0])
		heappop(a2)
		heappush(a2,-1*a[i])
	l2.append(sum_a2)


ans=[]
for i in range(N+1):
	heappush(ans, -1*(l1[i]-l2[N-i]))

print ans[0]*-1