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: Runtime Error)

import heapq
import bisect

n = int(input())
n = n*3
a = list(map(int,input().split()))

big = a[0:n//3]
big.sort()
tempmin = a[n//3::]
tempmin.sort()
small = tempmin[0:n//3]
spare = tempmin[n//3::]

ans = sum(big)-sum(small)
mxm = ans

heapq.heapify(small)
heapq.heapify(spare)

for i in range(n//3,2*n//3):
    if len(spare) != 0 and a[i] >= spare[0]:
        index = bisect.bisect_left(spare,a[i])
        spare.pop(index)

    if a[i] > big[0]:
        ans += a[i]-big[0]
        index = bisect.bisect_left(big,a[i])
        big.insert(index,a[i])
        big.pop(0)
    
    if a[i] <= small[-1]:
        ans -= spare[0]-a[i]
        heapq.heappush(small,spare[0])
        heapq.heappop(spare)
        index = bisect.bisect_left(small,a[i])
        small.pop(index)
    
    if ans > mxm:
        mxm = ans
print(mxm)