# Dynamic Programming - Linear

# Journey from west to east

There are **n** cities standing on a straight line from west to east. The cities are numbered from **1** to **n**, in order from west to east. Each point on the line has its own one-dimensional coordinate, and the point closer to the east has a large coordinate. The coordinate of the **i**-th city is `x`

._{i}

You are now in city **1**, and want to visit all cities. You have two ways to travel:

- Walk in a straight line. At the same time, your level of fatigue will increase by
**a**units each time you move a distance of**1**, regardless of the direction. - Teleport to any point you want. Your fatigue level will increase by
**b**units, regardless of teleported distance.

#### Input

First line contains three numbers **n** (**2** ≤ **n** ≤ `10`

), ^{5}**a** and **b** (**1** ≤ **a**, **b** ≤ `10`

). Next line contains ^{9}**n** integers `x`

, _{1}`x`

, ... , _{2}`x`

(_{n}**1** ≤ `x`

≤ _{i}`10`

). For all ^{9}**i** (**1** ≤ **i** ≤ **n** – **1**) holds inequality `x`

< _{i}`x`

._{i+1}

#### Output

Print the lowest possible level of fatigue, at which you will visit all the cities.

#### Explanation

Test 1.

From city **1** we go to **2**-nd, then teleport to **3**-rd. Then go to **4**-th. The level of fatigue at the end will be equal to **2** * **1** + **5** + **2** * **2** = **11**, what is the lowest possible.

Test 2.

From city **1** you simply go to all others till the **7**-th. As a result, the level of fatigue will be equal to **84**, which is the lowest possible.

Test 3.

Visit all cities, in any order, teleporting six times. The level of fatigue will be equal to **12**, which is the lowest possible.

4 2 5 1 2 5 7

11

6 3 7 1 3 6 10 11 13

29

7 1 2 24 35 40 68 72 99 103

12