D - 3N Numbers

Time Limit: 2 sec / Memory Limit: 256 MB

問題文

N1 以上の整数とします。

a' のスコアの最大値を求めてください。

制約

• 1 ≤ N ≤ 10^5
• a_i は整数である。
• 1 ≤ a_i ≤ 10^9

部分点

• 300 点分のテストケースでは、N ≤ 1,000 が成り立つ。

入力

N
a_1 a_2 ... a_{3N}


出力

a' のスコアの最大値を出力せよ。

入力例 1

2
3 1 4 1 5 9


出力例 1

1


a_2, a_6 を取り除くと、a' = (3, 4, 1, 5) となり、スコアは (3 + 4) - (1 + 5) = 1 となります。

入力例 2

1
1 2 3


出力例 2

-1


入力例 3

3
8 2 2 7 4 6 5 3 8


出力例 3

5


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.