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 Julia (0.5.0) (judge verdict: Accepted)

using Base.Collections
N=parse(Int,readline())
A=map(x->parse(Int,x),split(readline()))
ans=-1145141919810931893
L=PriorityQueue(Int,Int)
now=0
for i=1:N
	now+=A[i]
	L[i]=A[i]
end
Lsum=Int[now]
for i=N+1:2N
	now+=A[i]
	L[i]=A[i]
	now-=peek(L).second
	dequeue!(L)
	push!(Lsum,now)
end
L=PriorityQueue(Int,Int)
now=0
for i=3N:-1:2N+1
	now+=A[i]
	L[i]=-A[i]
end
Rsum=Int[now]
for i=2N:-1:N+1
	now+=A[i]
	L[i]=-A[i]
	now+=peek(L).second
	dequeue!(L)
	push!(Rsum,now)
end
reverse!(Rsum)
for i=1:N+1
	ans=max(ans,Lsum[i]-Rsum[i])
end
println(ans)