### Problem Statement

You are given two Strings A and B that have the same length and contain only lowercase letters ('a'-'z'). The distance between two letters is defined as the absolute value of their difference. The distance between A and B is defined as the sum of the differences between each letter in A and the letter in B at the same position. For example, the distance between "abcd" and "bcda" is 6 (1 + 1 + 1 + 3).

You must change exactly K characters in A into other lowercase letters. Return the minimum possible distance between A and B after you perform that change.

### Definition

 Class: ChangingString Method: distance Parameters: String, String, int Returns: int Method signature: int distance(String A, String B, int K) (be sure your method is public)

### Constraints

-A and B will each contain between 1 and 50 characters, inclusive.
-K will be between 1 and the length of A, inclusive.
-A and B will contain the same number of characters.
-A and B will contain only lowercase letters ('a' - 'z').

### Examples

0)

 `"ab"` `"ba"` `2`
`Returns: 0`
 The minimum distance (equal to 0) can be achieved when we change 'a' to 'b' and 'b' to 'a'.
1)

 `"aa"` `"aa"` `2`
`Returns: 2`
 We must change both letters 'a' to some other letters. Changing them to 'b' results in the smallest distance.
2)

 `"aaa"` `"baz"` `1`
`Returns: 1`
3)

 `"fdfdfdfdfdsfabasd"` `"jhlakfjdklsakdjfk"` `8`
`Returns: 24`
4)

 `"aa"` `"bb"` `2`
`Returns: 0`

#### Problem url:

http://www.topcoder.com/stat?c=problem_statement&pm=7585

#### Problem stats url:

http://www.topcoder.com/tc?module=ProblemDetail&rd=10665&pm=7585

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#### Testers:

PabloGilberto , brett1479 , Olexiy , Andrew_Lazarev

#### Problem categories:

Brute Force, String Manipulation