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 PyPy3 (2.4.0) (judge verdict: Wrong Answer)


import sys
from collections import deque, defaultdict
import copy
import bisect
#sys.setrecursionlimit(10 ** 9)
import math
import heapq
from itertools import combinations, permutations

import sys
def input():
	return sys.stdin.readline().strip()

N = int(input())
a = list(map(int, input().split()))

a_max = a[:N]
a_min = a[2*N:]

a_max_sum = sum(a_max)
score = [a_max_sum]
heapq.heapify(a_max)
for i in range(N):
	heapq.heappush(a_max, a[N + i])
	a_max_sum += a[N + i]
	a_max_sum -= heapq.heappop(a_max)
	score.append(a_max_sum)
print(score)

a_min_sum = sum(a_min)
score[N] -= a_min_sum
for i in range(len(a_min)):
	a_min[i] *= -1
heapq.heapify(a_min)
for i in range(N):
	heapq.heappush(a_min, -a[2*N - 1 - i])
	a_min_sum += a[2*N - 1 - i]
	a_min_sum += heapq.heappop(a_min)
	score[N - i - 1] -=a_min_sum
print(score)

print(max(score))