### Problem Statement

N checkers are placed on an infinitely large board. The i-th checker is in the cell at row x[i], column y[i]. There can be more than one checker in the same cell. A move consists of taking one checker and moving it one cell up, down, left or right.

Return a int[] containing exactly N elements, where the i-th element (0-based) is the minimum number of moves necessary to end up with at least i+1 checkers in the same cell.

### Definition

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

### Constraints

-x will contain between 1 and 50 elements, inclusive.
-y will contain the same number of elements as x.
-Each element of x will be between 1 and 1,000,000, inclusive.
-Each element of y will be between 1 and 1,000,000, inclusive.

### Examples

0)

 `{1, 2, 4, 9}` `{1, 1, 1, 1}`
`Returns: {0, 1, 3, 10 }`
 Here is one possible way to get the minimal number of moves: for 1 checker: do nothing for 2 checkers: put the first two checkers at cell (1, 1) for 3 checkers: put the first three checkers at cell (2, 1) for 4 checkers: put all the checkers at cell (3, 1)
1)

 `{15, 15, 14, 16}` `{14, 16, 15, 15}`
`Returns: {0, 2, 3, 4 }`
 Whenever we need to have more than one checker in a single cell, we can put them in cell (15, 15).
2)

 `{4, 4}` `{7, 7}`
`Returns: {0, 0 }`
 They are already at the same cell.

#### Problem url:

http://www.topcoder.com/stat?c=problem_statement&pm=9976

#### Problem stats url:

http://www.topcoder.com/tc?module=ProblemDetail&rd=13514&pm=9976

Vasyl[alphacom]

#### Testers:

PabloGilberto , bmerry , Olexiy , ivan_metelsky

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