Home

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, $N ≤ 1000$.

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 $(8 + 7 + 4) - (6 + 5 + 3) = 5$.