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)

import heapq

n = int(input())
array = [int(i) for i in input().split()]
ans=-1e14
l_array = []
r_array = []
l_sum = [0]*(n+1)
r_sum = [0]*(n+1)

# left-n and right-n numbers
for i in range(n):
    heapq.heappush(l_array, array[i])
    heapq.heappush(r_array, (-array[3*n-1-i], array[3*n-1-i]))

l_sum[0] = sum(l_array)
r_sum[n] = sum([i[1] for i in r_array])

for i in range(n, 2*n):
    heapq.heappush(l_array, array[i])
    heapq.heappush(r_array, (-array[3*n-1-i], array[3*n-1-i]))
    l_min = heapq.heappop(l_array)
    r_max = heapq.heappop(r_array)[1]

    # l_sum[i-n+1] = sum(l_array)
    # r_sum[2*n-1-i] = sum([j[1] for j in r_array])
    l_sum[i-n+1] = l_sum[i-n] - l_min + array[i]
    r_sum[2*n-1-i] = r_sum[2*n-i] - r_max + array[3*n-1-i]

for i in range(n+1):
    ans = max(ans, l_sum[i]-r_sum[i])

print(ans)