### Problem Statement

A traveling salesman is going to sell his wares in Linear Kingdom. Linear Kingdom has N cities on a coordinate plane. Each city is a point, and the i-th city is located at coordinates (x[i], y[i]). All the cities in Linear Kingdom are collinear, meaning that there exists a straight line which passes through all of them.

The traveling salesman is going to visit all of these cities. The distance he needs to travel between two cities located at (X1, Y1) and (X2, Y2) is equal to the Manhattan Distance between them, which is defined as |X1 - X2| + |Y1 - Y2|. He may start at any city and end at any city. Return the minimum total distance he will need to travel.

### Definition

 Class: LinearTravellingSalesman Method: findMinimumDistance Parameters: int[], int[] Returns: int Method signature: int findMinimumDistance(int[] x, int[] y) (be sure your method is public)

### Constraints

-x and y will contain between 2 and 50 elements, inclusive.
-x and y will have the same number of elements.
-Each element of x and y will be between 0 and 10000, inclusive.
-No two cities will have the same location.
-All cities will be collinear, meaning that there exists a straight line which passes through all of them.

### Examples

0)

 `{1,3,5}` `{2,2,2}`
`Returns: 4`
 One optimal journey is (1,2) -> (3,2) -> (5,2). The Manhattan Distance between each consecutive pair of cities is 2. The total distance is 4.
1)

 `{3,2,1}` `{3,2,1}`
`Returns: 4`
 One optimal journey is (1,1) -> (2,2) -> (3,3).
2)

 `{0,100,1000,10000}` `{0,10,100,1000}`
`Returns: 11000`
3)

 `{80,60,70,50}` `{50,70,60,80}`
`Returns: 60`
4)

 `{7,7,7,7,7,7,7}` `{105,1231,5663,295,3062,380,7777}`
`Returns: 7672`

#### Problem url:

http://www.topcoder.com/stat?c=problem_statement&pm=10917

#### Problem stats url:

http://www.topcoder.com/tc?module=ProblemDetail&rd=14153&pm=10917

dolphinigle

#### Testers:

PabloGilberto , ivan_metelsky , it4.kp

#### Problem categories:

Simple Search, Iteration