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: Wrong Answer)

parseInt(x)=parse(Int,x)
parseMap(x::Array{SubString{String},1})=map(parseInt,x)

function main()
	n = readline() |> parseInt
	a = readline() |> split |> parseMap
	a[1:n] = sort(a[1:n])
	a[2*n+1:3*n] = sort(a[2*n+1:3*n])
	b = zeros(Int,n+1)
	c = zeros(Int,n+1)
	c[n+1] = sum(a[2*n+1:3*n])
	b[1] = sum(a[1:n])
	nb = 1
	mb = a[1]
	nc = 3*n
	mc = a[3*n]
	for i in 1:n
		if a[n+i] > mb
			b[i+1] = b[i] - mb + a[n+i]
			nb += 1
			mb = a[nb]
		else
			b[i+1] = b[i]
			mb = a[n+i]
		end
		if a[2*n+1-i] < mc
			c[n+1-i] = c[n+2-i] - mc + a[2*n+1-i]
			nc -= 1
			mc = a[nc]
		else
			c[n+1-i] = c[n+2-i]
			mc = a[2*n+1-i]
		end
	end
	m = b[1]-c[1]
	for i in 2:n+1
		m = max(m, b[i]-c[i])
	end
	println(m)
end
main()