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.



Sample input:
2
3 1 4 1 5 9


Sample output:
1

Submission status: Runtime Error

Solution code:
#!/usr/bin/python
# -*- coding: utf-8 -*-
import sys
import math

sets = [
    set([1,3,5,7,8,10,12]),
    set([4,6,9,11]),
    set([2])
]

N = int(sys.stdin.readline().rstrip())
A = map(int, sys.stdin.readline().rstrip().split())

HEAD = list(sorted(A[:N]))
TAIL = list(reversed(sorted(A[2*N:])))
MID_ASC = A[N:2*N]
MID_DESC = list(reversed(A[N:2*N]))


score = sum(HEAD) - sum(TAIL)
for _ in range(N):
    #print(score)
    head_diff = MID_ASC[0] - HEAD[0]
    tail_diff = TAIL[0] - MID_DESC[0]
    #print(head_diff, tail_diff)
    if(head_diff < 0 and tail_diff < 0):
        break
    elif(head_diff > tail_diff):
        score += head_diff
        HEAD.pop(0)
        MID_ASC.pop(0)
    else:
        score += tail_diff
        TAIL.pop(0)
        MID_DESC.pop(0)
print(score)
exit(0)