Problem Statement

Given is a sequence of integers $A = (A_1, \ldots, A_N)$.
Consider a pair of sequences of integers $B = (B_1, \ldots, B_N)$ and $C = (C_1, \ldots, C_N)$ that satisfies the following conditions:

• A_i = B_i + C_i holds for each $1\leq i\leq N$;
• B is non-decreasing, that is$, B_i\leq B_{i+1}$ holds for each $1\leq i\leq N-1$;
• C is non-increasing, that is$, C_i\geq C_{i+1}$ holds for each $1\leq i\leq N-1$.

Find the minimum possible value of $\sum_{i=1}^N \bigl(\lvert B_i\rvert + \lvert C_i\rvert\bigr)$.

Input

Input is given from Standard Input in the following format:
N
$A_1 A_2 \ldots A_N$

Output

Print the answer.

Constraints

• $1\leq N\leq 2\times 10^5$
• -$10^8\leq A_i\leq 10^8$

Sample Input 1

3
1 -2 3

Sample Output 1

10

One pair of sequences $B = (B_1, \ldots, B_N)$ and $C = (C_1, \ldots, C_N)$ that yields the minimum value is:

• B = (0, 0, 5),
• C = (1, -2, -2).

Here we have $\sum_{i=1}^N \bigl(\lvert B_i\rvert + \lvert C_i\rvert\bigr) = (0+1) + (0+2) + (5+2) = 10$.

Sample Input 2

4
5 4 3 5

Sample Output 2

17

One pair of sequences B and C that yields the minimum value is:

• B = (0, 1, 2, 4),
• C = (5, 3, 1, 1).

Sample Input 3

1
-10

Sample Output 3

10

One pair of sequences B and C that yields the minimum value is:

• B = (-3),
• C = (-7).

见题面 Input 部分

见题面 Output 部分