Description

You have an alarm clock. The timer settings of the alarm clock can be represented by two variables $a_1, a_2$, both starting with an initial value of $0$. Adjusting a variable from $x$ to $y$ costs $|x-y|$.

Next, you are given $n$ numbers $k_1, k_2, \cdots, k_n$. On day $i$, you need to adjust the variables so that at least one of the two variables equals $k_i$. Find the minimum total cost.

Input Format

The first line contains an integer $n$.
The second line contains $n$ integers $k_1, k_2, \cdots, k_n$.

Output Format

Output one integer in one line, representing the minimum cost.

6
1 1 4 5 1 4

7

5
4 1 9 2 3

12

Hint

Sample Explanation

Sample explanation 1:
Day 1: $a=\{1,0\}$.
Day 2: $a=\{1,0\}$.
Day 3: $a=\{4,0\}$.
Day 4: $a=\{5,0\}$.
Day 5: $a=\{5,1\}$.
Day 6: $a=\{4,1\}$.

Sample explanation 2:
Day 1: $a=\{4,0\}$.
Day 2: $a=\{4,1\}$.
Day 3: $a=\{9,1\}$.
Day 4: $a=\{9,2\}$.
Day 5: $a=\{9,3\}$.

Constraints

In addition, to catch some incorrect solutions, this problem includes several hack test points. The testdata of the hack test points satisfy $n\le 10$ and $k_i\le 100$. If your program does not pass at least one hack test point, then the score for this problem will be $0$.

For $100\%$ of the testdata, $1\le n\le 10^5$ and $1\le k_i\le 10^9$.

Translated by ChatGPT 5