3N Numbers

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

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'.

Examples

Input

2 3 1 4 1 5 9

Output

1

Input

1 1 2 3

Output

-1

Input

3 8 2 2 7 4 6 5 3 8

Output

5

inputFormat

Input

Input is given from Standard Input in the following format:

N a_1 a_2 ... a_{3N}

outputFormat

Output

Print the maximum possible score of a'.

Examples

Input

2 3 1 4 1 5 9

Output

1

Input

1 1 2 3

Output

-1

Input

3 8 2 2 7 4 6 5 3 8

Output

5

样例

2
3 1 4 1 5 9

1