## Task Description

Write a program to calculate the cost of fuel to go through a series of mountains.

We will go through a series of $n$ mountains. Let $m_1, m_2, \cdots, m_n$ denote the mountains. The height of $m_i$ is denoted by $h_i$. We will start from $m_1$, then go $m_2$, then $m_3$, etc, and finally stop at $m_n$.

A transition describes how we get from one mountain to the next. There are two kinds of transitions when we go from $m_i$ to $m_{i+1}$. If $h_{i+1}$ is greater than $h_i$, then this transition is an *uphill*. Otherwise, it is a *downhill*.

There is a cost associated with every transition. The cost of a transition is determined by the type of this transition and the one in front of it. For example, the cost of transition from $m_4$ to $m_5$ is determined by itself and the type of the transition from $m_3$ to $m_4$. There are two cases:

- The cost of the first transition (from $m_1$ to $m_2$) is
**three times**of the difference between the heights of this transition if it is an*uphill*, and**twice**the difference between the heights of this transition if it is a*downhill*. - The cost of other transitions is defined as follows:
- When the transition is an
*uphill*, then the cost is**four times**the difference between the heights of the current transition if the previous transition is an*uphill*, and**three times**the difference if the previous transition is a*downhill*. - When the transition is a
*downhill*, then the cost is**three times**the difference between the heights of the current transition if the previous transition is an*uphill*, and**twice**the difference if the previous transition is a*downhill*.

- When the transition is an

We illustrate the concept with an example of four mountains. Let $h_1, h_2, h_3, h_4$ be $10, 20, 5$, and $3$.

- The cost from $m_1$ to $m_2$ is $\vert 20-10\vert \times 3 = 30$ since it is the first transition and is an
*uphill*. - The cost from $m_2$ to $m_3$ is $\vert 5-20\vert \times 3 = 45$ since it is a
*downhill*and the previous transition ($m_1$ to $m_2$) is an*uphill*. - The cost from $m_3$ to $m_4$ is $\vert 3-5\vert \times 2 = 4$ since it is a
*downhill*and the previous transition ($m_2$ to $m_3$) is also a*downhill*.

As a result, the total cost going from $m_1$ to $m_4$ is $30 + 45 + 4 = 79$.

Now given the heights of the mountains, please compute the cost going from mountain $m_1$ to mountain $m_n$.

Note that **the memory limit is 1MB**, so for some testcases with greater $n$, you **cannot** declare an array to store heights. As a result, you must **remember** the heights of the previous two mountains, so that you can calculate the cost when you read the next one.

## Input Format

The input contains two lines. The first line contains an integer $n$, denoting the number of mountains. The second line contains $n$ integers, denoting $h_1, h_2, \cdots, h_n$.

### Technical limitation

- $2 \leq n \leq 1000000$
- $1 \leq h_i \leq 500$

## Output Format

Output the total cost going from $m_1$ to $m_n$.

## Sample Input 1

`4`

`10 20 5 3`

## Sample Output 1

`79`

## Sample Input 2

`4`

`30 5 20 50`

## Sample Output 2

`215`