Given two arrays $a$ and $b$ of length $n$.

Please calculate:

$$ \sum_{i=1}^n \sum_{j=1}^n \min(|a_i - a_j|, |b_i - b_j|) $$

Input

The first line contains a positive integer $n$ ($1 \leq n \leq 10^5$), representing the length of the arrays.

The second line contains $n$ positive integers, representing the array $a_i$ ($1 \leq a_i \leq 10^6$).

The third line contains $n$ positive integers, representing the array $b_i$ ($1 \leq b_i \leq 10^6$).

Output

Output a single integer representing the answer.

Examples

Input 1

2
5 2
2 8

Output 1

6

Input 2

5
7 2 8 4 1
2 2 6 4 3

Output 2

34

Note

For $30\%$ of the test cases: $n \leq 1000$.

For another $20\%$ of the test cases: $a_i, b_i \leq 50$.

For another $30\%$ of the test cases: $a_i = b_i$.

For all test cases: $1 \leq n \leq 10^5, 1 \leq a_i, b_i \leq 10^6$.